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| <h1 align="center"><font color="#00006A">Computing Health |
content="text/html; charset=iso-8859-1">
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| Expectancies using IMaCh</font></h1> |
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<title></title>
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| <h1 align="center"><font color="#00006A" size="5">(a Maximum |
</head>
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| Likelihood Computer Program using Interpolation of Markov Chains)</font></h1> |
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<body bgcolor="#FFFFFF">
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| <p align="center"> </p> |
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<hr size="3" color="#EC5E5E">
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| <p align="center"><a href="http://www.ined.fr/"><img |
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| src="logo-ined.gif" border="0" width="151" height="76"></a><img |
<h1 align="center"><font color="#00006A">Computing Health
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| src="euroreves2.gif" width="151" height="75"></p> |
Expectancies using IMaCh</font></h1>
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| |
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| <h3 align="center"><a href="http://www.ined.fr/"><font |
<h1 align="center"><font color="#00006A" size="5">(a Maximum
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| color="#00006A">INED</font></a><font color="#00006A"> and </font><a |
Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
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| href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3> |
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<p align="center"> </p>
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| <p align="center"><font color="#00006A" size="4"><strong>March |
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| 2000</strong></font></p> |
<p align="center"><a href="http://www.ined.fr/"><img
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| |
src="logo-ined.gif" border="0" width="151" height="76"></a><img
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| <hr size="3" color="#EC5E5E"> |
src="euroreves2.gif" width="151" height="75"></p>
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| |
|
| <p align="center"><font color="#00006A"><strong>Authors of the |
<h3 align="center"><a href="http://www.ined.fr/"><font
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| program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font |
color="#00006A">INED</font></a><font color="#00006A"> and </font><a
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| color="#00006A"><strong>Nicolas Brouard</strong></font></a><font |
href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
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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 |
<p align="center"><font color="#00006A" size="4"><strong>Version
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| National d'Etudes Démographiques</strong></font></a><font |
0.8, March 2002</strong></font></p>
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| color="#00006A"><strong> (INED, Paris) in the "Mortality, |
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| Health and Epidemiology" Research Unit </strong></font></p> |
<hr size="3" color="#EC5E5E">
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| |
|
| <p align="center"><font color="#00006A"><strong>and Agnès |
<p align="center"><font color="#00006A"><strong>Authors of the
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| Lièvre<br clear="left"> |
program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
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| </strong></font></p> |
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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| <h4><font color="#00006A">Contribution to the mathematics: C. R. |
href="http://www.ined.fr"><font color="#00006A"><strong>Institut
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| Heathcote </font><font color="#00006A" size="2">(Australian |
National d'Etudes Démographiques</strong></font></a><font
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| National University, Canberra).</font></h4> |
color="#00006A"><strong> (INED, Paris) in the "Mortality,
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| |
Health and Epidemiology" Research Unit </strong></font></p>
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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 |
<p align="center"><font color="#00006A"><strong>and Agnès
|
| color="#00006A">) </font></h4> |
Lièvre<br clear="left">
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| |
</strong></font></p>
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| <hr> |
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| |
<h4><font color="#00006A">Contribution to the mathematics: C. R.
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| <ul> |
Heathcote </font><font color="#00006A" size="2">(Australian
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| <li><a href="#intro">Introduction</a> </li> |
National University, Canberra).</font></h4>
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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> |
<h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
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| <li><a href="#data">On what kind of data can it be used?</a></li> |
href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
|
| <li><a href="#datafile">The data file</a> </li> |
color="#00006A">) </font></h4>
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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> |
<hr>
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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> |
<ul>
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| </ul> |
<li><a href="#intro">Introduction</a> </li>
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| |
<li><a href="#data">On what kind of data can it be used?</a></li>
|
| <hr> |
<li><a href="#datafile">The data file</a> </li>
|
| |
<li><a href="#biaspar">The parameter file</a> </li>
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| <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2> |
<li><a href="#running">Running Imach</a> </li>
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| |
<li><a href="#output">Output files and graphs</a> </li>
|
| <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal |
<li><a href="#example">Exemple</a> </li>
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| data</b>. Within the family of Health Expectancies (HE), |
</ul>
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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 |
<hr>
|
| 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 |
<h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
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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 |
<p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
|
| href="http://euroreves/reves">REVES</a> network on Health |
data</b> using the methodology pioneered by Laditka and Wolf (1).
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| expectancy, and most HE indices based on these data, are <em>cross-sectional</em>. |
Within the family of Health Expectancies (HE), Disability-free
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| It means that the information collected comes from a single |
life expectancy (DFLE) is probably the most important index to
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| cross-sectional survey: people from various ages (but mostly old |
monitor. In low mortality countries, there is a fear that when
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| people) are surveyed on their health status at a single date. |
mortality declines, the increase in DFLE is not proportionate to
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| Proportion of people disabled at each age, can then be measured |
the increase in total Life expectancy. This case is called the <em>Expansion
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| at that date. This age-specific prevalence curve is then used to |
of morbidity</em>. Most of the data collected today, in
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| distinguish, within the stationary population (which, by |
particular by the international <a href="http://www.reves.org">REVES</a>
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| definition, is the life table estimated from the vital statistics |
network on Health expectancy, and most HE indices based on these
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| on mortality at the same date), the disable population from the |
data, are <em>cross-sectional</em>. It means that the information
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| disability-free population. Life expectancy (LE) (or total |
collected comes from a single cross-sectional survey: people from
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| population divided by the yearly number of births or deaths of |
various ages (but mostly old people) are surveyed on their health
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| this stationary population) is then decomposed into DFLE and DLE. |
status at a single date. Proportion of people disabled at each
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| This method of computing HE is usually called the Sullivan method |
age, can then be measured at that date. This age-specific
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| (from the name of the author who first described it).</p> |
prevalence curve is then used to distinguish, within the
|
| |
stationary population (which, by definition, is the life table
|
| <p>Age-specific proportions of people disable are very difficult |
estimated from the vital statistics on mortality at the same
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| to forecast because each proportion corresponds to historical |
date), the disable population from the disability-free
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| conditions of the cohort and it is the result of the historical |
population. Life expectancy (LE) (or total population divided by
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| flows from entering disability and recovering in the past until |
the yearly number of births or deaths of this stationary
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| today. The age-specific intensities (or incidence rates) of |
population) is then decomposed into DFLE and DLE. This method of
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| entering disability or recovering a good health, are reflecting |
computing HE is usually called the Sullivan method (from the name
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| actual conditions and therefore can be used at each age to |
of the author who first described it).</p>
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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 |
<p>Age-specific proportions of people disable are very difficult
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| recovering the ability to walk will be higher at each (old) age, |
to forecast because each proportion corresponds to historical
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| but the prevalence of disability will only slightly reflect an |
conditions of the cohort and it is the result of the historical
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| improve because the prevalence is mostly affected by the history |
flows from entering disability and recovering in the past until
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| of the cohort and not by recent period effects. To measure the |
today. The age-specific intensities (or incidence rates) of
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| period improvement we have to simulate the future of a cohort of |
entering disability or recovering a good health, are reflecting
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| new-borns entering or leaving at each age the disability state or |
actual conditions and therefore can be used at each age to
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| dying according to the incidence rates measured today on |
forecast the future of this cohort. For example if a country is
|
| different cohorts. The proportion of people disabled at each age |
improving its technology of prosthesis, the incidence of
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| in this simulated cohort will be much lower (using the exemple of |
recovering the ability to walk will be higher at each (old) age,
