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| <title>Computing Health Expectancies using IMaCh</title> |
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<title>Computing Health Expectancies using IMaCh</title>
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| <h1 align="center"><font color="#00006A">Computing Health |
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| Expectancies using IMaCh</font></h1> |
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| <h1 align="center"><font color="#00006A" size="5">(a Maximum |
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| Likelihood Computer Program using Interpolation of Markov Chains)</font></h1> |
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| <p align="center"> </p> |
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| <p align="center"><a href="http://www.ined.fr/"><img |
<o:Author>agnes lievre</o:Author>
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| src="logo-ined.gif" border="0" width="151" height="76"></a><img |
<o:Template>Normal</o:Template>
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| src="euroreves2.gif" width="151" height="75"></p> |
<o:LastAuthor>agnes lievre</o:LastAuthor>
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<o:Revision>23</o:Revision>
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| <h3 align="center"><a href="http://www.ined.fr/"><font |
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| color="#00006A">INED</font></a><font color="#00006A"> and </font><a |
<o:Created>2002-03-02T16:20:00Z</o:Created>
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| href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3> |
<o:LastSaved>2002-03-03T21:50:00Z</o:LastSaved>
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<o:Pages>15</o:Pages>
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| <p align="center"><font color="#00006A" size="4"><strong>March |
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| 2000</strong></font></p> |
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| <p align="center"><font color="#00006A"><strong>Authors of the |
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| program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font |
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| color="#00006A"><strong>Nicolas Brouard</strong></font></a><font |
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| color="#00006A"><strong>, senior researcher at the </strong></font><a |
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| href="http://www.ined.fr"><font color="#00006A"><strong>Institut |
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| National d'Etudes Démographiques</strong></font></a><font |
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| color="#00006A"><strong> (INED, Paris) in the "Mortality, |
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| Health and Epidemiology" Research Unit </strong></font></p> |
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| <p align="center"><font color="#00006A"><strong>and Agnès |
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| Lièvre<br clear="left"> |
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| </strong></font></p> |
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| <h4><font color="#00006A">Contribution to the mathematics: C. R. |
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| Heathcote </font><font color="#00006A" size="2">(Australian |
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| National University, Canberra).</font></h4> |
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| <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a |
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| href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font |
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| color="#00006A">) </font></h4> |
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| <hr> |
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| <ul> |
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| <li><a href="#intro">Introduction</a> </li> |
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| <li>The detailed statistical model (<a href="docmath.pdf">PDF |
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| version</a>),(<a href="docmath.ps">ps version</a>) </li> |
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| <li><a href="#data">On what kind of data can it be used?</a></li> |
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| <li><a href="#datafile">The data file</a> </li> |
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| <li><a href="#biaspar">The parameter file</a> </li> |
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| <li><a href="#running">Running Imach</a> </li> |
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| <li><a href="#output">Output files and graphs</a> </li> |
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| <li><a href="#example">Exemple</a> </li> |
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| </ul> |
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| <hr> |
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| <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2> |
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| <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal |
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| data</b>. Within the family of Health Expectancies (HE), |
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| Disability-free life expectancy (DFLE) is probably the most |
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| important index to monitor. In low mortality countries, there is |
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| a fear that when mortality declines, the increase in DFLE is not |
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| proportionate to the increase in total Life expectancy. This case |
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| is called the <em>Expansion of morbidity</em>. Most of the data |
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| collected today, in particular by the international <a |
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| href="http://euroreves/reves">REVES</a> network on Health |
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| expectancy, and most HE indices based on these data, are <em>cross-sectional</em>. |
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| It means that the information collected comes from a single |
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| cross-sectional survey: people from various ages (but mostly old |
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| people) are surveyed on their health status at a single date. |
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| Proportion of people disabled at each age, can then be measured |
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| at that date. This age-specific prevalence curve is then used to |
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| distinguish, within the stationary population (which, by |
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| definition, is the life table estimated from the vital statistics |
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| on mortality at the same date), the disable population from the |
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| disability-free population. Life expectancy (LE) (or total |
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| population divided by the yearly number of births or deaths of |
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| this stationary population) is then decomposed into DFLE and DLE. |
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| This method of computing HE is usually called the Sullivan method |
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| (from the name of the author who first described it).</p> |
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| |
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| <p>Age-specific proportions of people disable are very difficult |
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| to forecast because each proportion corresponds to historical |
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| conditions of the cohort and it is the result of the historical |
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| flows from entering disability and recovering in the past until |
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| today. The age-specific intensities (or incidence rates) of |
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| entering disability or recovering a good health, are reflecting |
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| actual conditions and therefore can be used at each age to |
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| forecast the future of this cohort. For example if a country is |
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| improving its technology of prosthesis, the incidence of |
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| recovering the ability to walk will be higher at each (old) age, |
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| but the prevalence of disability will only slightly reflect an |
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| improve because the prevalence is mostly affected by the history |
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| of the cohort and not by recent period effects. To measure the |
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| period improvement we have to simulate the future of a cohort of |
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| new-borns entering or leaving at each age the disability state or |
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| dying according to the incidence rates measured today on |
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| different cohorts. The proportion of people disabled at each age |
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| in this simulated cohort will be much lower (using the exemple of |
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| an improvement) that the proportions observed at each age in a |
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| cross-sectional survey. This new prevalence curve introduced in a |
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| life table will give a much more actual and realistic HE level |
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| than the Sullivan method which mostly measured the History of |
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| health conditions in this country.</p> |
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| <p>Therefore, the main question is how to measure incidence rates |
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| from cross-longitudinal surveys? This is the goal of the IMaCH |
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| program. From your data and using IMaCH you can estimate period |
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| HE and not only Sullivan's HE. Also the standard errors of the HE |
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| are computed.</p> |
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| |
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| <p>A cross-longitudinal survey consists in a first survey |
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| ("cross") where individuals from different ages are |
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| interviewed on their health status or degree of disability. At |
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| least a second wave of interviews ("longitudinal") |
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| should measure each new individual health status. Health |
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| expectancies are computed from the transitions observed between |
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| waves and are computed for each degree of severity of disability |
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| (number of life states). More degrees you consider, more time is |
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| necessary to reach the Maximum Likelihood of the parameters |
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| involved in the model. Considering only two states of disability |
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| (disable and healthy) is generally enough but the computer |
@page Section1
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| program works also with more health statuses.<br> |
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| <br> |
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| The simplest model is the multinomial logistic model where <i>pij</i> |
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| is the probability to be observed in state <i>j</i> at the second |
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| wave conditional to be observed in state <em>i</em> at the first |
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| wave. Therefore a simple model is: log<em>(pij/pii)= aij + |
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| bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>' |
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| is a covariate. The advantage that this computer program claims, |
/* List Definitions */
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| comes from that if the delay between waves is not identical for |
@list l0
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| each individual, or if some individual missed an interview, the |
{mso-list-id:184488806;
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| information is not rounded or lost, but taken into account using |
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| an interpolation or extrapolation. <i>hPijx</i> is the |
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| probability to be observed in state <i>i</i> at age <i>x+h</i> |
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| conditional to the observed state <i>i</i> at age <i>x</i>. The |
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| delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>) |
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| of unobserved intermediate states. This elementary transition (by |
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| month or quarter trimester, semester or year) is modeled as a |
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| multinomial logistic. The <i>hPx</i> matrix is simply the matrix |
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| product of <i>nh*stepm</i> elementary matrices and the |
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| contribution of each individual to the likelihood is simply <i>hPijx</i>. |
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| <br> |
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| </p> |
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| |
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| <p>The program presented in this manual is a quite general |
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| program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated |
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| <strong>MA</strong>rkov <strong>CH</strong>ain), designed to |
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| analyse transition data from longitudinal surveys. The first step |
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| is the parameters estimation of a transition probabilities model |
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| between an initial status and a final status. From there, the |
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| computer program produces some indicators such as observed and |
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| stationary prevalence, life expectancies and their variances and |
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| graphs. Our transition model consists in absorbing and |
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| non-absorbing states with the possibility of return across the |
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| non-absorbing states. The main advantage of this package, |
{mso-list-id:441344838;
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| compared to other programs for the analysis of transition data |
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| (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole |
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| individual information is used even if an interview is missing, a |
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| status or a date is unknown or when the delay between waves is |
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| not identical for each individual. The program can be executed |
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| according to parameters: selection of a sub-sample, number of |
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| absorbing and non-absorbing states, number of waves taken in |
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| account (the user inputs the first and the last interview), a |
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| tolerance level for the maximization function, the periodicity of |
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| the transitions (we can compute annual, quaterly or monthly |
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| transitions), covariates in the model. It works on Windows or on |
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| Unix.<br> |
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| </p> |
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| |
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| <hr> |
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| |
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| <h2><a name="data"><font color="#00006A">On what kind of data can |
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| it be used?</font></a></h2> |
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| |
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| <p>The minimum data required for a transition model is the |
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| recording of a set of individuals interviewed at a first date and |
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| interviewed again at least one another time. From the |
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| observations of an individual, we obtain a follow-up over time of |
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| the occurrence of a specific event. In this documentation, the |
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| event is related to health status at older ages, but the program |
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| can be applied on a lot of longitudinal studies in different |
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| contexts. To build the data file explained into the next section, |
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| you must have the month and year of each interview and the |
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| corresponding health status. But in order to get age, date of |
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| birth (month and year) is required (missing values is allowed for |
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| month). Date of death (month and year) is an important |
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| information also required if the individual is dead. Shorter |
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| steps (i.e. a month) will more closely take into account the |
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| survival time after the last interview.</p> |
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| |
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| <hr> |
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| |
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| <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2> |
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| |
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| <p>In this example, 8,000 people have been interviewed in a |
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| cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). |
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| Some people missed 1, 2 or 3 interviews. Health statuses are |
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| healthy (1) and disable (2). The survey is not a real one. It is |
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| a simulation of the American Longitudinal Survey on Aging. The |
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| disability state is defined if the individual missed one of four |
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| ADL (Activity of daily living, like bathing, eating, walking). |
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| Therefore, even is the individuals interviewed in the sample are |
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| virtual, the information brought with this sample is close to the |
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| situation of the United States. Sex is not recorded is this |
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| sample.</p> |
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| |
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| <p>Each line of the data set (named <a href="data1.txt">data1.txt</a> |
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| in this first example) is an individual record which fields are: </p> |
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| |
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| <ul> |
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| <li><b>Index number</b>: positive number (field 1) </li> |
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| <li><b>First covariate</b> positive number (field 2) </li> |
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| <li><b>Second covariate</b> positive number (field 3) </li> |
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| <li><a name="Weight"><b>Weight</b></a>: positive number |
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| (field 4) . In most surveys individuals are weighted |
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| according to the stratification of the sample.</li> |
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| <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are |
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| coded as 99/9999 (field 5) </li> |
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| <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are |
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| coded as 99/9999 (field 6) </li> |
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| <li><b>Date of first interview</b>: coded as mm/yyyy. Missing |
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| dates are coded as 99/9999 (field 7) </li> |
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| <li><b>Status at first interview</b>: positive number. |
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| Missing values ar coded -1. (field 8) </li> |
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| <li><b>Date of second interview</b>: coded as mm/yyyy. |
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| Missing dates are coded as 99/9999 (field 9) </li> |
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| <li><strong>Status at second interview</strong> positive |
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| number. Missing values ar coded -1. (field 10) </li> |
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| <li><b>Date of third interview</b>: coded as mm/yyyy. Missing |
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| dates are coded as 99/9999 (field 11) </li> |
{mso-level-number-format:bullet;
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| <li><strong>Status at third interview</strong> positive |
mso-level-text:\F0B7;
|
| number. Missing values ar coded -1. (field 12) </li> |
mso-level-tab-stop:36.0pt;
|
| <li><b>Date of fourth interview</b>: coded as mm/yyyy. |
mso-level-number-position:left;
|
| Missing dates are coded as 99/9999 (field 13) </li> |
text-indent:-18.0pt;
|
| <li><strong>Status at fourth interview</strong> positive |
font-family:Symbol;}
|
| number. Missing values are coded -1. (field 14) </li> |
@list l9
|
| <li>etc</li> |
{mso-list-id:1168903496;
|
| </ul> |
mso-list-type:hybrid;
|
| |
mso-list-template-ids:-2008413052 -1461950228 -1012751362 -919308802 443596168 -1469662014 -359112926 504948540 1759957928 1612641564;}
|
| <p> </p> |
@list l9:level1
|
| |
{mso-level-number-format:bullet;
|
| <p>If your longitudinal survey do not include information about |
mso-level-text:\F0B7;
|
| weights or covariates, you must fill the column with a number |
mso-level-tab-stop:36.0pt;
|
| (e.g. 1) because a missing field is not allowed.</p> |
mso-level-number-position:left;
|
| |
text-indent:-18.0pt;
|
| <hr> |
mso-ansi-font-size:10.0pt;
|
| |
font-family:Symbol;}
|
| <h2><font color="#00006A">Your first example parameter file</font><a |
@list l10
|
| href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> |
{mso-list-id:1190214980;
|
| |
mso-list-type:hybrid;
|
| <h2><a name="biaspar"></a>#Imach version 0.63, February 2000, |
mso-list-template-ids:934709936 -291345380 -81906558 -968867310 665229182 1336730126 -1107941388 -20391304 -674328264 -1574639962;}
|
| INED-EUROREVES </h2> |
@list l10:level1
|
| |
{mso-level-number-format:bullet;
|
| <p>This is a comment. Comments start with a '#'.</p> |
mso-level-text:\F0B7;
|
| |
mso-level-tab-stop:36.0pt;
|
| <h4><font color="#FF0000">First uncommented line</font></h4> |
mso-level-number-position:left;
|
| |
text-indent:-18.0pt;
|
| <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> |
mso-ansi-font-size:10.0pt;
|
| |
font-family:Symbol;}
|
| <ul> |
@list l11
|
| <li><b>title=</b> 1st_example is title of the run. </li> |
{mso-list-id:1384715951;
|
| <li><b>datafile=</b>data1.txt is the name of the data set. |
mso-list-type:hybrid;
|
| Our example is a six years follow-up survey. It consists |
mso-list-template-ids:-515744014 -566093190 799967300 770599756 -1594063690 -869741144 1377056636 315393812 -1370061484 1511570004;}
|
| in a baseline followed by 3 reinterviews. </li> |
@list l11:level1
|
| <li><b>lastobs=</b> 8600 the program is able to run on a |
{mso-level-number-format:bullet;
|
| subsample where the last observation number is lastobs. |
mso-level-text:\F0B7;
|
| It can be set a bigger number than the real number of |
mso-level-tab-stop:36.0pt;
|
| observations (e.g. 100000). In this example, maximisation |
mso-level-number-position:left;
|
| will be done on the 8600 first records. </li> |
text-indent:-18.0pt;
|
| <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more |
mso-ansi-font-size:10.0pt;
|
| than two interviews in the survey, the program can be run |
font-family:Symbol;}
|
| on selected transitions periods. firstpass=1 means the |
@list l12
|
| first interview included in the calculation is the |
{mso-list-id:1593661621;
|
| baseline survey. lastpass=4 means that the information |
mso-list-type:hybrid;
|
| brought by the 4th interview is taken into account.</li> |
mso-list-template-ids:-1035417432 1271449484 -308236740 -1122210034 -380844018 1478807872 266132728 -1091829500 812926462 -1442827238;}
|
| </ul> |
@list l12:level1
|
| |
{mso-level-number-format:bullet;
|
| <p> </p> |
mso-level-text:\F0B7;
|
| |
mso-level-tab-stop:36.0pt;
|
| <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented |
mso-level-number-position:left;
|
| line</font></a></h4> |
text-indent:-18.0pt;
|
| |
mso-ansi-font-size:10.0pt;
|
| <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
font-family:Symbol;}
|
| |
@list l13
|
| <ul> |
{mso-list-id:1636450504;
|
| <li><b>ftol=1e-8</b> Convergence tolerance on the function |
mso-list-type:hybrid;
|
| value in the maximisation of the likelihood. Choosing a |
mso-list-template-ids:-711022678 -1038569226 1304059700 -837663288 -1699980300 571783806 -231993906 -744861656 1958002196 -1476655198;}
|
| correct value for ftol is difficult. 1e-8 is a correct |
@list l13:level1
|
| value for a 32 bits computer.</li> |
{mso-level-number-format:bullet;
|
| <li><b>stepm=1</b> Time unit in months for interpolation. |
mso-level-text:\F0B7;
|
| Examples:<ul> |
mso-level-tab-stop:36.0pt;
|
| <li>If stepm=1, the unit is a month </li> |
mso-level-number-position:left;
|
| <li>If stepm=4, the unit is a trimester</li> |
text-indent:-18.0pt;
|
| <li>If stepm=12, the unit is a year </li> |
mso-ansi-font-size:10.0pt;
|
| <li>If stepm=24, the unit is two years</li> |
font-family:Symbol;}
|
| <li>... </li> |
@list l14
|
| </ul> |
{mso-list-id:1752386307;
|
| </li> |
mso-list-type:hybrid;
|
| <li><b>ncov=2</b> Number of covariates to be add to the |
mso-list-template-ids:-347696224 -386773934 1871641532 667840386 1914592500 1728978276 -196066776 1566372654 -755335742 341755130;}
|
| model. The intercept and the age parameter are counting |
@list l14:level1
|
| for 2 covariates. For example, if you want to add gender |
{mso-level-number-format:bullet;
|
| in the covariate vector you must write ncov=3 else |
mso-level-text:\F0B7;
|
| ncov=2. </li> |
mso-level-tab-stop:36.0pt;
|
| <li><b>nlstate=2</b> Number of non-absorbing (live) states. |
mso-level-number-position:left;
|
| Here we have two alive states: disability-free is coded 1 |
text-indent:-18.0pt;
|
| and disability is coded 2. </li> |
mso-ansi-font-size:10.0pt;
|
| <li><b>ndeath=1</b> Number of absorbing states. The absorbing |
font-family:Symbol;}
|
| state death is coded 3. </li> |
@list l14:level2
|
| <li><b>maxwav=4</b> Maximum number of waves. The program can |
{mso-level-number-format:bullet;
|
| not include more than 4 interviews. </li> |
mso-level-text:o;
|
| <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the |
mso-level-tab-stop:72.0pt;
|
| Maximisation Likelihood Estimation. <ul> |
mso-level-number-position:left;
|
| <li>If mle=1 the program does the maximisation and |
text-indent:-18.0pt;
|
| the calculation of heath expectancies </li> |
mso-ansi-font-size:10.0pt;
|
| <li>If mle=0 the program only does the calculation of |
font-family:"Courier New";
|
| the health expectancies. </li> |
mso-bidi-font-family:"Times New Roman";}
|
| </ul> |
@list l15
|
| </li> |
{mso-list-id:1756245288;
|
| <li><b>weight=0</b> Possibility to add weights. <ul> |
mso-list-type:hybrid;
|
| <li>If weight=0 no weights are included </li> |
mso-list-template-ids:531934386 67895297 67895299 67895301 67895297 67895299 67895301 67895297 67895299 67895301;}
|
| <li>If weight=1 the maximisation integrates the |
@list l15:level1
|
| weights which are in field <a href="#Weight">4</a></li> |
{mso-level-number-format:bullet;
|
| </ul> |
mso-level-text:\F0B7;
|
| </li> |
mso-level-tab-stop:36.0pt;
|
| </ul> |
mso-level-number-position:left;
|
| |
text-indent:-18.0pt;
|
| <h4><font color="#FF0000">Guess values for optimization</font><font |
font-family:Symbol;}
|
| color="#00006A"> </font></h4> |
@list l16
|
| |
{mso-list-id:1839273133;
|
| <p>You must write the initial guess values of the parameters for |
mso-list-type:hybrid;
|
| optimization. The number of parameters, <em>N</em> depends on the |
mso-list-template-ids:-556523634 -715873828 -243865004 563531560 -898876536 640947630 967865102 1305671924 1810678544 -1115658030;}
|
| number of absorbing states and non-absorbing states and on the |
@list l16:level1
|
| number of covariates. <br> |
{mso-level-number-format:bullet;
|
| <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> + |
mso-level-text:\F0B7;
|
| <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br> |
mso-level-tab-stop:36.0pt;
|
| <br> |
mso-level-number-position:left;
|
| Thus in the simple case with 2 covariates (the model is log |
text-indent:-18.0pt;
|
| (pij/pii) = aij + bij * age where intercept and age are the two |
mso-ansi-font-size:10.0pt;
|
| covariates), and 2 health degrees (1 for disability-free and 2 |
font-family:Symbol;}
|
| for disability) and 1 absorbing state (3), you must enter 8 |
@list l17
|
| initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can |
{mso-list-id:1841849959;
|
| start with zeros as in this example, but if you have a more |
mso-list-type:hybrid;
|
| precise set (for example from an earlier run) you can enter it |
mso-list-template-ids:2053128728 -543362536 926470224 151426154 998932566 84972724 844683600 1807279286 -841218426 -1132452502;}
|
| and it will speed up them<br> |
@list l17:level1
|
| Each of the four lines starts with indices "ij": <br> |
{mso-level-number-format:bullet;
|
| <br> |
mso-level-text:\F0B7;
|
| <b>ij aij bij</b> </p> |
mso-level-tab-stop:36.0pt;
|
| |
mso-level-number-position:left;
|
| <blockquote> |
text-indent:-18.0pt;
|
| <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age |
mso-ansi-font-size:10.0pt;
|
| 12 -14.155633 0.110794 |
font-family:Symbol;}
|
| 13 -7.925360 0.032091 |
@list l18
|
| 21 -1.890135 -0.029473 |
{mso-list-id:1848639524;
|
| 23 -6.234642 0.022315 </pre> |
mso-list-type:hybrid;
|
| </blockquote> |
mso-list-template-ids:638092306 940881202 -784414886 1026841176 1011505968 -653358884 -269310374 2133217052 1173680566 -1995784172;}
|
| |
@list l18:level1
|
| <p>or, to simplify: </p> |
{mso-level-number-format:bullet;
|
| |
mso-level-text:\F0B7;
|
| <blockquote> |
mso-level-tab-stop:36.0pt;
|
| <pre>12 0.0 0.0 |
mso-level-number-position:left;
|
| 13 0.0 0.0 |
text-indent:-18.0pt;
|
| 21 0.0 0.0 |
mso-ansi-font-size:10.0pt;
|
| 23 0.0 0.0</pre> |
font-family:Symbol;}
|
| </blockquote> |
ol
|
| |
{margin-bottom:0cm;}
|
| <h4><font color="#FF0000">Guess values for computing variances</font></h4> |
ul
|
| |
{margin-bottom:0cm;}
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
-->
|
| used as an input to get the vairous output data files (Health |
</style>
|
| expectancies, stationary prevalence etc.) and figures without |
<!--[if gte mso 9]><xml>
|
| rerunning the rather long maximisation phase (mle=0). </p> |
<o:shapedefaults v:ext="edit" spidmax="1027"/>
|
| |
</xml><![endif]-->
|
| <p>The scales are small values for the evaluation of numerical |
<!--[if gte mso 9]><xml>
|
| derivatives. These derivatives are used to compute the hessian |
<o:shapelayout v:ext="edit">
|
| matrix of the parameters, that is the inverse of the covariance |
<o:idmap v:ext="edit" data="1"/>
|
| matrix, and the variances of health expectancies. Each line |
</o:shapelayout></xml><![endif]-->
|
| consists in indices "ij" followed by the initial scales |