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| an improvement) that the proportions observed at each age in a |
but the prevalence of disability will only slightly reflect an
|
| cross-sectional survey. This new prevalence curve introduced in a |
improve because the prevalence is mostly affected by the history
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| life table will give a much more actual and realistic HE level |
of the cohort and not by recent period effects. To measure the
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| than the Sullivan method which mostly measured the History of |
period improvement we have to simulate the future of a cohort of
|
| health conditions in this country.</p> |
new-borns entering or leaving at each age the disability state or
|
| |
dying according to the incidence rates measured today on
|
| <p>Therefore, the main question is how to measure incidence rates |
different cohorts. The proportion of people disabled at each age
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| from cross-longitudinal surveys? This is the goal of the IMaCH |
in this simulated cohort will be much lower (using the exemple of
|
| program. From your data and using IMaCH you can estimate period |
an improvement) that the proportions observed at each age in a
|
| HE and not only Sullivan's HE. Also the standard errors of the HE |
cross-sectional survey. This new prevalence curve introduced in a
|
| are computed.</p> |
life table will give a much more actual and realistic HE level
|
| |
than the Sullivan method which mostly measured the History of
|
| <p>A cross-longitudinal survey consists in a first survey |
health conditions in this country.</p>
|
| ("cross") where individuals from different ages are |
|
| interviewed on their health status or degree of disability. At |
<p>Therefore, the main question is how to measure incidence rates
|
| least a second wave of interviews ("longitudinal") |
from cross-longitudinal surveys? This is the goal of the IMaCH
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| should measure each new individual health status. Health |
program. From your data and using IMaCH you can estimate period
|
| expectancies are computed from the transitions observed between |
HE and not only Sullivan's HE. Also the standard errors of the HE
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| waves and are computed for each degree of severity of disability |
are computed.</p>
|
| (number of life states). More degrees you consider, more time is |
|
| necessary to reach the Maximum Likelihood of the parameters |
<p>A cross-longitudinal survey consists in a first survey
|
| involved in the model. Considering only two states of disability |
("cross") where individuals from different ages are
|
| (disable and healthy) is generally enough but the computer |
interviewed on their health status or degree of disability. At
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| program works also with more health statuses.<br> |
least a second wave of interviews ("longitudinal")
|
| <br> |
should measure each new individual health status. Health
|
| The simplest model is the multinomial logistic model where <i>pij</i> |
expectancies are computed from the transitions observed between
|
| is the probability to be observed in state <i>j</i> at the second |
waves and are computed for each degree of severity of disability
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| wave conditional to be observed in state <em>i</em> at the first |
(number of life states). More degrees you consider, more time is
|
| wave. Therefore a simple model is: log<em>(pij/pii)= aij + |
necessary to reach the Maximum Likelihood of the parameters
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| bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>' |
involved in the model. Considering only two states of disability
|
| is a covariate. The advantage that this computer program claims, |
(disable and healthy) is generally enough but the computer
|
| comes from that if the delay between waves is not identical for |
program works also with more health statuses.<br>
|
| each individual, or if some individual missed an interview, the |
<br>
|
| information is not rounded or lost, but taken into account using |
The simplest model is the multinomial logistic model where <i>pij</i>
|
| an interpolation or extrapolation. <i>hPijx</i> is the |
is the probability to be observed in state <i>j</i> at the second
|
| probability to be observed in state <i>i</i> at age <i>x+h</i> |
wave conditional to be observed in state <em>i</em> at the first
|
| conditional to the observed state <i>i</i> at age <i>x</i>. The |
wave. Therefore a simple model is: log<em>(pij/pii)= aij +
|
| delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>) |
bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
|
| of unobserved intermediate states. This elementary transition (by |
is a covariate. The advantage that this computer program claims,
|
| month or quarter trimester, semester or year) is modeled as a |
comes from that if the delay between waves is not identical for
|
| multinomial logistic. The <i>hPx</i> matrix is simply the matrix |
each individual, or if some individual missed an interview, the
|
| product of <i>nh*stepm</i> elementary matrices and the |
information is not rounded or lost, but taken into account using
|
| contribution of each individual to the likelihood is simply <i>hPijx</i>. |
an interpolation or extrapolation. <i>hPijx</i> is the
|
| <br> |
probability to be observed in state <i>i</i> at age <i>x+h</i>
|
| </p> |
conditional to the observed state <i>i</i> at age <i>x</i>. The
|
| |
delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
|
| <p>The program presented in this manual is a quite general |
of unobserved intermediate states. This elementary transition (by
|
| program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated |
month or quarter trimester, semester or year) is modeled as a
|
| <strong>MA</strong>rkov <strong>CH</strong>ain), designed to |
multinomial logistic. The <i>hPx</i> matrix is simply the matrix
|
| analyse transition data from longitudinal surveys. The first step |
product of <i>nh*stepm</i> elementary matrices and the
|
| is the parameters estimation of a transition probabilities model |
contribution of each individual to the likelihood is simply <i>hPijx</i>.
|
| between an initial status and a final status. From there, the |
<br>
|
| computer program produces some indicators such as observed and |
</p>
|
| stationary prevalence, life expectancies and their variances and |
|
| graphs. Our transition model consists in absorbing and |
<p>The program presented in this manual is a quite general
|
| non-absorbing states with the possibility of return across the |
program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
|
| non-absorbing states. The main advantage of this package, |
<strong>MA</strong>rkov <strong>CH</strong>ain), designed to
|
| compared to other programs for the analysis of transition data |
analyse transition data from longitudinal surveys. The first step
|
| (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole |
is the parameters estimation of a transition probabilities model
|
| individual information is used even if an interview is missing, a |
between an initial status and a final status. From there, the
|
| status or a date is unknown or when the delay between waves is |
computer program produces some indicators such as observed and
|
| not identical for each individual. The program can be executed |
stationary prevalence, life expectancies and their variances and
|
| according to parameters: selection of a sub-sample, number of |
graphs. Our transition model consists in absorbing and
|
| absorbing and non-absorbing states, number of waves taken in |
non-absorbing states with the possibility of return across the
|
| account (the user inputs the first and the last interview), a |
non-absorbing states. The main advantage of this package,
|
| tolerance level for the maximization function, the periodicity of |
compared to other programs for the analysis of transition data
|
| the transitions (we can compute annual, quaterly or monthly |
(For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
|
| transitions), covariates in the model. It works on Windows or on |
individual information is used even if an interview is missing, a
|
| Unix.<br> |
status or a date is unknown or when the delay between waves is
|
| </p> |
not identical for each individual. The program can be executed
|
| |
according to parameters: selection of a sub-sample, number of
|
| <hr> |
absorbing and non-absorbing states, number of waves taken in
|
| |
account (the user inputs the first and the last interview), a
|
| <h2><a name="data"><font color="#00006A">On what kind of data can |
tolerance level for the maximization function, the periodicity of
|
| it be used?</font></a></h2> |
the transitions (we can compute annual, quarterly or monthly
|
| |
transitions), covariates in the model. It works on Windows or on
|
| <p>The minimum data required for a transition model is the |
Unix.<br>
|
| recording of a set of individuals interviewed at a first date and |
</p>
|
| interviewed again at least one another time. From the |
|
| observations of an individual, we obtain a follow-up over time of |
<hr>
|
| the occurrence of a specific event. In this documentation, the |
|
| event is related to health status at older ages, but the program |
<p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
|
| can be applied on a lot of longitudinal studies in different |
Methods for Analyzing Active Life Expectancy". <i>Journal of
|
| contexts. To build the data file explained into the next section, |
Aging and Health</i>. Vol 10, No. 2. </p>
|
| you must have the month and year of each interview and the |
|
| corresponding health status. But in order to get age, date of |
<hr>
|
| birth (month and year) is required (missing values is allowed for |
|
| month). Date of death (month and year) is an important |
<h2><a name="data"><font color="#00006A">On what kind of data can
|
| information also required if the individual is dead. Shorter |
it be used?</font></a></h2>
|
| steps (i.e. a month) will more closely take into account the |
|
| survival time after the last interview.</p> |
<p>The minimum data required for a transition model is the
|
| |
recording of a set of individuals interviewed at a first date and
|
| <hr> |
interviewed again at least one another time. From the
|
| |
observations of an individual, we obtain a follow-up over time of
|
| <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2> |
the occurrence of a specific event. In this documentation, the
|
| |
event is related to health status at older ages, but the program
|
| <p>In this example, 8,000 people have been interviewed in a |
can be applied on a lot of longitudinal studies in different
|
| cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). |
contexts. To build the data file explained into the next section,
|
| Some people missed 1, 2 or 3 interviews. Health statuses are |
you must have the month and year of each interview and the
|
| healthy (1) and disable (2). The survey is not a real one. It is |
corresponding health status. But in order to get age, date of
|
| a simulation of the American Longitudinal Survey on Aging. The |
birth (month and year) is required (missing values is allowed for
|
| disability state is defined if the individual missed one of four |
month). Date of death (month and year) is an important
|
| ADL (Activity of daily living, like bathing, eating, walking). |
information also required if the individual is dead. Shorter
|
| Therefore, even is the individuals interviewed in the sample are |
steps (i.e. a month) will more closely take into account the
|
| virtual, the information brought with this sample is close to the |
survival time after the last interview.</p>
|
| situation of the United States. Sex is not recorded is this |
|
| sample.</p> |
<hr>
|
| |
|
| <p>Each line of the data set (named <a href="data1.txt">data1.txt</a> |
<h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
|
| in this first example) is an individual record which fields are: </p> |
|
| |
<p>In this example, 8,000 people have been interviewed in a
|
| <ul> |
cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
|
| <li><b>Index number</b>: positive number (field 1) </li> |
Some people missed 1, 2 or 3 interviews. Health statuses are
|
| <li><b>First covariate</b> positive number (field 2) </li> |
healthy (1) and disable (2). The survey is not a real one. It is
|
| <li><b>Second covariate</b> positive number (field 3) </li> |
a simulation of the American Longitudinal Survey on Aging. The
|
| <li><a name="Weight"><b>Weight</b></a>: positive number |
disability state is defined if the individual missed one of four
|
| (field 4) . In most surveys individuals are weighted |
ADL (Activity of daily living, like bathing, eating, walking).
|
| according to the stratification of the sample.</li> |
Therefore, even is the individuals interviewed in the sample are
|
| <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are |
virtual, the information brought with this sample is close to the
|
| coded as 99/9999 (field 5) </li> |
situation of the United States. Sex is not recorded is this
|
| <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are |
sample.</p>
|
| coded as 99/9999 (field 6) </li> |
|
| <li><b>Date of first interview</b>: coded as mm/yyyy. Missing |
<p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
|
| dates are coded as 99/9999 (field 7) </li> |
in this first example) is an individual record which fields are: </p>
|
| <li><b>Status at first interview</b>: positive number. |
|
| Missing values ar coded -1. (field 8) </li> |
<ul>
|
| <li><b>Date of second interview</b>: coded as mm/yyyy. |
<li><b>Index number</b>: positive number (field 1) </li>
|
| Missing dates are coded as 99/9999 (field 9) </li> |
<li><b>First covariate</b> positive number (field 2) </li>
|
| <li><strong>Status at second interview</strong> positive |
<li><b>Second covariate</b> positive number (field 3) </li>
|
| number. Missing values ar coded -1. (field 10) </li> |
<li><a name="Weight"><b>Weight</b></a>: positive number
|
| <li><b>Date of third interview</b>: coded as mm/yyyy. Missing |
(field 4) . In most surveys individuals are weighted
|
| dates are coded as 99/9999 (field 11) </li> |
according to the stratification of the sample.</li>
|
| <li><strong>Status at third interview</strong> positive |
<li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
|
| number. Missing values ar coded -1. (field 12) </li> |
coded as 99/9999 (field 5) </li>
|
| <li><b>Date of fourth interview</b>: coded as mm/yyyy. |
<li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
|
| Missing dates are coded as 99/9999 (field 13) </li> |
coded as 99/9999 (field 6) </li>
|
| <li><strong>Status at fourth interview</strong> positive |
<li><b>Date of first interview</b>: coded as mm/yyyy. Missing
|
| number. Missing values are coded -1. (field 14) </li> |
dates are coded as 99/9999 (field 7) </li>
|
| <li>etc</li> |
<li><b>Status at first interview</b>: positive number.
|
| </ul> |
Missing values ar coded -1. (field 8) </li>
|
| |
<li><b>Date of second interview</b>: coded as mm/yyyy.
|
| <p> </p> |
Missing dates are coded as 99/9999 (field 9) </li>
|
| |
<li><strong>Status at second interview</strong> positive
|
| <p>If your longitudinal survey do not include information about |
number. Missing values ar coded -1. (field 10) </li>
|
| weights or covariates, you must fill the column with a number |
<li><b>Date of third interview</b>: coded as mm/yyyy. Missing
|
| (e.g. 1) because a missing field is not allowed.</p> |
dates are coded as 99/9999 (field 11) </li>
|
| |
<li><strong>Status at third interview</strong> positive
|
| <hr> |
number. Missing values ar coded -1. (field 12) </li>
|
| |
<li><b>Date of fourth interview</b>: coded as mm/yyyy.
|
| <h2><font color="#00006A">Your first example parameter file</font><a |
Missing dates are coded as 99/9999 (field 13) </li>
|
| href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> |
<li><strong>Status at fourth interview</strong> positive
|
| |
number. Missing values are coded -1. (field 14) </li>
|
| <h2><a name="biaspar"></a>#Imach version 0.63, February 2000, |
<li>etc</li>
|
| INED-EUROREVES </h2> |
</ul>
|
| |
|
| <p>This is a comment. Comments start with a '#'.</p> |
<p> </p>
|
| |
|
| <h4><font color="#FF0000">First uncommented line</font></h4> |
<p>If your longitudinal survey do not include information about
|
| |
weights or covariates, you must fill the column with a number
|
| <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> |
(e.g. 1) because a missing field is not allowed.</p>
|
| |
|
| <ul> |
<hr>
|
| <li><b>title=</b> 1st_example is title of the run. </li> |
|
| <li><b>datafile=</b>data1.txt is the name of the data set. |
<h2><font color="#00006A">Your first example parameter file</font><a
|
| Our example is a six years follow-up survey. It consists |
href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
|
| in a baseline followed by 3 reinterviews. </li> |
|
| <li><b>lastobs=</b> 8600 the program is able to run on a |
<h2><a name="biaspar"></a>#Imach version 0.8, March 2002,
|
| subsample where the last observation number is lastobs. |
INED-EUROREVES </h2>
|
| It can be set a bigger number than the real number of |
|
| observations (e.g. 100000). In this example, maximisation |
<p>This is a comment. Comments start with a '#'.</p>
|
| will be done on the 8600 first records. </li> |
|
| <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more |
<h4><font color="#FF0000">First uncommented line</font></h4>
|
| than two interviews in the survey, the program can be run |
|
| on selected transitions periods. firstpass=1 means the |
<pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
|
| first interview included in the calculation is the |
|
| baseline survey. lastpass=4 means that the information |
<ul>
|
| brought by the 4th interview is taken into account.</li> |
<li><b>title=</b> 1st_example is title of the run. </li>
|
| </ul> |
<li><b>datafile=</b>data1.txt is the name of the data set.
|
| |
Our example is a six years follow-up survey. It consists
|
| <p> </p> |
in a baseline followed by 3 reinterviews. </li>
|
| |
<li><b>lastobs=</b> 8600 the program is able to run on a
|
| <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented |
subsample where the last observation number is lastobs.
|
| line</font></a></h4> |
It can be set a bigger number than the real number of
|
| |
observations (e.g. 100000). In this example, maximisation
|
| <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
will be done on the 8600 first records. </li>
|
| |
<li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
|
| <ul> |
than two interviews in the survey, the program can be run
|
| <li><b>ftol=1e-8</b> Convergence tolerance on the function |
on selected transitions periods. firstpass=1 means the
|
| value in the maximisation of the likelihood. Choosing a |
first interview included in the calculation is the
|
| correct value for ftol is difficult. 1e-8 is a correct |
baseline survey. lastpass=4 means that the information
|
| value for a 32 bits computer.</li> |
brought by the 4th interview is taken into account.</li>
|
| <li><b>stepm=1</b> Time unit in months for interpolation. |
</ul>
|
| Examples:<ul> |
|
| <li>If stepm=1, the unit is a month </li> |
<p> </p>
|
| <li>If stepm=4, the unit is a trimester</li> |
|
| <li>If stepm=12, the unit is a year </li> |
<h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
|
| <li>If stepm=24, the unit is two years</li> |
line</font></a></h4>
|
| <li>... </li> |
|
| </ul> |
<pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
| </li> |
|
| <li><b>ncov=2</b> Number of covariates to be add to the |
<ul>
|
| model. The intercept and the age parameter are counting |
<li><b>ftol=1e-8</b> Convergence tolerance on the function
|
| for 2 covariates. For example, if you want to add gender |
value in the maximisation of the likelihood. Choosing a
|
| in the covariate vector you must write ncov=3 else |
correct value for ftol is difficult. 1e-8 is a correct
|
| ncov=2. </li> |
value for a 32 bits computer.</li>
|
| <li><b>nlstate=2</b> Number of non-absorbing (live) states. |
<li><b>stepm=1</b> Time unit in months for interpolation.