<!-- Changed by: Agnes Lievre, 12-Oct-2000 -->
|
| (zero to simplify) associated with aij and bij. </p> |
</head>
|
| |
|
| <ul> |
<body bgcolor="#FFFFFF" link="#0000FF" vlink="#0000FF" lang="FR"
|
| <li>If mle=1 you can enter zeros:</li> |
style="tab-interval:35.4pt">
|
| </ul> |
|
| |
<hr size="3" noshade color="#EC5E5E">
|
| <blockquote> |
|
| <pre># Scales (for hessian or gradient estimation) |
<h1 align="center" style="text-align:center"><span lang="EN-GB" style="color:#00006A;
|
| 12 0. 0. |
mso-ansi-language:EN-GB">Computing Health
|
| 13 0. 0. |
Expectancies using IMaCh</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
|
| 21 0. 0. |
|
| 23 0. 0. </pre> |
<h1 align="center" style="text-align:center"><span lang="EN-GB" style="font-size:
|
| </blockquote> |
18.0pt;color:#00006A;mso-ansi-language:EN-GB">(a Maximum
|
| |
Likelihood Computer Program using Interpolation of Markov Chains)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
|
| <ul> |
|
| <li>If mle=0 you must enter a covariance matrix (usually |
<p align="center" style="text-align:center"><span lang="EN-GB" style="mso-ansi-language:
|
| obtained from an earlier run).</li> |
EN-GB"> <o:p></o:p></span></p>
|
| </ul> |
|
| |
<p align="center" style="text-align:center"><a
|
| <h4><font color="#FF0000">Covariance matrix of parameters</font></h4> |
href="http://www.ined.fr/"><span style="text-decoration:none;text-underline:none"><img src="logo-ined.gif" border="0"
|
| |
width="151" height="76" id="_x0000_i1026"></span></a><img
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
src="euroreves2.gif" width="151" height="75" id="_x0000_i1027"></p>
|
| used as an input to get the vairous output data files (Health |
|
| expectancies, stationary prevalence etc.) and figures without |
<h3 align="center" style="text-align:center"><a
|
| rerunning the rather long maximisation phase (mle=0). </p> |
href="http://www.ined.fr/"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">INED</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a> and </span><a
|
| |
href="http://euroreves.ined.fr"><span lang="EN-GB" style="color:#00006A;
|
| <p>Each line starts with indices "ijk" followed by the |
mso-ansi-language:EN-GB">EUROREVES</span><span lang="EN-GB" style="mso-ansi-language:
|
| covariances between aij and bij: </p> |
EN-GB"><o:p></o:p></span></a></h3>
|
| |
|
| <pre> |
<p align="center" style="text-align:center"><strong><span lang="EN-GB" style="font-size:13.5pt;color:#00006A;mso-ansi-language:EN-GB">Version 0.7,
|
| 121 Var(a12) |
February 2002</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
|
| 122 Cov(b12,a12) Var(b12) |
|
| ... |
<hr size="3" noshade color="#EC5E5E">
|
| 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> |
|
| |
<p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Authors of
|
| <ul> |
the program: </span></strong><a href="http://sauvy.ined.fr/brouard"><strong><span lang="EN-GB" style="color:#00006A;
|
| <li>If mle=1 you can enter zeros. </li> |
mso-ansi-language:EN-GB">Nicolas
|
| </ul> |
Brouard</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></strong></a><strong>, senior researcher at the </span></strong><a
|
| |
href="http://www.ined.fr"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Institut National d'Etudes
|
| <blockquote> |
Démographiques</span><span lang="EN-GB" style="color:#00006A;
|
| <pre># Covariance matrix |
mso-ansi-language:EN-GB"></strong></a><strong> (INED, Paris) in the
|
| 121 0. |
"Mortality, Health and Epidemiology" Research Unit </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
|
| 122 0. 0. |
|
| 131 0. 0. 0. |
<p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">and Agnès
|
| 132 0. 0. 0. 0. |
Lièvre</span></strong><b><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"><br clear="left"
|
| 211 0. 0. 0. 0. 0. |
style="mso-special-character:line-break">
|
| 212 0. 0. 0. 0. 0. 0. |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></b></p>
|
| 231 0. 0. 0. 0. 0. 0. 0. |
|
| 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> |
<h4><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Contribution to the mathematics: C. R. Heathcote </span><span lang="EN-GB" style="font-size:
|
| </blockquote> |
10.0pt;color:#00006A;mso-ansi-language:EN-GB">(Australian
|
| |
National University, Canberra).</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| <ul> |
|
| <li>If mle=0 you must enter a covariance matrix (usually |
<h4><span style="color:#00006A">Contact: Agnès Lièvre (</span><a href="mailto:lievre@ined.fr"><i><span style="color:#00006A">lievre@ined.fr</span><span style="color:#00006A"></i></a>)
|
| obtained from an earlier run).<br> |
</span></h4>
|
| </li> |
|
| </ul> |
<hr>
|
| |
<span style="font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
|
| <h4><a name="biaspar-l"></a><font color="#FF0000">last |
"Times New Roman";mso-ansi-language:FR;mso-fareast-language:FR;mso-bidi-language:
|
| uncommented line</font></h4> |
AR-SA">
|
| |
<ul type="disc">
|
| <pre>agemin=70 agemax=100 bage=50 fage=100</pre> |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <p>Once we obtained the estimated parameters, the program is able |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| to calculated stationary prevalence, transitions probabilities |
href="#intro"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Introduction</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| and life expectancies at any age. Choice of age ranges is useful |
<li class="MsoNormal"
|
| for extrapolation. In our data file, ages varies from age 70 to |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 102. Setting bage=50 and fage=100, makes the program computing |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| life expectancy from age bage to age fage. As we use a model, we |
href="#data"><span lang="EN-GB" style="mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
|
| can compute life expectancy on a wider age range than the age |
<li class="MsoNormal"
|
| range from the data. But the model can be rather wrong on big |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| intervals.</p> |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| |
href="#datafile"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The data file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| <p>Similarly, it is possible to get extrapolated stationary |
<li class="MsoNormal"
|
| prevalence by age raning from agemin to agemax. </p> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| <ul> |
href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The parameter file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| <li><b>agemin=</b> Minimum age for calculation of the |
<li class="MsoNormal"
|
| stationary prevalence </li> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <li><b>agemax=</b> Maximum age for calculation of the |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| stationary prevalence </li> |
href="#running"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Running Imach</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| <li><b>bage=</b> Minimum age for calculation of the health |
<li class="MsoNormal"
|
| expectancies </li> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <li><b>fage=</b> Maximum ages for calculation of the health |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| expectancies </li> |
href="#output"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output files and graphs</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| </ul> |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <hr> |
mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
|
| |
href="#example">Exemple</a> </li>
|
| <h2><a name="running"></a><font color="#00006A">Running Imach |
</ul>
|
| with this example</font></h2> |
</span>
|
| |
<hr>
|
| <p>We assume that you entered your <a href="biaspar.txt">1st_example |
|
| parameter file</a> as explained <a href="#biaspar">above</a>. To |
<h2><a name="intro"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Introduction</span><span style="mso-bookmark:intro"></span><span lang="EN-GB" style="mso-ansi-language:
|
| run the program you should click on the imach.exe icon and enter |
EN-GB"><o:p></o:p></span></a></h2>
|
| the name of the parameter file which is for example <a |
|
| href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a> |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This program computes <b>Healthy
|
| (you also can click on the biaspar.txt icon located in <br> |
Life Expectancies</b> from <b>cross-longitudinal data</b> using
|
| <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with |
the methodology pioneered by Laditka and Wolf (1). Within the
|
| the mouse on the imach window).<br> |
family of Health Expectancies (HE), Disability-free life
|
| </p> |
expectancy (DFLE) is probably the most important index to
|
| |
monitor. In low mortality countries, there is a fear that when
|
| <p>The time to converge depends on the step unit that you used (1 |
mortality declines, the increase in DFLE is not proportionate to
|
| month is cpu consuming), on the number of cases, and on the |
the increase in total Life expectancy. This case is called the <em>Expansion
|
| number of variables.</p> |
of morbidity</em>. Most of the data collected today, in
|
| |
particular by the international </span><a href="http://euroreves/reves"><span lang="EN-GB" style="mso-ansi-language:EN-GB">REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
|
| <p>The program outputs many files. Most of them are files which |
network on Health expectancy, and most HE indices based on these
|
| will be plotted for better understanding.</p> |
data, are <em>cross-sectional</em>. It means that the information
|
| |
collected comes from a single cross-sectional survey: people from
|
| <hr> |
various ages (but mostly old people) are surveyed on their health
|
| |
status at a single date. Proportion of people disabled at each
|
| <h2><a name="output"><font color="#00006A">Output of the program |
age, can then be measured at that date. This age-specific
|
| and graphs</font> </a></h2> |
prevalence curve is then used to distinguish, within the
|
| |
stationary population (which, by definition, is the life table
|
| <p>Once the optimization is finished, some graphics can be made |
estimated from the vital statistics on mortality at the same
|
| with a grapher. We use Gnuplot which is an interactive plotting |
date), the disable population from the disability-free
|
| program copyrighted but freely distributed. Imach outputs the |
population. Life expectancy (LE) (or total population divided by
|
| source of a gnuplot file, named 'graph.gp', which can be directly |
the yearly number of births or deaths of this stationary
|
| input into gnuplot.<br> |
population) is then decomposed into DFLE and DLE. This method of
|
| When the running is finished, the user should enter a caracter |
computing HE is usually called the Sullivan method (from the name
|
| for plotting and output editing. </p> |
of the author who first described it).<o:p></o:p></span></p>
|
| |
|
| <p>These caracters are:</p> |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age-specific proportions of people
|
| |
disable are very difficult to forecast because each proportion
|
| <ul> |
corresponds to historical conditions of the cohort and it is the
|
| <li>'c' to start again the program from the beginning.</li> |
result of the historical flows from entering disability and
|
| <li>'g' to made graphics. The output graphs are in GIF format |
recovering in the past until today. The age-specific intensities
|
| and you have no control over which is produced. If you |
(or incidence rates) of entering disability or recovering a good
|
| want to modify the graphics or make another one, you |
health, are reflecting actual conditions and therefore can be
|
| should modify the parameters in the file <b>graph.gp</b> |
used at each age to forecast the future of this cohort. For
|
| located in imach\bin. A gnuplot reference manual is |
example if a country is improving its technology of prosthesis,
|
| available <a |
the incidence of recovering the ability to walk will be higher at
|
| href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>. |
each (old) age, but the prevalence of disability will only
|
| </li> |
slightly reflect an improve because the prevalence is mostly
|
| <li>'e' opens the <strong>index.htm</strong> file to edit the |
affected by the history of the cohort and not by recent period
|
| output files and graphs. </li> |
effects. To measure the period improvement we have to simulate
|
| <li>'q' for exiting.</li> |
the future of a cohort of new-borns entering or leaving at each
|
| </ul> |
age the disability state or dying according to the incidence
|
| |
rates measured today on different cohorts. The proportion of
|
| <h5><font size="4"><strong>Results files </strong></font><br> |
people disabled at each age in this simulated cohort will be much
|
| <br> |
lower (using the example of an improvement) that the proportions
|
| <font color="#EC5E5E" size="3"><strong>- </strong></font><a |
observed at each age in a cross-sectional survey. This new
|
| name="Observed prevalence in each state"><font color="#EC5E5E" |
prevalence curve introduced in a life table will give a much more
|
| size="3"><strong>Observed prevalence in each state</strong></font></a><font |
actual and realistic HE level than the Sullivan method which
|
| color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>: |
mostly measured the History of health conditions in this country.<o:p></o:p></span></p>
|
| </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br> |
|
| </h5> |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Therefore, the main question is how
|
| |
to measure incidence rates from cross-longitudinal surveys? This
|
| <p>The first line is the title and displays each field of the |
is the goal of the IMaCH program. From your data and using IMaCH
|
| file. The first column is age. The fields 2 and 6 are the |
you can estimate period HE and not only Sullivan's HE. Also the
|
| proportion of individuals in states 1 and 2 respectively as |
standard errors of the HE are computed.<o:p></o:p></span></p>
|
| observed during the first exam. Others fields are the numbers of |
|
| people in states 1, 2 or more. The number of columns increases if |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">A cross-longitudinal survey
|
| the number of states is higher than 2.<br> |
consists in a first survey ("cross") where individuals
|
| The header of the file is </p> |
from different ages are interviewed on their health status or
|
| |
degree of disability. At least a second wave of interviews
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
("longitudinal") should measure each new individual
|
| 70 1.00000 631 631 70 0.00000 0 631 |
health status. Health expectancies are computed from the
|
| 71 0.99681 625 627 71 0.00319 2 627 |
transitions observed between waves and are computed for each
|
| 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> |
degree of severity of disability (number of life states). More
|
| |
degrees you consider, more time is necessary to reach the Maximum
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
Likelihood of the parameters involved in the model. Considering
|
| 70 0.95721 604 631 70 0.04279 27 631</pre> |
only two states of disability (disable and healthy) is generally
|
| |
enough but the computer program works also with more health
|
| <p>It means that at age 70, the prevalence in state 1 is 1.000 |
statuses.<span style="mso-spacerun:
|
| and in state 2 is 0.00 . At age 71 the number of individuals in |
yes"> </span><br>
|
| state 1 is 625 and in state 2 is 2, hence the total number of |
<br>
|
| people aged 71 is 625+2=627. <br> |
The simplest model is the multinomial logistic model where <i>pij</i>
|
| </p> |
is the probability to be observed in state <i>j</i> at the second
|
| |
wave conditional to be observed in state <em>i</em> at the first
|
| <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and |
wave. Therefore a simple model is: log<em>(pij/pii)= aij +
|
| covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5> |
bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
|
| |
is a covariate. The advantage that this computer program claims,
|
| <p>This file contains all the maximisation results: </p> |
comes from that if the delay between waves is not identical for
|
| |
each individual, or if some individual missed an interview, the
|
| <pre> Number of iterations=47 |
information is not rounded or lost, but taken into account using
|
| -2 log likelihood=46553.005854373667 |
an interpolation or extrapolation. <i>hPijx</i> is the
|
| Estimated parameters: a12 = -12.691743 b12 = 0.095819 |
probability to be observed in state <i>i</i> at age <i>x+h</i>
|
| a13 = -7.815392 b13 = 0.031851 |
conditional to the observed state <i>i</i> at age <i>x</i>. The
|
| a21 = -1.809895 b21 = -0.030470 |
delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
|
| a23 = -7.838248 b23 = 0.039490 |
of unobserved intermediate states. This elementary transition (by
|
| Covariance matrix: Var(a12) = 1.03611e-001 |
month or quarter trimester, semester or year) is modeled as a
|
| Var(b12) = 1.51173e-005 |
multinomial logistic. The <i>hPx</i> matrix is simply the matrix
|
| Var(a13) = 1.08952e-001 |
product of <i>nh*stepm</i> elementary matrices and the
|
| Var(b13) = 1.68520e-005 |
contribution of each individual to the likelihood is simply <i>hPijx</i>.