|
| Here we have two alive states: disability-free is coded 1 |
Examples:<ul>
|
| and disability is coded 2. </li> |
<li>If stepm=1, the unit is a month </li>
|
| <li><b>ndeath=1</b> Number of absorbing states. The absorbing |
<li>If stepm=4, the unit is a trimester</li>
|
| state death is coded 3. </li> |
<li>If stepm=12, the unit is a year </li>
|
| <li><b>maxwav=4</b> Maximum number of waves. The program can |
<li>If stepm=24, the unit is two years</li>
|
| not include more than 4 interviews. </li> |
<li>... </li>
|
| <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the |
</ul>
|
| Maximisation Likelihood Estimation. <ul> |
</li>
|
| <li>If mle=1 the program does the maximisation and |
<li><b>ncovcol=2</b> Number of covariate columns in the datafile
|
| the calculation of heath expectancies </li> |
which precede the date of birth. Here you can put variables that
|
| <li>If mle=0 the program only does the calculation of |
won't necessary be used during the run. It is not the number of
|
| the health expectancies. </li> |
covariates that will be specified by the model. The 'model'
|
| </ul> |
syntax describe the covariates to take into account. </li>
|
| </li> |
<li><b>nlstate=2</b> Number of non-absorbing (alive) states.
|
| <li><b>weight=0</b> Possibility to add weights. <ul> |
Here we have two alive states: disability-free is coded 1
|
| <li>If weight=0 no weights are included </li> |
and disability is coded 2. </li>
|
| <li>If weight=1 the maximisation integrates the |
<li><b>ndeath=1</b> Number of absorbing states. The absorbing
|
| weights which are in field <a href="#Weight">4</a></li> |
state death is coded 3. </li>
|
| </ul> |
<li><b>maxwav=4</b> Number of waves in the datafile.</li>
|
| </li> |
<li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
|
| </ul> |
Maximisation Likelihood Estimation. <ul>
|
| |
<li>If mle=1 the program does the maximisation and
|
| <h4><font color="#FF0000">Guess values for optimization</font><font |
the calculation of health expectancies </li>
|
| color="#00006A"> </font></h4> |
<li>If mle=0 the program only does the calculation of
|
| |
the health expectancies. </li>
|
| <p>You must write the initial guess values of the parameters for |
</ul>
|
| optimization. The number of parameters, <em>N</em> depends on the |
</li>
|
| number of absorbing states and non-absorbing states and on the |
<li><b>weight=0</b> Possibility to add weights. <ul>
|
| number of covariates. <br> |
<li>If weight=0 no weights are included </li>
|
| <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> + |
<li>If weight=1 the maximisation integrates the
|
| <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br> |
weights which are in field <a href="#Weight">4</a></li>
|
| <br> |
</ul>
|
| Thus in the simple case with 2 covariates (the model is log |
</li>
|
| (pij/pii) = aij + bij * age where intercept and age are the two |
</ul>
|
| covariates), and 2 health degrees (1 for disability-free and 2 |
|
| for disability) and 1 absorbing state (3), you must enter 8 |
<h4><font color="#FF0000">Covariates</font></h4>
|
| initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can |
|
| start with zeros as in this example, but if you have a more |
<p>Intercept and age are systematically included in the model.
|
| precise set (for example from an earlier run) you can enter it |
Additional covariates can be included with the command: </p>
|
| and it will speed up them<br> |
|
| Each of the four lines starts with indices "ij": <br> |
<pre>model=<em>list of covariates</em></pre>
|
| <br> |
|
| <b>ij aij bij</b> </p> |
<ul>
|
| |
<li>if<strong> model=. </strong>then no covariates are
|
| <blockquote> |
included</li>
|
| <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age |
<li>if <strong>model=V1</strong> the model includes the first
|
| 12 -14.155633 0.110794 |
covariate (field 2)</li>
|
| 13 -7.925360 0.032091 |
<li>if <strong>model=V2 </strong>the model includes the
|
| 21 -1.890135 -0.029473 |
second covariate (field 3)</li>
|
| 23 -6.234642 0.022315 </pre> |
<li>if <strong>model=V1+V2 </strong>the model includes the
|
| </blockquote> |
first and the second covariate (fields 2 and 3)</li>
|
| |
<li>if <strong>model=V1*V2 </strong>the model includes the
|
| <p>or, to simplify: </p> |
product of the first and the second covariate (fields 2
|
| |
and 3)</li>
|
| <blockquote> |
<li>if <strong>model=V1+V1*age</strong> the model includes
|
| <pre>12 0.0 0.0 |
the product covariate*age</li>
|
| 13 0.0 0.0 |
</ul>
|
| 21 0.0 0.0 |
|
| 23 0.0 0.0</pre> |
<p>In this example, we have two covariates in the data file
|
| </blockquote> |
(fields 2 and 3). The number of covariates included in the data file
|
| |
between the id and the date of birth is ncovcol=2 (it was named ncov
|
| <h4><font color="#FF0000">Guess values for computing variances</font></h4> |
in version prior to 0.8). If you have 3 covariates in the datafile
|
| |
(fields 2, 3 and 4), you will set ncovcol=3. Then you can run the
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
programme with a new parametrisation taking into account the
|
| used as an input to get the vairous output data files (Health |
third covariate. For example, <strong>model=V1+V3 </strong>estimates
|
| expectancies, stationary prevalence etc.) and figures without |
a model with the first and third covariates. More complicated
|
| rerunning the rather long maximisation phase (mle=0). </p> |
models can be used, but it will takes more time to converge. With
|
| |
a simple model (no covariates), the programme estimates 8
|
| <p>The scales are small values for the evaluation of numerical |
parameters. Adding covariates increases the number of parameters
|
| derivatives. These derivatives are used to compute the hessian |
: 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
|
| matrix of the parameters, that is the inverse of the covariance |
</strong>and 20 for <strong>model=V1+V2+V3.</strong></p>
|
| matrix, and the variances of health expectancies. Each line |
|
| consists in indices "ij" followed by the initial scales |
<h4><font color="#FF0000">Guess values for optimization</font><font
|
| (zero to simplify) associated with aij and bij. </p> |
color="#00006A"> </font></h4>
|
| |
|
| <ul> |
<p>You must write the initial guess values of the parameters for
|
| <li>If mle=1 you can enter zeros:</li> |
optimization. The number of parameters, <em>N</em> depends on the
|
| </ul> |
number of absorbing states and non-absorbing states and on the
|
| |
number of covariates. <br>
|
| <blockquote> |
<em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
|
| <pre># Scales (for hessian or gradient estimation) |
<em>ndeath</em>-1)*<em>nlstate</em>*<em>ncovmodel</em> . <br>
|
| 12 0. 0. |
<br>
|
| 13 0. 0. |
Thus in the simple case with 2 covariates (the model is log
|
| 21 0. 0. |
(pij/pii) = aij + bij * age where intercept and age are the two
|
| 23 0. 0. </pre> |
covariates), and 2 health degrees (1 for disability-free and 2
|
| </blockquote> |
for disability) and 1 absorbing state (3), you must enter 8
|
| |
initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
|
| <ul> |
start with zeros as in this example, but if you have a more
|
| <li>If mle=0 you must enter a covariance matrix (usually |
precise set (for example from an earlier run) you can enter it
|
| obtained from an earlier run).</li> |
and it will speed up them<br>
|
| </ul> |
Each of the four lines starts with indices "ij": <b>ij
|
| |
aij bij</b> </p>
|
| <h4><font color="#FF0000">Covariance matrix of parameters</font></h4> |
|
| |
<blockquote>
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
<pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
|
| used as an input to get the vairous output data files (Health |
12 -14.155633 0.110794
|
| expectancies, stationary prevalence etc.) and figures without |
13 -7.925360 0.032091
|
| rerunning the rather long maximisation phase (mle=0). </p> |
21 -1.890135 -0.029473
|
| |
23 -6.234642 0.022315 </pre>