|
| Var(a21) = 4.82801e-001 |
<o:p></o:p></span></p>
|
| Var(b21) = 6.86392e-005 |
|
| Var(a23) = 2.27587e-001 |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The program presented in this
|
| Var(b23) = 3.04465e-005 |
manual is a quite general program named <strong>IMaCh</strong>
|
| </pre> |
(for <strong>I</strong>nterpolated <strong>MA</strong>rkov <strong>CH</strong>ain),
|
| |
designed to analyse transition data from longitudinal surveys.
|
| <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>: |
The first step is the parameters estimation of a transition
|
| </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5> |
probabilities model between an initial status and a final status.
|
| |
From there, the computer program produces some indicators such as
|
| <p>Here are the transitions probabilities Pij(x, x+nh) where nh |
observed and stationary prevalence, life expectancies and their
|
| is a multiple of 2 years. The first column is the starting age x |
variances and graphs. Our transition model consists in absorbing
|
| (from age 50 to 100), the second is age (x+nh) and the others are |
and non-absorbing states with the possibility of return across
|
| the transition probabilities p11, p12, p13, p21, p22, p23. For |
the non-absorbing states. The main advantage of this package,
|
| example, line 5 of the file is: </p> |
compared to other programs for the analysis of transition data
|
| |
(For example: Proc Catmod of SAS<sup>(r)</sup>) is that the whole
|
| <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre> |
individual information is used even if an interview is missing, a
|
| |
status or a date is unknown or when the delay between waves is
|
| <p>and this means: </p> |
not identical for each individual. The program can be executed
|
| |
according to parameters: selection of a sub-sample, number of
|
| <pre>p11(100,106)=0.03286 |
absorbing and non-absorbing states, number of waves taken in
|
| p12(100,106)=0.23512 |
account (the user inputs the first and the last interview), a
|
| p13(100,106)=0.73202 |
tolerance level for the maximization function, the periodicity of
|
| p21(100,106)=0.02330 |
the transitions (we can compute annual, quarterly or monthly
|
| p22(100,106)=0.19210 |
transitions), covariates in the model. It works on Windows or on
|
| p22(100,106)=0.78460 </pre> |
Unix.<o:p></o:p></span></p>
|
| |
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
<hr>
|
| name="Stationary prevalence in each state"><font color="#EC5E5E" |
|
| size="3"><b>Stationary prevalence in each state</b></font></a><b>: |
<p><span lang="EN-GB" style="mso-ansi-language:EN-GB">(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
|
| </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5> |
Methods for Analyzing Active Life Expectancy". <i>Journal of
|
| |
Aging and Health</i>. </span>Vol 10, No. 2. </p>
|
| <pre>#Age 1-1 2-2 |
|
| 70 0.92274 0.07726 |
<hr>
|
| 71 0.91420 0.08580 |
|
| 72 0.90481 0.09519 |
<h2><a name="data"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span style="mso-bookmark:data"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
|
| 73 0.89453 0.10547</pre> |
|
| |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The minimum data required for a
|
| <p>At age 70 the stationary prevalence is 0.92274 in state 1 and |
transition model is the recording of a set of individuals
|
| 0.07726 in state 2. This stationary prevalence differs from |
interviewed at a first date and interviewed again at least one
|
| observed prevalence. Here is the point. The observed prevalence |
another time. From the observations of an individual, we obtain a
|
| at age 70 results from the incidence of disability, incidence of |
follow-up over time of the occurrence of a specific event. In
|
| recovery and mortality which occurred in the past of the cohort. |
this documentation, the event is related to health status at
|
| Stationary prevalence results from a simulation with actual |
older ages, but the program can be applied on a lot of
|
| incidences and mortality (estimated from this cross-longitudinal |
longitudinal studies in different contexts. To build the data
|
| survey). It is the best predictive value of the prevalence in the |
file explained into the next section, you must have the month and
|
| future if "nothing changes in the future". This is |
year of each interview and the corresponding health status. But
|
| exactly what demographers do with a Life table. Life expectancy |
in order to get age, date of birth (month and year) is required
|
| is the expected mean time to survive if observed mortality rates |
(missing values is allowed for month). Date of death (month and
|
| (incidence of mortality) "remains constant" in the |
year) is an important information also required if the individual
|
| future. </p> |
is dead. Shorter steps (i.e. a month) will more closely take into
|
| |
account the survival time after the last interview.<o:p></o:p></span></p>
|
| <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of |
|
| stationary prevalence</b></font><b>: </b><a |
<hr>
|
| href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5> |
|
| |
<h2><a name="datafile"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:
|
| <p>The stationary prevalence has to be compared with the observed |
EN-GB">The data file</span><span style="mso-bookmark:datafile"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
|
| prevalence by age. But both are statistical estimates and |
|
| subjected to stochastic errors due to the size of the sample, the |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, 8,000 people have
|
| design of the survey, and, for the stationary prevalence to the |
been interviewed in a cross-longitudinal survey of 4 waves (1984,
|
| model used and fitted. It is possible to compute the standard |
1986, 1988, 1990). Some people missed 1, 2 or 3 interviews.
|
| deviation of the stationary prevalence at each age.</p> |
Health statuses are healthy (1) and disable (2). The survey is
|
| |
not a real one. It is a simulation of the American Longitudinal
|
| <h6><font color="#EC5E5E" size="3">Observed and stationary |
Survey on Aging. The disability state is defined if the
|
| prevalence in state (2=disable) with the confident interval</font>:<b> |
individual missed one of four ADL (Activity of daily living, like
|
| vbiaspar2.gif</b></h6> |
bathing, eating, walking). Therefore, even is the individuals
|
| |
interviewed in the sample are virtual, the information brought
|
| <p><br> |
with this sample is close to the situation of the United States.
|
| This graph exhibits the stationary prevalence in state (2) with |
Sex is not recorded is this sample.<o:p></o:p></span></p>
|
| the confidence interval in red. The green curve is the observed |
|
| prevalence (or proportion of individuals in state (2)). Without |
<p><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each line of the data set (named </span><a href="data1.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| discussing the results (it is not the purpose here), we observe |
EN-GB">data1.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
|
| that the green curve is rather below the stationary prevalence. |
in this first example) is an individual record which fields are: <o:p></o:p></span></p>
|
| It suggests an increase of the disability prevalence in the |
|
| future.</p> |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| <p><img src="vbiaspar2.gif" width="400" height="300"></p> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Index
|
| <h6><font color="#EC5E5E" size="3"><b>Convergence to the |
number</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number (field 1) <o:p></o:p></span></li>
|
| stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br> |
<li class="MsoNormal"
|
| <img src="pbiaspar1.gif" width="400" height="300"> </h6> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
|
| <p>This graph plots the conditional transition probabilities from |
covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 2) <o:p></o:p></span></li>
|
| an initial state (1=healthy in red at the bottom, or 2=disable in |
<li class="MsoNormal"
|
| green on top) at age <em>x </em>to the final state 2=disable<em> </em>at |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| age <em>x+h. </em>Conditional means at the condition to be alive |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Second
|
| at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The |
covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 3) <o:p></o:p></span></li>
|
| curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i> |
<li class="MsoNormal"
|
| + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| prevalence of disability</em>. In order to get the stationary |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><a
|
| prevalence at age 70 we should start the process at an earlier |
name="Weight"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Weight</span><span style="mso-bookmark:Weight"></span><span lang="EN-GB" style="mso-ansi-language:
|
| age, i.e.50. If the disability state is defined by severe |
EN-GB"></b></a>: positive number (field
|
| disability criteria with only a few chance to recover, then the |
4) . In most surveys individuals are weighted according
|
| incidence of recovery is low and the time to convergence is |
to the stratification of the sample.<o:p></o:p></span></li>
|
| probably longer. But we don't have experience yet.</p> |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| and initial health status</b></font><b>: </b><a |
of birth</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
|
| href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5> |
as 99/9999 (field 5) <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| <pre># Health expectancies |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| # Age 1-1 1-2 2-1 2-2 |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| 70 10.7297 2.7809 6.3440 5.9813 |
of death</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
|
| 71 10.3078 2.8233 5.9295 5.9959 |
as 99/9999 (field 6) <o:p></o:p></span></li>
|
| 72 9.8927 2.8643 5.5305 6.0033 |
<li class="MsoNormal"
|
| 73 9.4848 2.9036 5.1474 6.0035 </pre> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means: |
of first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
|
| e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre> |
are coded as 99/9999 (field 7) <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| <pre><img src="exbiaspar1.gif" width="400" height="300"><img |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| src="exbiaspar2.gif" width="400" height="300"></pre> |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
|
| |
at first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number. Missing values
|
| <p>For example, life expectancy of a healthy individual at age 70 |
ar coded -1. (field 8) <o:p></o:p></span></li>
|
| is 10.73 in the healthy state and 2.78 in the disability state |
<li class="MsoNormal"
|
| (=13.51 years). If he was disable at age 70, his life expectancy |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| will be shorter, 6.34 in the healthy state and 5.98 in the |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| disability state (=12.32 years). The total life expectancy is a |
of second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
|
| weighted mean of both, 13.51 and 12.32; weight is the proportion |
are coded as 99/9999 (field 9) <o:p></o:p></span></li>
|
| of people disabled at age 70. In order to get a pure period index |
<li class="MsoNormal"
|
| (i.e. based only on incidences) we use the <a |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| href="#Stationary prevalence in each state">computed or |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
|
| stationary prevalence</a> at age 70 (i.e. computed from |
at second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
|
| incidences at earlier ages) instead of the <a |
values ar coded -1. (field 10) <o:p></o:p></span></li>
|
| href="#Observed prevalence in each state">observed prevalence</a> |
<li class="MsoNormal"
|
| (for example at first exam) (<a href="#Health expectancies">see |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| below</a>).</p> |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| |
of third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
|
| <h5><font color="#EC5E5E" size="3"><b>- Variances of life |
are coded as 99/9999 (field 11) <o:p></o:p></span></li>
|
| expectancies by age and initial health status</b></font><b>: </b><a |
<li class="MsoNormal"
|
| href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
|
| <p>For example, the covariances of life expectancies Cov(ei,ej) |
at third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
|
| at age 50 are (line 3) </p> |
values ar coded -1. (field 12) <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| <pre> Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183</pre> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
of fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
|
| name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health |
are coded as 99/9999 (field 13) <o:p></o:p></span></li>
|
| expectancies</b></font></a><font color="#EC5E5E" size="3"><b> |
<li class="MsoNormal"
|
| with standard errors in parentheses</b></font><b>: </b><a |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5> |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
|
| |
at fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
|
| <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> |
values are coded -1. (field 14) <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| <pre>70 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09) </pre> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">etc<o:p></o:p></span></li>
|
| <p>Thus, at age 70 the total life expectancy, e..=13.42 years is |
</ul>
|
| the weighted mean of e1.=13.51 and e2.=12.32 by the stationary |
|
| prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in |
<p><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></p>
|
| state 2, respectively (the sum is equal to one). e.1=10.39 is the |
|
| Disability-free life expectancy at age 70 (it is again a weighted |
<p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If your longitudinal survey do not
|
| mean of e11 and e21). e.2=3.03 is also the life expectancy at age |
include information about weights or covariates, you must fill
|
| 70 to be spent in the disability state.</p> |
the column with a number (e.g. 1) because a missing field is not
|
| |
allowed.<o:p></o:p></span></p>
|
| <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by |
|
| age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>: |
<hr>
|
| ebiaspar.gif</b></h6> |
|
| |
<h2><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Your first example parameter file</span><a
|
| <p>This figure represents the health expectancies and the total |
href="http://euroreves.ined.fr/imach"></a><a name="uio"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
|
| life expectancy with the confident interval in dashed curve. </p> |
|
| |
<h2><a name="biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>#Imach version 0.7, February 2002,
|
| <pre> <img src="ebiaspar.gif" width="400" height="300"></pre> |
INED-EUROREVES <o:p></o:p></span></h2>
|
| |
|
| <p>Standard deviations (obtained from the information matrix of |
<p><span lang="EN-GB" style="mso-ansi-language:EN-GB">This is a comment. Comments start with a '#'.<o:p></o:p></span></p>
|
| the model) of these quantities are very useful. |
|
| Cross-longitudinal surveys are costly and do not involve huge |
<h4><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">First uncommented line</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| samples, generally a few thousands; therefore it is very |
|
| important to have an idea of the standard deviation of our |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4<o:p></o:p></span></pre>
|
| estimates. It has been a big challenge to compute the Health |
|
| Expectancy standard deviations. Don't be confuse: life expectancy |
<ul type="disc">
|
| is, as any expected value, the mean of a distribution; but here |
<li class="MsoNormal"
|
| we are not computing the standard deviation of the distribution, |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| but the standard deviation of the estimate of the mean.</p> |
text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
1st_example is title of the run. <o:p></o:p></span></li>
|
| <p>Our health expectancies estimates vary according to the sample |
<li class="MsoNormal"
|
| size (and the standard deviations give confidence intervals of |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| the estimate) but also according to the model fitted. Let us |
text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">datafile=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>data1.txt
|
| explain it in more details.</p> |
is the name of the data set. Our example is a six years
|
| |
follow-up survey. It consists in a baseline followed by 3
|
| <p>Choosing a model means ar least two kind of choices. First we |
reinterviews. <o:p></o:p></span></li>
|
| have to decide the number of disability states. Second we have to |
<li class="MsoNormal"
|
| design, within the logit model family, the model: variables, |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| covariables, confonding factors etc. to be included.</p> |
text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">lastobs=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
8600 the program is able to run on a subsample where the
|
| <p>More disability states we have, better is our demographical |
last observation number is lastobs. It can be set a
|
| approach of the disability process, but smaller are the number of |
bigger number than the real number of observations (e.g.