|
| <p>Each line starts with indices "ijk" followed by the |
</blockquote>
|
| covariances between aij and bij: </p> |
|
| |
<p>or, to simplify (in most of cases it converges but there is no
|
| <pre> |
warranty!): </p>
|
| 121 Var(a12) |
|
| 122 Cov(b12,a12) Var(b12) |
<blockquote>
|
| ... |
<pre>12 0.0 0.0
|
| 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> |
13 0.0 0.0
|
| |
21 0.0 0.0
|
| <ul> |
23 0.0 0.0</pre>
|
| <li>If mle=1 you can enter zeros. </li> |
</blockquote>
|
| </ul> |
|
| |
<p> In order to speed up the convergence you can make a first run with
|
| <blockquote> |
a large stepm i.e stepm=12 or 24 and then decrease the stepm until
|
| <pre># Covariance matrix |
stepm=1 month. If newstepm is the new shorter stepm and stepm can be
|
| 121 0. |
expressed as a multiple of newstepm, like newstepm=n stepm, then the
|
| 122 0. 0. |
following approximation holds:
|
| 131 0. 0. 0. |
<pre>aij(stepm) = aij(n . stepm) - ln(n)
|
| 132 0. 0. 0. 0. |
</pre> and
|
| 211 0. 0. 0. 0. 0. |
<pre>bij(stepm) = bij(n . stepm) .</pre>
|
| 212 0. 0. 0. 0. 0. 0. |
|
| 231 0. 0. 0. 0. 0. 0. 0. |
<p> For example if you already ran for a 6 months interval and
|
| 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> |
got:<br>
|
| </blockquote> |
<pre># Parameters
|
| |
12 -13.390179 0.126133
|
| <ul> |
13 -7.493460 0.048069
|
| <li>If mle=0 you must enter a covariance matrix (usually |
21 0.575975 -0.041322
|
| obtained from an earlier run).<br> |
23 -4.748678 0.030626
|
| </li> |
</pre>
|
| </ul> |
If you now want to get the monthly estimates, you can guess the aij by
|
| |
substracting ln(6)= 1,7917<br> and running<br>
|
| <h4><a name="biaspar-l"></a><font color="#FF0000">last |
<pre>12 -15.18193847 0.126133
|
| uncommented line</font></h4> |
13 -9.285219469 0.048069
|
| |
21 -1.215784469 -0.041322
|
| <pre>agemin=70 agemax=100 bage=50 fage=100</pre> |
23 -6.540437469 0.030626
|
| |
</pre>
|
| <p>Once we obtained the estimated parameters, the program is able |
and get<br>
|
| to calculated stationary prevalence, transitions probabilities |
<pre>12 -15.029768 0.124347
|
| and life expectancies at any age. Choice of age ranges is useful |
13 -8.472981 0.036599
|
| for extrapolation. In our data file, ages varies from age 70 to |
21 -1.472527 -0.038394
|
| 102. Setting bage=50 and fage=100, makes the program computing |
23 -6.553602 0.029856
|
| life expectancy from age bage to age fage. As we use a model, we |
</br>
|
| can compute life expectancy on a wider age range than the age |
which is closer to the results. The approximation is probably useful
|
| range from the data. But the model can be rather wrong on big |
only for very small intervals and we don't have enough experience to
|
| intervals.</p> |
know if you will speed up the convergence or not.
|
| |
<pre> -ln(12)= -2.484
|
| <p>Similarly, it is possible to get extrapolated stationary |
-ln(6/1)=-ln(6)= -1.791
|
| prevalence by age raning from agemin to agemax. </p> |
-ln(3/1)=-ln(3)= -1.0986
|
| |
-ln(12/6)=-ln(2)= -0.693
|
| <ul> |
</pre>
|
| <li><b>agemin=</b> Minimum age for calculation of the |
|
| stationary prevalence </li> |
<h4><font color="#FF0000">Guess values for computing variances</font></h4>
|
| <li><b>agemax=</b> Maximum age for calculation of the |
|
| stationary prevalence </li> |
<p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
| <li><b>bage=</b> Minimum age for calculation of the health |
used as an input to get the various output data files (Health
|
| expectancies </li> |
expectancies, stationary prevalence etc.) and figures without
|
| <li><b>fage=</b> Maximum ages for calculation of the health |
rerunning the rather long maximisation phase (mle=0). </p>
|
| expectancies </li> |
|
| </ul> |
<p>The scales are small values for the evaluation of numerical
|
| |
derivatives. These derivatives are used to compute the hessian
|
| <hr> |
matrix of the parameters, that is the inverse of the covariance
|
| |
matrix, and the variances of health expectancies. Each line
|
| <h2><a name="running"></a><font color="#00006A">Running Imach |
consists in indices "ij" followed by the initial scales
|
| with this example</font></h2> |
(zero to simplify) associated with aij and bij. </p>
|
| |
<ul> <li>If mle=1 you can enter zeros:</li>
|
| <p>We assume that you entered your <a href="biaspar.txt">1st_example |
<blockquote><pre># Scales (for hessian or gradient estimation)
|
| parameter file</a> as explained <a href="#biaspar">above</a>. To |
12 0. 0.
|
| run the program you should click on the imach.exe icon and enter |
13 0. 0.
|
| the name of the parameter file which is for example <a |
21 0. 0.
|
| href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a> |
23 0. 0. </pre>
|
| (you also can click on the biaspar.txt icon located in <br> |
</blockquote>
|
| <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with |
<li>If mle=0 you must enter a covariance matrix (usually
|
| the mouse on the imach window).<br> |
obtained from an earlier run).</li>
|
| </p> |
</ul>
|
| |
|
| <p>The time to converge depends on the step unit that you used (1 |
<h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
|
| month is cpu consuming), on the number of cases, and on the |
|
| number of variables.</p> |
<p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
| |
used as an input to get the various output data files (Health
|
| <p>The program outputs many files. Most of them are files which |
expectancies, stationary prevalence etc.) and figures without
|
| will be plotted for better understanding.</p> |
rerunning the rather long maximisation phase (mle=0). <br>
|
| |
Each line starts with indices "ijk" followed by the
|
| <hr> |
covariances between aij and bij:<br>
|
| |
<pre>
|
| <h2><a name="output"><font color="#00006A">Output of the program |
121 Var(a12)
|
| and graphs</font> </a></h2> |
122 Cov(b12,a12) Var(b12)
|
| |
...
|
| <p>Once the optimization is finished, some graphics can be made |
232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
|
| with a grapher. We use Gnuplot which is an interactive plotting |
<ul>
|
| program copyrighted but freely distributed. Imach outputs the |
<li>If mle=1 you can enter zeros. </li>
|
| source of a gnuplot file, named 'graph.gp', which can be directly |
<pre># Covariance matrix
|
| input into gnuplot.<br> |
121 0.
|
| When the running is finished, the user should enter a caracter |
122 0. 0.
|
| for plotting and output editing. </p> |
131 0. 0. 0.
|
| |
132 0. 0. 0. 0.
|
| <p>These caracters are:</p> |
211 0. 0. 0. 0. 0.
|
| |
212 0. 0. 0. 0. 0. 0.
|
| <ul> |
231 0. 0. 0. 0. 0. 0. 0.
|
| <li>'c' to start again the program from the beginning.</li> |
232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
|
| <li>'g' to made graphics. The output graphs are in GIF format |
<li>If mle=0 you must enter a covariance matrix (usually
|
| and you have no control over which is produced. If you |
obtained from an earlier run). </li>
|
| want to modify the graphics or make another one, you |
</ul>
|
| should modify the parameters in the file <b>graph.gp</b> |
|
| located in imach\bin. A gnuplot reference manual is |
<h4><font color="#FF0000">Age range for calculation of stationary
|
| available <a |
prevalences and health expectancies</font></h4>
|
| href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>. |
|
| </li> |
<pre>agemin=70 agemax=100 bage=50 fage=100</pre>
|
| <li>'e' opens the <strong>index.htm</strong> file to edit the |
|
| output files and graphs. </li> |
<br>Once we obtained the estimated parameters, the program is able
|
| <li>'q' for exiting.</li> |
to calculated stationary prevalence, transitions probabilities
|
| </ul> |
and life expectancies at any age. Choice of age range is useful
|
| |
for extrapolation. In our data file, ages varies from age 70 to
|
| <h5><font size="4"><strong>Results files </strong></font><br> |
102. It is possible to get extrapolated stationary prevalence by
|
| <br> |
age ranging from agemin to agemax.