|
| transitions between each state and higher is the noise in the |
100000). In this example, maximisation will be done on
|
| measurement. We do not have enough experiments of the various |
the 8600 first records. <o:p></o:p></span></li>
|
| models to summarize the advantages and disadvantages, but it is |
<li class="MsoNormal"
|
| important to say that even if we had huge and unbiased samples, |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| the total life expectancy computed from a cross-longitudinal |
text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">firstpass=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| survey, varies with the number of states. If we define only two |
, <b>lastpass=4 </b>In case of more than two interviews
|
| states, alive or dead, we find the usual life expectancy where it |
in the survey, the program can be run on selected
|
| is assumed that at each age, people are at the same risk to die. |
transitions periods. firstpass=1 means the first
|
| If we are differentiating the alive state into healthy and |
interview included in the calculation is the baseline
|
| disable, and as the mortality from the disability state is higher |
survey. lastpass=4 means that the information brought by
|
| than the mortality from the healthy state, we are introducing |
the 4th interview is taken into account.<o:p></o:p></span></li>
|
| heterogeneity in the risk of dying. The total mortality at each |
</ul>
|
| age is the weighted mean of the mortality in each state by the |
|
| prevalence in each state. Therefore if the proportion of people |
<p
|
| at each age and in each state is different from the stationary |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></p>
|
| equilibrium, there is no reason to find the same total mortality |
|
| at a particular age. Life expectancy, even if it is a very useful |
<h4
|
| tool, has a very strong hypothesis of homogeneity of the |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Second
|
| population. Our main purpose is not to measure differential |
uncommented line</span><a name="biaspar-2"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h4>
|
| mortality but to measure the expected time in a healthy or |
|
| disability state in order to maximise the former and minimize the |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
|
| latter. But the differential in mortality complexifies the |
|
| measurement.</p> |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| <p>Incidences of disability or recovery are not affected by the |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| number of states if these states are independant. But incidences |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1e-8</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| estimates are dependant on the specification of the model. More |
Convergence tolerance on the function value in the
|
| covariates we added in the logit model better is the model, but |
maximisation of the likelihood. Choosing a correct value
|
| some covariates are not well measured, some are confounding |
for ftol is difficult. 1e-8 is a correct value for a 32
|
| factors like in any statistical model. The procedure to "fit |
bits computer.<o:p></o:p></span></li>
|
| the best model' is similar to logistic regression which itself is |
<li class="MsoNormal"
|
| similar to regression analysis. We haven't yet been sofar because |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| we also have a severe limitation which is the speed of the |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">stepm=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| convergence. On a Pentium III, 500 MHz, even the simplest model, |
Time unit in months for interpolation. Examples:<o:p></o:p></span></li>
|
| estimated by month on 8,000 people may take 4 hours to converge. |
<li><ul type="circle">
|
| Also, the program is not yet a statistical package, which permits |
<li class="MsoNormal"
|
| a simple writing of the variables and the model to take into |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| account in the maximisation. The actual program allows only to |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| add simple variables without covariations, like age+sex but |
stepm=1, the unit is a month <o:p></o:p></span></li>
|
| without age+sex+ age*sex . This can be done from the source code |
<li class="MsoNormal"
|
| (you have to change three lines in the source code) but will |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| never be general enough. But what is to remember, is that |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| incidences or probability of change from one state to another is |
stepm=4, the unit is a trimester<o:p></o:p></span></li>
|
| affected by the variables specified into the model.</p> |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| <p>Also, the age range of the people interviewed has a link with |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| the age range of the life expectancy which can be estimated by |
stepm=12, the unit is a year <o:p></o:p></span></li>
|
| extrapolation. If your sample ranges from age 70 to 95, you can |
<li class="MsoNormal"
|
| clearly estimate a life expectancy at age 70 and trust your |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| confidence interval which is mostly based on your sample size, |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| but if you want to estimate the life expectancy at age 50, you |
stepm=24, the unit is two years<o:p></o:p></span></li>
|
| should rely in your model, but fitting a logistic model on a age |
<li class="MsoNormal"
|
| range of 70-95 and estimating probabilties of transition out of |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| this age range, say at age 50 is very dangerous. At least you |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">...
|
| should remember that the confidence interval given by the |
<o:p></o:p></span> </li>
|
| standard deviation of the health expectancies, are under the |
</ul>
|
| strong assumption that your model is the 'true model', which is |
</li>
|
| probably not the case.</p> |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ncov=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5> |
Number of covariates in the datafile. The intercept and
|
| |
the age parameter are counting for 2 covariates.<o:p></o:p></span></li>
|
| <p>This copy of the parameter file can be useful to re-run the |
<li class="MsoNormal"
|
| program while saving the old output files. </p> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">nlstate=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| <hr> |
Number of non-absorbing (alive) states. Here we have two
|
| |
alive states: disability-free is coded 1 and disability
|
| <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2> |
is coded 2. <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| <p>Since you know how to run the program, it is time to test it |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| on your own computer. Try for example on a parameter file named <a |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ndeath=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a |
Number of absorbing states. The absorbing state death is
|
| copy of <font size="2" face="Courier New">mypar.txt</font> |
coded 3. <o:p></o:p></span></li>
|
| included in the subdirectory of imach, <font size="2" |
<li class="MsoNormal"
|
| face="Courier New">mytry</font>. Edit it to change the name of |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| the data file to <font size="2" face="Courier New">..\data\mydata.txt</font> |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">maxwav=4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| if you don't want to copy it on the same directory. The file <font |
Number of waves in the datafile.<o:p></o:p></span></li>
|
| face="Courier New">mydata.txt</font> is a smaller file of 3,000 |
<li class="MsoNormal"
|
| people but still with 4 waves. </p> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><a
|
| <p>Click on the imach.exe icon to open a window. Answer to the |
name="mle"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b></a><b>=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for the
|
| question:'<strong>Enter the parameter file name:'</strong></p> |
Maximisation Likelihood Estimation. <o:p></o:p></span></li>
|
| |
<li><ul type="circle">
|
| <table border="1"> |
<li class="MsoNormal"
|
| <tr> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| the parameter file name: ..\mytry\imachpar.txt</strong></p> |
mle=1 the program does the maximisation and the
|
| </td> |
calculation of health expectancies <o:p></o:p></span></li>
|
| </tr> |
<li class="MsoNormal"
|
| </table> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| <p>Most of the data files or image files generated, will use the |
mle=0 the program only does the calculation of
|
| 'imachpar' string into their name. The running time is about 2-3 |
the health expectancies. <o:p></o:p></span></li>
|
| minutes on a Pentium III. If the execution worked correctly, the |
</ul>
|
| outputs files are created in the current directory, and should be |
</li>
|
| the same as the mypar files initially included in the directory <font |
<li class="MsoNormal"
|
| size="2" face="Courier New">mytry</font>.</p> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">weight=0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| <ul> |
Possibility to add weights. <o:p></o:p></span></li>
|
| <li><pre><u>Output on the screen</u> The output screen looks like <a |
<li><ul type="circle">
|
| href="imachrun.LOG">this Log file</a> |
<li class="MsoNormal"
|
| # |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 |
weight=0 no weights are included <o:p></o:p></span></li>
|
| ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
<li class="MsoNormal"
|
| </li> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
|
| <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 |
auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| |
weight=1 the maximisation integrates the weights
|
| Warning, no any valid information for:126 line=126 |
which are in field </span><a href="#Weight"><span lang="EN-GB" style="mso-ansi-language:EN-GB">4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
|
| Warning, no any valid information for:2307 line=2307 |
</ul>
|
| Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 |
</li>
|
| <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font> |
</ul>
|
| Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 |
|
| prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 |
<h4
|
| Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariates</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| </li> |
|
| </ul> |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Intercept
|
| <p> </p> |
and age are systematically included in the model. Additional
|
| |
covariates can be included with the command <o:p></o:p></span></p>
|
| <ul> |
|
| <li>Maximisation with the Powell algorithm. 8 directions are |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">model=<em>list of covariates<o:p></o:p></span></em></pre>
|
| given corresponding to the 8 parameters. this can be |
|
| rather long to get convergence.<br> |
<ul type="disc">
|
| <font size="1" face="Courier New"><br> |
<li class="MsoNormal"
|
| Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 0.000000000000 3<br> |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if<strong>
|
| 0.000000000000 4 0.000000000000 5 0.000000000000 6 |
model=. </strong>then no covariates are included<o:p></o:p></span></li>
|
| 0.000000000000 7 <br> |
<li class="MsoNormal"
|
| 0.000000000000 8 0.000000000000<br> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 1..........2.................3..........4.................5.........<br> |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
|
| 6................7........8...............<br> |
<strong>model=V1</strong> the model includes the first
|
| Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 |
covariate (field 2)<o:p></o:p></span></li>
|
| <br> |
<li class="MsoNormal"
|
| 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br> |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
|
| 8 0.051272038506<br> |
<strong>model=V2 </strong>the model includes the second
|
| 1..............2...........3..............4...........<br> |
covariate (field 3)<o:p></o:p></span></li>
|
| 5..........6................7...........8.........<br> |
<li class="MsoNormal"
|
| #Number of iterations = 23, -2 Log likelihood = |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 6744.954042573691<br> |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
|
| # Parameters<br> |
<strong>model=V1+V2 </strong>the model includes the first
|
| 12 -12.966061 0.135117 <br> |
and the second covariate (fields 2 and 3)<o:p></o:p></span></li>
|
| 13 -7.401109 0.067831 <br> |
<li class="MsoNormal"
|
| 21 -0.672648 -0.006627 <br> |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| 23 -5.051297 0.051271 </font><br> |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
|
| </li> |
<strong>model=V1*V2 </strong>the model includes the
|
| <li><pre><font size="2">Calculation of the hessian matrix. Wait... |
product of the first and the second covariate (fields 2
|
| 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78 |
and 3)<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| Inverting the hessian to get the covariance matrix. Wait... |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
|
| #Hessian matrix# |
<strong>model=V1+V1*age</strong> the model includes the
|
| 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 |
product covariate*age<o:p></o:p></span></li>
|
| 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 |
</ul>
|
| -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 |
|
| -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 |
<h4
|
| -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
|
| -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 |
values for optimisation</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 |
|
| 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 |
<p
|
| # Scales |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">You
|
| 12 1.00000e-004 1.00000e-006 |
must write the initial guess values of the parameters for
|
| 13 1.00000e-004 1.00000e-006 |
optimisation. The number of parameters, <em>N</em> depends on the
|
| 21 1.00000e-003 1.00000e-005 |
number of absorbing states and non-absorbing states and on the
|
| 23 1.00000e-004 1.00000e-005 |
number of covariates. <br>
|
| # Covariance |
<em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
|
| 1 5.90661e-001 |
<em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br>
|
| 2 -7.26732e-003 8.98810e-005 |
<br>
|
| 3 8.80177e-002 -1.12706e-003 5.15824e-001 |
Thus in the simple case with 2 covariates (the model is log
|
| 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 |
(pij/pii) = aij + bij * age where intercept and age are the two
|
| 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 |
covariates), and 2 health degrees (1 for disability-free and 2
|
| 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 |
for disability) and 1 absorbing state (3), you must enter 8
|
| 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 |
initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
|
| 8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004 |
start with zeros as in this example, but if you have a more
|
| # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). |
precise set (for example from an earlier run) you can enter it
|
| |
and it will speed up them<br>
|
| |
Each of the four lines starts with indices "ij": <b>ij
|
| agemin=70 agemax=100 bage=50 fage=100 |
aij bij</b> <o:p></o:p></span></p>
|
| Computing prevalence limit: result on file 'plrmypar.txt' |
|
| Computing pij: result on file 'pijrmypar.txt' |
<pre
|
| Computing Health Expectancies: result on file 'ermypar.txt' |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
|
| Computing Variance-covariance of DFLEs: file 'vrmypar.txt' |
36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Guess values of aij and bij in log (pij/pii) = aij + bij * age<o:p></o:p></span></pre>
|
| Computing Total LEs with variances: file 'trmypar.txt' |
|
| Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' |
<pre
|
| End of Imach |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| </font></pre> |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| </li> |
EN-GB">12 -14.155633<span style="mso-spacerun: yes"> </span>0.110794 <o:p></o:p></span></pre>
|
| </ul> |
|
| |
<pre
|
| <p><font size="3">Once the running is finished, the program |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| requires a caracter:</font></p> |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">13<span style="mso-spacerun: yes"> </span>-7.925360<span style="mso-spacerun: yes"> </span>0.032091 <o:p></o:p></span></pre>
|
| <table border="1"> |
|
| <tr> |
<pre
|
| <td width="100%"><strong>Type g for plotting (available |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| if mle=1), e to edit output files, c to start again,</strong><p><strong>and |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| q for exiting:</strong></p> |
EN-GB">21<span style="mso-spacerun: yes"> </span>-1.890135 -0.029473 <o:p></o:p></span></pre>
|
| </td> |
|
| </tr> |
<pre
|
| </table> |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| <p><font size="3">First you should enter <strong>g</strong> to |
EN-GB">23<span style="mso-spacerun: yes"> </span>-6.234642<span style="mso-spacerun: yes"> </span>0.022315 <o:p></o:p></span></pre>
|
| make the figures and then you can edit all the results by typing <strong>e</strong>. |
|
| </font></p> |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">or,
|
| <ul> |
to simplify: <o:p></o:p></span></p>
|
| <li><u>Outputs files</u> <br> |
|
| - index.htm, this file is the master file on which you |
<pre
|
| should click first.<br> |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
|
| - Observed prevalence in each state: <a |
36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12 0.0 0.0<o:p></o:p></span></pre>
|
| href="..\mytry\prmypar.txt">mypar.txt</a> <br> |
|
| - Estimated parameters and the covariance matrix: <a |
<pre
|
| href="..\mytry\rmypar.txt">rmypar.txt</a> <br> |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| - Stationary prevalence in each state: <a |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br> |
EN-GB">13 0.0 0.0<o:p></o:p></span></pre>
|
| - Transition probabilities: <a |
|
| href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br> |
<pre
|
| - Copy of the parameter file: <a |
style="margin-top:0cm;margin-right:
|
| href="..\mytry\ormypar.txt">ormypar.txt</a> <br> |
36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
|
| - Life expectancies by age and initial health status: <a |
justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">21 0.0 0.0<o:p></o:p></span></pre>
|
| href="..\mytry\ermypar.txt">ermypar.txt</a> <br> |
|
| - Variances of life expectancies by age and initial |
<pre
|
| health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| <br> |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| - Health expectancies with their variances: <a |
EN-GB">23 0.0 0.0<o:p></o:p></span></pre>
|
| href="..\mytry\trmypar.txt">trmypar.txt</a> <br> |
|
| - Standard deviation of stationary prevalence: <a |
<h4
|
| href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br> |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
|
| <br> |
values for computing variances</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| </li> |
|
| <li><u>Graphs</u> <br> |
<p
|
| <br> |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| -<a href="..\mytry\vmypar1.gif">Observed and stationary |
is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
|
| prevalence in state (1) with the confident interval</a> <br> |
an input to get the various output data files (Health
|
| -<a href="..\mytry\vmypar2.gif">Observed and stationary |
expectancies, stationary prevalence etc.) and figures without
|
| prevalence in state (2) with the confident interval</a> <br> |
rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
|
| -<a href="..\mytry\exmypar1.gif">Health life expectancies |
|
| by age and initial health state (1)</a> <br> |
<p
|
| -<a href="..\mytry\exmypar2.gif">Health life expectancies |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| by age and initial health state (2)</a> <br> |
scales are small values for the evaluation of numerical
|
| -<a href="..\mytry\emypar.gif">Total life expectancy by |
derivatives. These derivatives are used to compute the hessian
|
| age and health expectancies in states (1) and (2).</a> </li> |
matrix of the parameters, that is the inverse of the covariance
|
| </ul> |
matrix, and the variances of health expectancies. Each line
|
| |
consists in indices "ij" followed by the initial scales
|
| <p>This software have been partly granted by <a |
(zero to simplify) associated with aij and bij. <o:p></o:p></span></p>
|
| href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted |
|
| action from the European Union. It will be copyrighted |
<ul type="disc">
|
| identically to a GNU software product, i.e. program and software |
<li class="MsoNormal"
|
| can be distributed freely for non commercial use. Sources are not |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| widely distributed today. You can get them by asking us with a |
text-align:justify;mso-list:l16 level1 lfo18;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| simple justification (name, email, institute) <a |
mle=1 you can enter zeros:<o:p></o:p></span></li>
|
| href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a |
</ul>
|
| href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p> |
|
| |
<pre
|
| <p>Latest version (0.63 of 16 march 2000) can be accessed at <a |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
|
| href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br> |
36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Scales (for hessian or gradient estimation)<o:p></o:p></span></pre>
|
| </p> |
|
| </body> |
<pre
|
| </html> |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">12 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:
|
| |
36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
|
| |
justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">13 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">21 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:
|
| |
36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
|
| |
justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">23 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l11 level1 lfo21;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| |
mle=0 you must enter a covariance matrix (usually
|
| |
obtained from an earlier run).<o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariance
|
| |
matrix of parameters</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
|
| |
an input to get the various output data files (Health
|
| |
expectancies, stationary prevalence etc.) and figures without
|
| |
rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each
|
| |
line starts with indices "ijk" followed by the
|
| |
covariances between aij and bij: <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>121 Var(a12) <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>122 Cov(b12,a12)<span style="mso-spacerun: yes"> </span>Var(b12) <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>...<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>232 Cov(b23,a12)<span style="mso-spacerun: yes"> </span>Cov(b23,b12) ... Var (b23) <o:p></o:p></span></pre>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l18 level1 lfo24;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| |
mle=1 you can enter zeros. <o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
|
| |
36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Covariance matrix<o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">121 0.<o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:
|
| |
36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
|
| |
justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">122 0. 0.<o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">131 0. 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;
|
| |
margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
|
| |
text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">132 0. 0. 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">211 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;
|
| |
margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
|
| |
text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">212 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
|
| |
margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">231 0. 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
|
| |
|
| |
<pre
|
| |
style="margin-top:
|
| |
0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:
|
| |
.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">232 0. 0. 0. 0. 0. 0. 0. 0.<o:p></o:p></span></pre>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l7 level1 lfo27;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
|
| |
mle=0 you must enter a covariance matrix (usually
|
| |
obtained from an earlier run).<o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Age
|
| |
range for calculation of stationary prevalences and health
|
| |
expectancies</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
|
| |
we obtained the estimated parameters, the program is able to
|
| |
calculated stationary prevalence, transitions probabilities and
|
| |
life expectancies at any age. Choice of age range is useful for
|
| |
extrapolation. In our data file, ages varies from age 70 to 102.
|
| |
Setting bage=50 and fage=100, makes the program computing life
|
| |
expectancy from age bage to age fage. As we use a model, we can
|
| |
compute life expectancy on a wider age range than the age range
|
| |
from the data. But the model can be rather wrong on big
|
| |
intervals.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Similarly,
|
| |
it is possible to get extrapolated stationary prevalence by age
|
| |
ranging from agemin to agemax. <o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
Minimum age for calculation of the stationary prevalence <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemax=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
Maximum age for calculation of the stationary prevalence <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">bage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
Minimum age for calculation of the health expectancies <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">fage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
Maximum age for calculation of the health expectancies <o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
|
| |
name="Computing"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Computing</span><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB"></a> the observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=1/1/1984 end-prev-date=1/6/1988 <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Statements
|
| |
'begin-prev-date' and 'end-prev-date' allow to select the period
|
| |
in which we calculate the observed prevalences in each state. In
|
| |
this example, the prevalences are calculated on data survey
|
| |
collected between 1 January 1984 and 1 June 1988. <o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=
|
| |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> </strong>Starting date (day/month/year)<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">end-prev-date=
|
| |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> </strong>Final date (day/month/year)<o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Population-
|
| |
or status-based health expectancies</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pop_based=0<o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| |
user has the possibility to choose between population-based or
|
| |
status-based health expectancies. If pop_based=0 then
|
| |
status-based health expectancies are computed and if pop_based=1,
|
| |
the programme computes population-based health expectancies.
|
| |
Health expectancies are weighted averages of health expectancies
|
| |
respective of the initial state. For a status-based index, the
|
| |
weights are the cross-sectional prevalences observed between two
|
| |
dates, as </span><a href="#Computing"><span lang="EN-GB" style="mso-ansi-language:EN-GB">previously explained</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, whereas
|
| |
for a population-based index, the weights are the stationary
|
| |
prevalences.<o:p></o:p></span></p>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Prevalence
|
| |
forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Prevalence
|
| |
and population projections are available only if the
|
| |
interpolation unit is a month, i.e. stepm=1. The programme
|
| |
estimates the prevalence in each state at a precise date
|
| |
expressed in day/month/year. The programme computes one
|
| |
forecasted prevalence a year from a starting date (1 January of
|
| |
1989 in this example) to a final date (1 January 1992). The
|
| |
statement mov_average allows to compute smoothed forecasted
|
| |
prevalences with a five-age moving average centred at the mid-age
|
| |
of the five-age period. <o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
|
| |
starting date (day/month/year) of forecasting<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">final-proj-date=
|
| |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> </strong>final date (day/month/year) of forecasting<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">mov_average</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
|
| |
smoothing with a five-age moving average centred at the
|
| |
mid-age of the five-age period. The command<strong>
|
| |
mov_average</strong> takes value 1 if the prevalences are
|
| |
smoothed and 0 otherwise.<o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h4
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Last
|
| |
uncommented line : Population forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
|
| |
|
| |
<pre><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992<o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
command is available if the interpolation unit is a month, i.e.