|
| <font color="#EC5E5E" size="3"><strong>- </strong></font><a |
|
| name="Observed prevalence in each state"><font color="#EC5E5E" |
<br>Setting bage=50 (begin age) and fage=100 (final age), makes
|
| size="3"><strong>Observed prevalence in each state</strong></font></a><font |
the program computing life expectancy from age 'bage' to age
|
| color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>: |
'fage'. As we use a model, we can interessingly compute life
|
| </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br> |
expectancy on a wider age range than the age range from the data.
|
| </h5> |
But the model can be rather wrong on much larger intervals.
|
| |
Program is limited to around 120 for upper age!
|
| <p>The first line is the title and displays each field of the |
<ul>
|
| file. The first column is age. The fields 2 and 6 are the |
<li><b>agemin=</b> Minimum age for calculation of the
|
| proportion of individuals in states 1 and 2 respectively as |
stationary prevalence </li>
|
| observed during the first exam. Others fields are the numbers of |
<li><b>agemax=</b> Maximum age for calculation of the
|
| people in states 1, 2 or more. The number of columns increases if |
stationary prevalence </li>
|
| the number of states is higher than 2.<br> |
<li><b>bage=</b> Minimum age for calculation of the health
|
| The header of the file is </p> |
expectancies </li>
|
| |
<li><b>fage=</b> Maximum age for calculation of the health
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
expectancies </li>
|
| 70 1.00000 631 631 70 0.00000 0 631 |
</ul>
|
| 71 0.99681 625 627 71 0.00319 2 627 |
|
| 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> |
<h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
|
| |
color="#FF0000"> the observed prevalence</font></h4>
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
|
| 70 0.95721 604 631 70 0.04279 27 631</pre> |
<pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
|
| |
|
| <p>It means that at age 70, the prevalence in state 1 is 1.000 |
<br>Statements 'begin-prev-date' and 'end-prev-date' allow to
|
| and in state 2 is 0.00 . At age 71 the number of individuals in |
select the period in which we calculate the observed prevalences
|
| state 1 is 625 and in state 2 is 2, hence the total number of |
in each state. In this example, the prevalences are calculated on
|
| people aged 71 is 625+2=627. <br> |
data survey collected between 1 january 1984 and 1 june 1988.
|
| </p> |
<ul>
|
| |
<li><strong>begin-prev-date= </strong>Starting date
|
| <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and |
(day/month/year)</li>
|
| covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5> |
<li><strong>end-prev-date= </strong>Final date
|
| |
(day/month/year)</li>
|
| <p>This file contains all the maximisation results: </p> |
</ul>
|
| |
|
| <pre> Number of iterations=47 |
<h4><font color="#FF0000">Population- or status-based health
|
| -2 log likelihood=46553.005854373667 |
expectancies</font></h4>
|
| Estimated parameters: a12 = -12.691743 b12 = 0.095819 |
|
| a13 = -7.815392 b13 = 0.031851 |
<pre>pop_based=0</pre>
|
| a21 = -1.809895 b21 = -0.030470 |
|
| a23 = -7.838248 b23 = 0.039490 |
<p>The program computes status-based health expectancies, i.e
|
| Covariance matrix: Var(a12) = 1.03611e-001 |
health expectancies which depends on your initial health state.
|
| Var(b12) = 1.51173e-005 |
If you are healthy your healthy life expectancy (e11) is higher
|
| Var(a13) = 1.08952e-001 |
than if you were disabled (e21, with e11 > e21).<br>
|
| Var(b13) = 1.68520e-005 |
To compute a healthy life expectancy independant of the initial
|
| Var(a21) = 4.82801e-001 |
status we have to weight e11 and e21 according to the probability
|
| Var(b21) = 6.86392e-005 |
to be in each state at initial age or, with other word, according
|
| Var(a23) = 2.27587e-001 |
to the proportion of people in each state.<br>
|
| Var(b23) = 3.04465e-005 |
We prefer computing a 'pure' period healthy life expectancy based
|
| </pre> |
only on the transtion forces. Then the weights are simply the
|
| |
stationnary prevalences or 'implied' prevalences at the initial
|
| <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>: |
age.<br>
|
| </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5> |
Some other people would like to use the cross-sectional
|
| |
prevalences (the "Sullivan prevalences") observed at
|
| <p>Here are the transitions probabilities Pij(x, x+nh) where nh |
the initial age during a period of time <a href="#Computing">defined
|
| is a multiple of 2 years. The first column is the starting age x |
just above</a>. <br>
|
| (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 |
<ul>
|
| example, line 5 of the file is: </p> |
<li><strong>popbased= 0 </strong>Health expectancies are
|
| |
computed at each age from stationary prevalences
|
| <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre> |
'expected' at this initial age.</li>
|
| |
<li><strong>popbased= 1 </strong>Health expectancies are
|
| <p>and this means: </p> |
computed at each age from cross-sectional 'observed'
|
| |
prevalence at this initial age. As all the population is
|
| <pre>p11(100,106)=0.03286 |
not observed at the same exact date we define a short
|
| p12(100,106)=0.23512 |
period were the observed prevalence is computed.</li>
|
| p13(100,106)=0.73202 |
</ul>
|
| p21(100,106)=0.02330 |
|
| p22(100,106)=0.19210 |
<h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
|
| p22(100,106)=0.78460 </pre> |
|
| |
<pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
|
| name="Stationary prevalence in each state"><font color="#EC5E5E" |
<p>Prevalence and population projections are only available if
|
| size="3"><b>Stationary prevalence in each state</b></font></a><b>: |
the interpolation unit is a month, i.e. stepm=1 and if there are
|
| </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5> |
no covariate. The programme estimates the prevalence in each
|
| |
state at a precise date expressed in day/month/year. The
|
| <pre>#Age 1-1 2-2 |
programme computes one forecasted prevalence a year from a
|
| 70 0.92274 0.07726 |
starting date (1 january of 1989 in this example) to a final date
|
| 71 0.91420 0.08580 |
(1 january 1992). The statement mov_average allows to compute
|
| 72 0.90481 0.09519 |
smoothed forecasted prevalences with a five-age moving average
|
| 73 0.89453 0.10547</pre> |
centered at the mid-age of the five-age period. <br>
|
| |
|
| <p>At age 70 the stationary prevalence is 0.92274 in state 1 and |
<ul>
|
| 0.07726 in state 2. This stationary prevalence differs from |
<li><strong>starting-proj-date</strong>= starting date
|
| observed prevalence. Here is the point. The observed prevalence |
(day/month/year) of forecasting</li>
|
| at age 70 results from the incidence of disability, incidence of |
<li><strong>final-proj-date= </strong>final date
|
| recovery and mortality which occurred in the past of the cohort. |
(day/month/year) of forecasting</li>
|
| Stationary prevalence results from a simulation with actual |
<li><strong>mov_average</strong>= smoothing with a five-age
|
| incidences and mortality (estimated from this cross-longitudinal |
moving average centered at the mid-age of the five-age
|
| survey). It is the best predictive value of the prevalence in the |
period. The command<strong> mov_average</strong> takes
|
| future if "nothing changes in the future". This is |
value 1 if the prevalences are smoothed and 0 otherwise.</li>
|
| exactly what demographers do with a Life table. Life expectancy |
</ul>
|
| is the expected mean time to survive if observed mortality rates |
|
| (incidence of mortality) "remains constant" in the |
<h4><font color="#FF0000">Last uncommented line : Population
|
| future. </p> |
forecasting </font></h4>
|
| |
|
| <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of |
<pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
|
| stationary prevalence</b></font><b>: </b><a |
|
| href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5> |
<p>This command is available if the interpolation unit is a
|
| |
month, i.e. stepm=1 and if popforecast=1. From a data file
|
| <p>The stationary prevalence has to be compared with the observed |
including age and number of persons alive at the precise date
|
| prevalence by age. But both are statistical estimates and |
‘popfiledate’, you can forecast the number of persons
|
| subjected to stochastic errors due to the size of the sample, the |
in each state until date ‘last-popfiledate’. In this
|
| design of the survey, and, for the stationary prevalence to the |
example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
|
| model used and fitted. It is possible to compute the standard |
includes real data which are the Japanese population in 1989.<br>
|
| deviation of the stationary prevalence at each age.</p> |
|
| |
<ul type="disc">
|
| <h6><font color="#EC5E5E" size="3">Observed and stationary |
<li class="MsoNormal"
|
| prevalence in state (2=disable) with the confident interval</font>:<b> |
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
|
| vbiaspar2.gif</b></h6> |
0 </b>Option for population forecasting. If
|
| |
popforecast=1, the programme does the forecasting<b>.</b></li>
|
| <p><br> |
<li class="MsoNormal"
|
| This graph exhibits the stationary prevalence in state (2) with |
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
|
| the confidence interval in red. The green curve is the observed |
</b>name of the population file</li>
|
| prevalence (or proportion of individuals in state (2)). Without |
<li class="MsoNormal"
|
| discussing the results (it is not the purpose here), we observe |
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
|
| that the green curve is rather below the stationary prevalence. |
date of the population population</li>
|
| It suggests an increase of the disability prevalence in the |
<li class="MsoNormal"
|
| future.</p> |
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
|
| |
date of the last population projection </li>
|
| <p><img src="vbiaspar2.gif" width="400" height="300"></p> |
</ul>
|
| |
|
| <h6><font color="#EC5E5E" size="3"><b>Convergence to the |
<hr>
|
| stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br> |
|
| <img src="pbiaspar1.gif" width="400" height="300"> </h6> |
<h2><a name="running"></a><font color="#00006A">Running Imach
|
| |
with this example</font></h2>
|
| <p>This graph plots the conditional transition probabilities from |
|
| an initial state (1=healthy in red at the bottom, or 2=disable in |
We assume that you typed in your <a href="biaspar.imach">1st_example
|
| green on top) at age <em>x </em>to the final state 2=disable<em> </em>at |
parameter file</a> as explained <a href="#biaspar">above</a>.
|
| age <em>x+h. </em>Conditional means at the condition to be alive |
<br>To run the program you should either:
|
| at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The |
<ul> <li> click on the imach.exe icon and enter
|
| curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i> |
the name of the parameter file which is for example <a
|
| + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary |
href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
|
| prevalence of disability</em>. In order to get the stationary |
<li> You also can locate the biaspar.imach icon in
|
| prevalence at age 70 we should start the process at an earlier |
<a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with
|
| age, i.e.50. If the disability state is defined by severe |
the mouse on the imach window).
|
| disability criteria with only a few chance to recover, then the |
<li> With latest version (0.7 and higher) if you setup windows in order to
|
| incidence of recovery is low and the time to convergence is |
understand ".imach" extension you can right click the
|
| probably longer. But we don't have experience yet.</p> |
biaspar.imach icon and either edit with notepad the parameter file or
|
| |
execute it with imach or whatever.
|
| <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age |
</ul>
|
| and initial health status</b></font><b>: </b><a |
|
| href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5> |
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
|
| <pre># Health expectancies |
number of variables.
|
| # Age 1-1 1-2 2-1 2-2 |
|
| 70 10.7297 2.7809 6.3440 5.9813 |
<br>The program outputs many files. Most of them are files which
|
| 71 10.3078 2.8233 5.9295 5.9959 |
will be plotted for better understanding.
|
| 72 9.8927 2.8643 5.5305 6.0033 |
|
| 73 9.4848 2.9036 5.1474 6.0035 </pre> |
<hr>
|
| |
|
| <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means: |
<h2><a name="output"><font color="#00006A">Output of the program
|
| e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre> |
and graphs</font> </a></h2>
|
| |
|
| <pre><img src="exbiaspar1.gif" width="400" height="300"><img |
<p>Once the optimization is finished, some graphics can be made
|
| src="exbiaspar2.gif" width="400" height="300"></pre> |
with a grapher. We use Gnuplot which is an interactive plotting
|
| |
program copyrighted but freely distributed. A gnuplot reference
|
| <p>For example, life expectancy of a healthy individual at age 70 |
manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
|
| is 10.73 in the healthy state and 2.78 in the disability state |
When the running is finished, the user should enter a caracter
|
| (=13.51 years). If he was disable at age 70, his life expectancy |
for plotting and output editing.
|
| will be shorter, 6.34 in the healthy state and 5.98 in the |
|
| disability state (=12.32 years). The total life expectancy is a |
<br>These caracters are:<br>
|
| weighted mean of both, 13.51 and 12.32; weight is the proportion |
|
| of people disabled at age 70. In order to get a pure period index |
<ul>
|
| (i.e. based only on incidences) we use the <a |
<li>'c' to start again the program from the beginning.</li>
|
| href="#Stationary prevalence in each state">computed or |
<li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
|
| stationary prevalence</a> at age 70 (i.e. computed from |
file to edit the output files and graphs. </li>
|
| incidences at earlier ages) instead of the <a |
<li>'q' for exiting.</li>
|
| href="#Observed prevalence in each state">observed prevalence</a> |
</ul>
|
| (for example at first exam) (<a href="#Health expectancies">see |
|
| below</a>).</p> |
<h5><font size="4"><strong>Results files </strong></font><br>
|
| |
<br>
|
| <h5><font color="#EC5E5E" size="3"><b>- Variances of life |
<font color="#EC5E5E" size="3"><strong>- </strong></font><a
|
| expectancies by age and initial health status</b></font><b>: </b><a |
name="Observed prevalence in each state"><font color="#EC5E5E"
|
| href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5> |
size="3"><strong>Observed prevalence in each state</strong></font></a><font
|
| |
color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
|
| <p>For example, the covariances of life expectancies Cov(ei,ej) |
</b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
|
| at age 50 are (line 3) </p> |
</h5>
|
| |
|
| <pre> Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183</pre> |
<p>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
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
proportion of individuals in states 1 and 2 respectively as
|
| name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health |
observed during the first exam. Others fields are the numbers of
|
| expectancies</b></font></a><font color="#EC5E5E" size="3"><b> |
people in states 1, 2 or more. The number of columns increases if
|
| with standard errors in parentheses</b></font><b>: </b><a |
the number of states is higher than 2.<br>
|
| href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5> |
The header of the file is </p>
|
| |
|
| <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> |
<pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
|
| |
70 1.00000 631 631 70 0.00000 0 631
|
| <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> |
71 0.99681 625 627 71 0.00319 2 627
|
| |
72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
|
| <p>Thus, at age 70 the total life expectancy, e..=13.42 years is |
|
| the weighted mean of e1.=13.51 and e2.=12.32 by the stationary |
<p>It means that at age 70, the prevalence in state 1 is 1.000
|
| prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in |
and in state 2 is 0.00 . At age 71 the number of individuals in
|
| state 2, respectively (the sum is equal to one). e.1=10.39 is the |
state 1 is 625 and in state 2 is 2, hence the total number of
|
| Disability-free life expectancy at age 70 (it is again a weighted |
people aged 71 is 625+2=627. <br>
|
| mean of e11 and e21). e.2=3.03 is also the life expectancy at age |
</p>
|
| 70 to be spent in the disability state.</p> |
|
| |
<h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
|
| <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by |
covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>
|
| age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>: |
|
| ebiaspar.gif</b></h6> |
<p>This file contains all the maximisation results: </p>
|
| |
|
| <p>This figure represents the health expectancies and the total |
<pre> -2 log likelihood= 21660.918613445392
|
| life expectancy with the confident interval in dashed curve. </p> |
Estimated parameters: a12 = -12.290174 b12 = 0.092161
|
| |
a13 = -9.155590 b13 = 0.046627
|
| <pre> <img src="ebiaspar.gif" width="400" height="300"></pre> |
a21 = -2.629849 b21 = -0.022030
|
| |
a23 = -7.958519 b23 = 0.042614
|
| <p>Standard deviations (obtained from the information matrix of |
Covariance matrix: Var(a12) = 1.47453e-001
|
| the model) of these quantities are very useful. |
Var(b12) = 2.18676e-005
|
| Cross-longitudinal surveys are costly and do not involve huge |
Var(a13) = 2.09715e-001
|
| samples, generally a few thousands; therefore it is very |
Var(b13) = 3.28937e-005
|
| important to have an idea of the standard deviation of our |
Var(a21) = 9.19832e-001
|
| estimates. It has been a big challenge to compute the Health |
Var(b21) = 1.29229e-004
|
| Expectancy standard deviations. Don't be confuse: life expectancy |
Var(a23) = 4.48405e-001
|
| is, as any expected value, the mean of a distribution; but here |
Var(b23) = 5.85631e-005
|
| we are not computing the standard deviation of the distribution, |
</pre>
|
| but the standard deviation of the estimate of the mean.</p> |
|
| |
<p>By substitution of these parameters in the regression model,
|
| <p>Our health expectancies estimates vary according to the sample |
we obtain the elementary transition probabilities:</p>
|
| size (and the standard deviations give confidence intervals of |
|
| the estimate) but also according to the model fitted. Let us |
<p><img src="pebiaspar1.gif" width="400" height="300"></p>
|
| explain it in more details.</p> |
|
| |
<h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
|