|
| |
stepm=1 and if popforecast=1. From a data file including age and
|
| |
number of persons alive at the precise date ‘</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Courier New";
|
| |
mso-ansi-language:EN-GB">popfiledate’,
|
| |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">you can forecast the number of persons in each state until date</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:
|
| |
12.0pt;font-family:"Courier New";mso-ansi-language:EN-GB">
|
| |
‘last-popfiledate’. </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, the popfile </span><a
|
| |
href="pyram.txt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">pyram.txt</span><span style="mso-ansi-language:EN-GB"></b></a><b> </span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><span style="mso-spacerun: yes"></b> </span>includes real
|
| |
data which are the Japanese population in 1989.<span style="mso-spacerun: yes"> </span><o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=
|
| |
0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for population forecasting. If
|
| |
popforecast=1, the programme does the forecasting<b>.<o:p></o:p></span></b></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfile=
|
| |
</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> </b>name of the population file<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfiledate=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
|
| |
date of the population population<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">last-popfiledate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>=
|
| |
date of the last population projection <o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<hr>
|
| |
|
| |
<h2
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
|
| |
name="running"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Running Imach with this example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">We
|
| |
assume that you entered your </span><a href="biaspar.imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">1st_example
|
| |
parameter file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> as explained </span><a href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">above</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. To
|
| |
run the program you should click on the imach.exe icon and enter
|
| |
the name of the parameter file which is for example </span><a
|
| |
href="..\mle\biaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle\biaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> (you
|
| |
also can click on the biaspar.txt icon located in </span><a
|
| |
href="..\mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and put it with the mouse on
|
| |
the imach window).<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| |
time to converge depends on the step unit that you used (1 month
|
| |
is cpu consuming), on the number of cases, and on the number of
|
| |
variables.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| |
program outputs many files. Most of them are files which will be
|
| |
plotted for better understanding.<o:p></o:p></span></p>
|
| |
|
| |
<hr>
|
| |
|
| |
<h2
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
|
| |
name="output"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Output of the program and graphs</span><span style="mso-bookmark:output"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
|
| |
the optimization is finished, some graphics can be made with a
|
| |
grapher. We use Gnuplot which is an interactive plotting program
|
| |
copyrighted but freely distributed. A gnuplot reference manual is
|
| |
available </span><a href="http://www.gnuplot.info/"><span lang="EN-GB" style="mso-ansi-language:EN-GB">here</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. <br>
|
| |
When the running is finished, the user should enter a character
|
| |
for plotting and output editing. <o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">These
|
| |
characters are:<o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'c'
|
| |
to start again the program from the beginning.<o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'e'
|
| |
opens the </span><a href="biaspar.htm"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">biaspar.htm</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong></a>
|
| |
file to edit the output files and graphs. <o:p></o:p></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'q'
|
| |
for exiting.<o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<h5
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:18.0pt;mso-bidi-font-size:10.0pt;color:#00006A;
|
| |
mso-ansi-language:EN-GB">Results
|
| |
files</span><strong><span lang="EN-GB" style="font-size:13.5pt;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong><br>
|
| |
<br>
|
| |
</span><strong><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;
|
| |
mso-ansi-language:EN-GB">- </strong><a name="Observed_prevalence_in_each_state"><strong>Observed
|
| |
prevalence in each state</strong></a><strong> (and at first pass)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>:
|
| |
</span><a href="prbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">prbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| |
first line is the title and displays each field of the file. The
|
| |
first column is age. The fields 2 and 6 are the proportion of
|
| |
individuals in states 1 and 2 respectively as observed during the
|
| |
first exam. Others fields are the numbers of people in states 1,
|
| |
2 or more. The number of columns increases if the number of
|
| |
states is higher than 2.<br>
|
| |
The header of the file is <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age Prev(1) N(1) N Age Prev(2) N(2) N<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 1.00000 631 631 70 0.00000 0 631<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.99681 625 627 71 0.00319 2 627 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.97125 1115 1148 72 0.02875 33 1148 <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">It
|
| |
means that at age 70, the prevalence in state 1 is 1.000 and in
|
| |
state 2 is 0.00 . At age 71 the number of individuals in state 1
|
| |
is 625 and in state 2 is 2, hence the total number of people aged
|
| |
71 is 625+2=627. <o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Estimated parameters and covariance matrix</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
|
| |
href="rbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
file contains all the maximisation results: <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>-2 log likelihood= 21660.918613445392<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> Estimated parameters: a12 = -12.290174 b12 = 0.092161 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span><span style="mso-spacerun: yes"> </span>a13 = -9.155590<span style="mso-spacerun: yes"> </span>b13 = 0.046627 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>a21 = -2.629849<span style="mso-spacerun: yes"> </span>b21 = -0.022030 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>a23 = -7.958519<span style="mso-spacerun: yes"> </span>b23 = 0.042614<span style="mso-spacerun: yes"> </span><o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Covariance matrix: Var(a12) = 1.47453e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Var(b12) = 2.18676e-005<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Var(a13) = 2.09715e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Var(b13) = 3.28937e-005<span style="mso-spacerun: yes"> </span><o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Var(a21) = 9.19832e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>Var(b21) = 1.29229e-004<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span></span><span lang="DE" style="mso-ansi-language:DE">Var(a23) = 4.48405e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes"> </span>Var(b23) = 5.85631e-005 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes"> </span><o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">By
|
| |
substitution of these parameters in the regression model, we
|
| |
obtain the elementary transition probabilities:<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><img
|
| |
src="pebiaspar1.gif" width="400" height="300" id="_x0000_i1037"></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Transition probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="pijrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">pijrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Here
|
| |
are the transitions probabilities Pij(x, x+nh) where nh is a
|
| |
multiple of 2 years. The first column is the starting age x (from
|
| |
age 50 to 100), the second is age (x+nh) and the others are the
|
| |
transition probabilities p11, p12, p13, p21, p22, p23. For
|
| |
example, line 5 of the file is: <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span>100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">and
|
| |
this means: <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p11(100,106)=0.02655<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p12(100,106)=0.17622<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p13(100,106)=0.79722<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p21(100,106)=0.01809<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.13678<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.84513 <o:p></o:p></span></pre>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
<a name="Stationary_prevalence_in_each_state">Stationary
|
| |
prevalence in each state</span><span style="mso-bookmark:Stationary_prevalence_in_each_state"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>: </span><a href="plrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">plrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Prevalence<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Age 1-1 2-2<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#************ <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 0.90134 0.09866<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.89177 0.10823 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.88139 0.11861 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.87015 0.12985 <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">At
|
| |
age 70 the stationary prevalence is 0.90134 in state 1 and
|
| |
0.09866 in state 2. This stationary prevalence differs from
|
| |
observed prevalence. Here is the point. The observed prevalence
|
| |
at age 70 results from the incidence of disability, incidence of
|
| |
recovery and mortality which occurred in the past of the cohort.
|
| |
Stationary prevalence results from a simulation with actual
|
| |
incidences and mortality (estimated from this cross-longitudinal
|
| |
survey). It is the best predictive value of the prevalence in the
|
| |
future if "nothing changes in the future". This is
|
| |
exactly what demographers do with a Life table. Life expectancy
|
| |
is the expected mean time to survive if observed mortality rates
|
| |
(incidence of mortality) "remains constant" in the
|
| |
future. <o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Standard deviation of stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
|
| |
href="vplrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vplrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
|
| |
stationary prevalence has to be compared with the observed
|
| |
prevalence by age. But both are statistical estimates and
|
| |
subjected to stochastic errors due to the size of the sample, the
|
| |
design of the survey, and, for the stationary prevalence to the
|
| |
model used and fitted. It is possible to compute the standard
|
| |
deviation of the stationary prevalence at each age.<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Observed
|
| |
and stationary prevalence in state (2=disable) with the confident
|
| |
interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="vbiaspar21.htm"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vbiaspar21.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
graph exhibits the stationary prevalence in state (2) with the
|
| |
confidence interval in red. The green curve is the observed
|
| |
prevalence (or proportion of individuals in state (2)). Without
|
| |
discussing the results (it is not the purpose here), we observe
|
| |
that the green curve is rather below the stationary prevalence.
|
| |
It suggests an increase of the disability prevalence in the
|
| |
future.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><img
|
| |
src="vbiaspar21.gif" width="400" height="300" id="_x0000_i1038"></p>
|
| |
|
| |
<h5
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Convergence
|
| |
to the stationary prevalence of disability</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
|
| |
href="pbiaspar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pbiaspar11.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
|
| |
</span><img src="pbiaspar11.gif" width="400" height="300"
|
| |
id="_x0000_i1039"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
graph plots the conditional transition probabilities from an
|
| |
initial state (1=healthy in red at the bottom, or 2=disable in
|
| |
green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
|
| |
age <em>x+h. </em>Conditional means at the condition to be alive
|
| |
at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
|
| |
curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
|
| |
+ <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
|
| |
prevalence of disability</em>. In order to get the stationary
|
| |
prevalence at age 70 we should start the process at an earlier
|
| |
age, i.e.50. If the disability state is defined by severe
|
| |
disability criteria with only a few chance to recover, then the
|
| |
incidence of recovery is low and the time to convergence is
|
| |
probably longer. But we don't have experience yet.<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
|
| |
href="erbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">erbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Health expectancies <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age 1-1 1-2 2-1 2-2 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 10.9226 3.0401 5.6488 6.2122 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 10.4384 3.0461 5.2477 6.1599 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 9.9667 3.0502 4.8663 6.1025 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 9.5077 3.0524 4.5044 6.0401 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For example 70 10.9226 3.0401 5.6488 6.2122 means:<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE">e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><img src="expbiaspar21.gif"
|
| |
width="400" height="300" id="_x0000_i1040"><img
|
| |
src="expbiaspar11.gif" width="400" height="300" id="_x0000_i1041"></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
|
| |
example, life expectancy of a healthy individual at age 70 is
|
| |
10.92 in the healthy state and 3.04 in the disability state
|
| |
(=13.96 years). If he was disable at age 70, his life expectancy
|
| |
will be shorter, 5.64 in the healthy state and 6.21 in the
|
| |
disability state (=11.85 years). The total life expectancy is a
|
| |
weighted mean of both, 13.96 and 11.85; weight is the proportion
|
| |
of people disabled at age 70. In order to get a pure period index
|
| |
(i.e. based only on incidences) we use the </span><a
|
| |
href="#Stationary prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:EN-GB">computed or
|
| |
stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> at age 70 (i.e. computed from
|
| |
incidences at earlier ages) instead of the </span><a
|
| |
href="#Observed prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a>
|
| |
(for example at first exam) (</span><a href="#Health expectancies"><span lang="EN-GB" style="mso-ansi-language:EN-GB">see
|
| |
below</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>).<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Variances of life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
|
| |
href="vrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
|
| |
example, the covariances of life expectancies Cov(ei,ej) at age
|
| |
50 are (line 3) <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span></span><span lang="DE" style="mso-ansi-language:DE">Cov(e1,e1)=0.4776<span style="mso-spacerun: yes"> </span>Cov(e1,e2)=0.0488=Cov(e2,e1)<span style="mso-spacerun: yes"> </span>Cov(e2,e2)=0.0424<o:p></o:p></span></pre>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
<a name="Health_expectancies">Health expectancies</a> with
|
| |
standard errors in parentheses</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="trbiaspar.txt"><span lang="EN-GB" style="font-family:"Courier New";
|
| |
mso-ansi-language:EN-GB">trbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) <o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Thus,
|
| |
at age 70 the total life expectancy, e..=13.76years is the
|
| |
weighted mean of e1.=13.96 and e2.=11.85 by the stationary
|
| |
prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
|
| |
state 2, respectively (the sum is equal to one). e.1=10.40 is the
|
| |
Disability-free life expectancy at age 70 (it is again a weighted
|
| |
mean of e11 and e21). e.2=3.35 is also the life expectancy at age
|
| |
70 to be spent in the disability state.<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Total
|
| |
life expectancy by age and health expectancies in states
|
| |
(1=healthy) and (2=disable)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="ebiaspar1.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ebiaspar1.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
figure represents the health expectancies and the total life
|
| |
expectancy with the confident interval in dashed curve. <o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes"> </span></span><img
|
| |
src="ebiaspar1.gif" width="400" height="300" id="_x0000_i1042"></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Standard
|
| |
deviations (obtained from the information matrix of the model) of
|
| |
these quantities are very useful. Cross-longitudinal surveys are
|
| |
costly and do not involve huge samples, generally a few
|
| |
thousands; therefore it is very important to have an idea of the
|
| |
standard deviation of our estimates. It has been a big challenge
|
| |
to compute the Health Expectancy standard deviations. Don't be
|
| |
confuse: life expectancy is, as any expected value, the mean of a
|
| |
distribution; but here we are not computing the standard
|
| |
deviation of the distribution, but the standard deviation of the
|
| |
estimate of the mean.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Our
|
| |
health expectancies estimates vary according to the sample size
|
| |
(and the standard deviations give confidence intervals of the
|
| |
estimate) but also according to the model fitted. Let us explain
|
| |
it in more details.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Choosing
|
| |
a model means at least two kind of choices. First we have to
|
| |
decide the number of disability states. Second we have to design,
|
| |
within the logit model family, the model: variables, covariables,
|
| |
confounding factors etc. to be included.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">More
|
| |
disability states we have, better is our demographical approach
|
| |
of the disability process, but smaller are the number of
|
| |
transitions between each state and higher is the noise in the
|
| |
measurement. We do not have enough experiments of the various
|
| |
models to summarize the advantages and disadvantages, but it is
|
| |
important to say that even if we had huge and unbiased samples,
|
| |
the total life expectancy computed from a cross-longitudinal
|
| |
survey, varies with the number of states. If we define only two
|
| |
states, alive or dead, we find the usual life expectancy where it
|
| |
is assumed that at each age, people are at the same risk to die.
|
| |
If we are differentiating the alive state into healthy and
|
| |
disable, and as the mortality from the disability state is higher
|
| |
than the mortality from the healthy state, we are introducing
|
| |
heterogeneity in the risk of dying. The total mortality at each
|
| |
age is the weighted mean of the mortality in each state by the
|
| |
prevalence in each state. Therefore if the proportion of people
|
| |
at each age and in each state is different from the stationary
|
| |
equilibrium, there is no reason to find the same total mortality
|
| |
at a particular age. Life expectancy, even if it is a very useful
|
| |
tool, has a very strong hypothesis of homogeneity of the
|
| |
population. Our main purpose is not to measure differential
|
| |
mortality but to measure the expected time in a healthy or
|
| |
disability state in order to maximise the former and minimize the
|
| |
latter. But the differential in mortality complexifies the
|
| |
measurement.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Incidences
|
| |
of disability or recovery are not affected by the number of
|
| |
states if these states are independant. But incidences estimates
|
| |
are dependant on the specification of the model. More covariates
|
| |
we added in the logit model better is the model, but some
|
| |
covariates are not well measured, some are confounding factors
|
| |
like in any statistical model. The procedure to "fit the
|
| |
best model' is similar to logistic regression which itself is
|
| |
similar to regression analysis. We haven't yet been so far
|
| |
because we also have a severe limitation which is the speed of
|
| |
the convergence. On a Pentium III, 500 MHz, even the simplest
|
| |
model, estimated by month on 8,000 people may take 4 hours to
|
| |
converge. Also, the program is not yet a statistical package,
|
| |
which permits a simple writing of the variables and the model to
|
| |
take into account in the maximisation. The actual program allows
|
| |
only to add simple variables like age+sex or age+sex+ age*sex but
|
| |
will never be general enough. But what is to remember, is that
|
| |
incidences or probability of change from one state to another is
|
| |
affected by the variables specified into the model.<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Also,
|
| |
the age range of the people interviewed has a link with the age
|
| |
range of the life expectancy which can be estimated by
|
| |
extrapolation. If your sample ranges from age 70 to 95, you can
|
| |
clearly estimate a life expectancy at age 70 and trust your
|
| |
confidence interval which is mostly based on your sample size,
|
| |
but if you want to estimate the life expectancy at age 50, you
|
| |
should rely in your model, but fitting a logistic model on a age
|
| |
range of 70-95 and estimating probabilities of transition out of
|
| |
this age range, say at age 50 is very dangerous. At least you
|
| |
should remember that the confidence interval given by the
|
| |
standard deviation of the health expectancies, are under the
|
| |
strong assumption that your model is the 'true model', which is
|
| |
probably not the case.<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Copy of the parameter file</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">: </span><a href="orbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">orbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
copy of the parameter file can be useful to re-run the program
|
| |
while saving the old output files. <o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Prevalence forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="frbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First,
|
| |
we have estimated the observed prevalence between 1/1/1984 and
|
| |
1/6/1988. <span style="mso-spacerun:
|
| |
yes"> </span>The mean date of interview (weighed average of
|
| |
the interviews performed between1/1/1984 and 1/6/1988) is
|
| |
estimated to be 13/9/1985, as written on the top on the file.
|
| |
Then we forecast the probability to be in each state. <o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Example,
|
| |
at date 1/1/1989 : <o:p></o:p></span></p>
|
| |
|
| |
<p class="MsoNormal"><span lang="DE" style="mso-ansi-language:DE"># StartingAge FinalAge P.1 P.2 P.3<o:p></o:p></span></p>
|
| |
|
| |
<p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></p>
|
| |
|
| |
<p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.807 0.078 0.115 <o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
|
| |
the minimum age is 70 on the 13/9/1985, the youngest forecasted
|
| |
age is 73. This means that at age a person aged 70 at 13/9/1989
|
| |
has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
|
| |
Similarly, the probability to be in state 2 is 0.078 and the
|
| |
probability to die is 0.115. Then, on the 1/1/1989, the
|
| |
prevalence of disability at age 73 is estimated to be 0.088.<o:p></o:p></span></p>
|
| |
|
| |
<h5
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
|
| |
Population forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="poprbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">poprbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><o:p></o:p></span></a></h5>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age P.1 P.2 P.3 [Population]<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">75 572685.22 83798.08 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">74 621296.51 79767.99 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 645857.70 69320.60 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1990<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="text-align:justify">76 442986.68 92721.14 120775.48</pre>
|
| |
|
| |
<pre style="text-align:justify">75 487781.02 91367.97 121915.51</pre>
|
| |
|
| |
<pre style="text-align:justify">74 512892.07 85003.47 117282.76 </pre>
|
| |
|
| |
<pre style="text-align:justify"> <o:p></o:p></pre>
|
| |
|
| |
<p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">From the population file, we estimate the
|
| |
number of people in each state. At age 73, 645857 persons are in
|
| |
state 1 and 69320 are in state 2. One year latter, 512892 are
|
| |
still in state 1, 85003 are in state 2 and 117282 died before
|
| |
1/1/1990.<o:p></o:p></span></p>
|
| |
|
| |
<pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<hr>
|
| |
|
| |
<h2
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
|
| |
name="example"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Trying an example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
|
| |
you know how to run the program, it is time to test it on your
|
| |
own computer. Try for example on a parameter file named </span><a
|
| |
href="..\mytry\imachpar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> which is a copy of </span><span lang="EN-GB" style="font-size:10.0pt;font-family:"Courier New";mso-ansi-language:EN-GB">mypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">
|
| |
included in the subdirectory of imach, </span><span lang="EN-GB" style="font-size:10.0pt;font-family:"Courier New";
|
| |
mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">. Edit it to change
|
| |
the name of the data file to </span><span lang="EN-GB" style="font-size:10.0pt;font-family:"Courier New";mso-ansi-language:
|
| |
EN-GB">..\data\mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> if you don't want
|
| |
to copy it on the same directory. The file </span><span lang="EN-GB" style="font-family:"Courier New";mso-ansi-language:EN-GB">mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> is a
|
| |
smaller file of 3,000 people but still with 4 waves. <o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Click
|
| |
on the imach.exe icon to open a window. Answer to the question: '<strong>Enter
|
| |
the parameter file name:'<o:p></o:p></span></strong></p>
|
| |
|
| |
<table border="1" cellpadding="0"
|
| |
style="mso-cellspacing:1.5pt;mso-padding-alt:
|
| |
0cm 0cm 0cm 0cm">
|
| |
<tr>
|
| |
<td width="100%"
|
| |
style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">IMACH,
|
| |
Version 0.7</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong><p style="text-align:justify"><strong><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">Enter
|
| |
the parameter file name: ..\mytry\imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
|
| |
</td>
|
| |
</tr>
|
| |
</table>
|
| |
|
| |
<p
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Most
|
| |
of the data files or image files generated, will use the
|
| |
'imachpar' string into their name. The running time is about 2-3
|
| |
minutes on a Pentium III. If the execution worked correctly, the
|
| |
outputs files are created in the current directory, and should be
|
| |
the same as the mypar files initially included in the directory </span><span lang="EN-GB" style="font-size:10.0pt;font-family:"Courier New";mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">.<o:p></o:p></span></p>
|
| |
|
| |
<pre
|
| |
style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l5 level1 lfo43"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt "Times New Roman""> </span></span><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output on the screen</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> The output screen looks like </span><a
|
| |
href="imachrun.LOG"><span lang="EN-GB" style="mso-ansi-language:EN-GB">this Log file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:126 line=126<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:2307 line=2307<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Delay (in months) between two waves Min=21 Max=51 Mean=24.495826<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="font-family:"Times New Roman";mso-ansi-language:EN-GB">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 <o:p></o:p></span></pre>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l6 level1 lfo46;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Maximisation
|
| |
with the Powell algorithm. 8 directions are given
|
| |
corresponding to the 8 parameters. This can be rather
|
| |
long to get convergence.<br>
|
| |
</span><span lang="EN-GB" style="font-size:7.5pt;font-family:"Courier New";
|
| |
mso-ansi-language:EN-GB"> <br>
|
| |
Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
|
| |
0.000000000000 3<br>
|
| |
0.000000000000 4 0.000000000000 5 0.000000000000 6
|
| |
0.000000000000 7 <br>
|
| |
0.000000000000 8 0.000000000000<br>
|
| |
1..........2.................3..........4.................5.........<br>
|
| |
6................7........8...............<br>
|
| |
Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
|
| |
<br>
|
| |
2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
|
| |
5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
|
| |
8 0.051272038506<br>
|
| |
1..............2...........3..............4...........<br>
|
| |
5..........6................7...........8.........<br>
|
| |
#Number of iterations = 23, -2 Log likelihood =
|
| |
6744.954042573691<br>
|
| |
# Parameters<br>
|
| |
12 -12.966061 0.135117 <br>
|
| |
13 -7.401109 0.067831 <br>
|
| |
21 -0.672648 -0.006627 <br>
|
| |
23 -5.051297 0.051271 </span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><o:p></o:p></span></li>
|
| |
</ul>
|
| |
|
| |
<pre
|
| |
style="margin-left:36.0pt;text-align:justify;text-indent:-18.0pt;
|
| |
mso-list:l6 level1 lfo46"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt "Times New Roman""> </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB">Calculation of the hessian matrix. Wait...<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Inverting the hessian to get the covariance matrix. </span>Wait...</pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"> <o:p></o:p></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify">#Hessian matrix#</pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"># Scales<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:
|
| |
justify"><span lang="DE" style="mso-ansi-language:DE">12 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE">13 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:
|
| |
18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE">21 1.00000e-003 1.00000e-005<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE">23 1.00000e-004 1.00000e-005<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:
|
| |
18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE"># Covariance<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>1 5.90661e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>2 -7.26732e-003 8.98810e-005<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>3 8.80177e-002 -1.12706e-003 5.15824e-001<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
|
| |
DE"><span style="mso-spacerun: yes"> </span>8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing prevalence limit: result on file 'plrmypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing pij: result on file 'pijrmypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Health Expectancies: result on file 'ermypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of DFLEs: file 'vrmypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Total LEs with variances: file 'trmypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' <o:p></o:p></span></pre>
|
| |
|
| |
<pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">End of Imach<o:p></o:p></span></pre>
|
| |
|
| |
<p
|
| |
style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
|
| |
the running is finished, the program requires a caracter:<o:p></o:p></span></p>
|
| |
|
| |
<table border="1" cellpadding="0"
|
| |
style="mso-cellspacing:1.5pt;mso-padding-alt:
|
| |
0cm 0cm 0cm 0cm">
|
| |
<tr>
|
| |
<td width="100%"
|
| |
style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Type
|
| |
e to edit output files, c to start again, and q for
|
| |
exiting:</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"><o:p></o:p></span></strong></td>
|
| |
</tr>
|
| |
</table>
|
| |
|
| |
<p
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
|
| |
you should enter <strong>e </strong>to edit the master file
|
| |
mypar.htm. <o:p></o:p></span></p>
|
| |
|
| |
<ul type="disc">
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Outputs
|
| |
files</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> <br>
|
| |
<br>
|
| |
- Observed prevalence in each state: </span><a
|
| |
href="..\mytry\prmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
- Estimated parameters and the covariance matrix: </span><a
|
| |
href="..\mytry\rmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
- Stationary prevalence in each state: </span><a
|
| |
href="..\mytry\plrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">plrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a> <br>
|
| |
- Transition probabilities: </span><a
|
| |
href="..\mytry\pijrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pijrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
- Copy of the parameter file: </span><a
|
| |
href="..\mytry\ormypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ormypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
- Life expectancies by age and initial health status: </span><a
|
| |
href="..\mytry\ermypar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">ermypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a> <br>
|
| |
- Variances of life expectancies by age and initial
|
| |
health status: </span><a href="..\mytry\vrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">vrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a>
|
| |
<br>
|
| |
- Health expectancies with their variances: </span><a
|
| |
href="..\mytry\trmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">trmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a> <br>
|
| |
- Standard deviation of stationary prevalence: </span><a
|
| |
href="..\mytry\vplrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">vplrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a><br>
|
| |
- Prevalences forecasting: </span><a href="frmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
|
| |
<br>
|
| |
- Population forecasting (if popforecast=1): </span><a
|
| |
href="poprmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">poprmypar.txt</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| |
<li class="MsoNormal"
|
| |
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
|
| |
mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Graphs</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u>
|
| |
<br>
|
| |
<br>
|
| |
-</span><a href="..\mytry\pemypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">One-step transition
|
| |
probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
|
| |
-</span><a href="..\mytry\pmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">Convergence to the
|
| |
stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
|
| |
-</span><a href="..\mytry\vmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">Observed and stationary
|
| |
prevalence in state (1) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
-</span><a href="..\mytry\vmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">Observed and stationary
|
| |
prevalence in state (2) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
|
| |
-</span><a href="..\mytry\expmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
|
| |
expectancies by age and initial health state (1)</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a> <br>
|
| |
-</span><a href="..\mytry\expmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
|
| |
expectancies by age and initial health state (2)</span><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB"></a> <br>
|
| |
-</span><a href="..\mytry\emypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
|
| |
EN-GB">Total life expectancy by
|
| |
age and health expectancies in states (1) and (2).</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
|
| |
</ul>
|
| |
|
| |
<p
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
|
| |
software have been partly granted by </span><a
|
| |
href="http://euroreves.ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Euro-REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, a concerted
|
| |
action from the European Union. It will be copyrighted
|
| |
identically to a GNU software product, i.e. program and software
|
| |
can be distributed freely for non commercial use. Sources are not
|
| |
widely distributed today. You can get them by asking us with a
|
| |
simple justification (name, email, institute) </span><a
|
| |
href="mailto:brouard@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:brouard@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and </span><a
|
| |
href="mailto:lievre@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:lievre@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> .<o:p></o:p></span></p>
|
| |
|
| |
<p
|
| |
style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Latest
|
| |
version (0.7 of February 2002) can be accessed at </span><a
|
| |
href="http://euroreves.ined.fr/imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">http://euroreves.ined.fr/imach</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></p>
|
| |
</body>
|
| |
</html>
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