| <p>Choosing a model means ar least two kind of choices. First we |
</b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
|
| have to decide the number of disability states. Second we have to |
|
| design, within the logit model family, the model: variables, |
<p>Here are the transitions probabilities Pij(x, x+nh) where nh
|
| covariables, confonding factors etc. to be included.</p> |
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
|
| <p>More disability states we have, better is our demographical |
the transition probabilities p11, p12, p13, p21, p22, p23. For
|
| approach of the disability process, but smaller are the number of |
example, line 5 of the file is: </p>
|
| transitions between each state and higher is the noise in the |
|
| measurement. We do not have enough experiments of the various |
<pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
|
| models to summarize the advantages and disadvantages, but it is |
|
| important to say that even if we had huge and unbiased samples, |
<p>and this means: </p>
|
| the total life expectancy computed from a cross-longitudinal |
|
| survey, varies with the number of states. If we define only two |
<pre>p11(100,106)=0.02655
|
| states, alive or dead, we find the usual life expectancy where it |
p12(100,106)=0.17622
|
| is assumed that at each age, people are at the same risk to die. |
p13(100,106)=0.79722
|
| If we are differentiating the alive state into healthy and |
p21(100,106)=0.01809
|
| disable, and as the mortality from the disability state is higher |
p22(100,106)=0.13678
|
| than the mortality from the healthy state, we are introducing |
p22(100,106)=0.84513 </pre>
|
| heterogeneity in the risk of dying. The total mortality at each |
|
| age is the weighted mean of the mortality in each state by the |
<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
| prevalence in each state. Therefore if the proportion of people |
name="Stationary prevalence in each state"><font color="#EC5E5E"
|
| at each age and in each state is different from the stationary |
size="3"><b>Stationary prevalence in each state</b></font></a><b>:
|
| equilibrium, there is no reason to find the same total mortality |
</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
|
| at a particular age. Life expectancy, even if it is a very useful |
|
| tool, has a very strong hypothesis of homogeneity of the |
<pre>#Prevalence
|
| population. Our main purpose is not to measure differential |
#Age 1-1 2-2
|
| 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 |
70 0.90134 0.09866
|
| measurement.</p> |
71 0.89177 0.10823
|
| |
72 0.88139 0.11861
|
| <p>Incidences of disability or recovery are not affected by the |
73 0.87015 0.12985 </pre>
|
| number of states if these states are independant. But incidences |
|
| estimates are dependant on the specification of the model. More |
<p>At age 70 the stationary prevalence is 0.90134 in state 1 and
|
| covariates we added in the logit model better is the model, but |
0.09866 in state 2. This stationary prevalence differs from
|
| some covariates are not well measured, some are confounding |
observed prevalence. Here is the point. The observed prevalence
|
| factors like in any statistical model. The procedure to "fit |
at age 70 results from the incidence of disability, incidence of
|
| the best model' is similar to logistic regression which itself is |
recovery and mortality which occurred in the past of the cohort.
|
| similar to regression analysis. We haven't yet been sofar because |
Stationary prevalence results from a simulation with actual
|
| we also have a severe limitation which is the speed of the |
incidences and mortality (estimated from this cross-longitudinal
|
| convergence. On a Pentium III, 500 MHz, even the simplest model, |
survey). It is the best predictive value of the prevalence in the
|
| estimated by month on 8,000 people may take 4 hours to converge. |
future if "nothing changes in the future". This is
|
| Also, the program is not yet a statistical package, which permits |
exactly what demographers do with a Life table. Life expectancy
|
| a simple writing of the variables and the model to take into |
is the expected mean time to survive if observed mortality rates
|
| account in the maximisation. The actual program allows only to |
(incidence of mortality) "remains constant" in the
|
| add simple variables without covariations, like age+sex but |
future. </p>
|
| without age+sex+ age*sex . This can be done from the source code |
|
| (you have to change three lines in the source code) but will |
<h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
|
| never be general enough. But what is to remember, is that |
stationary prevalence</b></font><b>: </b><a
|
| incidences or probability of change from one state to another is |
href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
|
| affected by the variables specified into the model.</p> |
|
| |
<p>The stationary prevalence has to be compared with the observed
|
| <p>Also, the age range of the people interviewed has a link with |
prevalence by age. But both are statistical estimates and
|
| the age range of the life expectancy which can be estimated by |
subjected to stochastic errors due to the size of the sample, the
|
| extrapolation. If your sample ranges from age 70 to 95, you can |
design of the survey, and, for the stationary prevalence to the
|
| clearly estimate a life expectancy at age 70 and trust your |
model used and fitted. It is possible to compute the standard
|
| confidence interval which is mostly based on your sample size, |
deviation of the stationary prevalence at each age.</p>
|
| 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 |
<h5><font color="#EC5E5E" size="3">-Observed and stationary
|
| range of 70-95 and estimating probabilties of transition out of |
prevalence in state (2=disable) with the confident interval</font>:<b>
|
| this age range, say at age 50 is very dangerous. At least you |
</b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
|
| should remember that the confidence interval given by the |
|
| standard deviation of the health expectancies, are under the |
<p>This graph exhibits the stationary prevalence in state (2)
|
| strong assumption that your model is the 'true model', which is |
with the confidence interval in red. The green curve is the
|
| probably not the case.</p> |
observed prevalence (or proportion of individuals in state (2)).
|
| |
Without discussing the results (it is not the purpose here), we
|
| <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter |
observe that the green curve is rather below the stationary
|
| file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5> |
prevalence. It suggests an increase of the disability prevalence
|
| |
in the future.</p>
|
| <p>This copy of the parameter file can be useful to re-run the |
|
| program while saving the old output files. </p> |
<p><img src="vbiaspar21.gif" width="400" height="300"></p>
|
| |
|
| <hr> |
<h5><font color="#EC5E5E" size="3"><b>-Convergence to the
|
| |
stationary prevalence of disability</b></font><b>: </b><a
|
| <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2> |
href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
|
| |
<img src="pbiaspar11.gif" width="400" height="300"> </h5>
|
| <p>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 <a |
<p>This graph plots the conditional transition probabilities from
|
| href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a |
an initial state (1=healthy in red at the bottom, or 2=disable in
|
| copy of <font size="2" face="Courier New">mypar.txt</font> |
green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
|
| included in the subdirectory of imach, <font size="2" |
age <em>x+h. </em>Conditional means at the condition to be alive
|
| face="Courier New">mytry</font>. Edit it to change the name of |
at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
|
| the data file to <font size="2" face="Courier New">..\data\mydata.txt</font> |
curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
|
| if you don't want to copy it on the same directory. The file <font |
+ <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
|
| face="Courier New">mydata.txt</font> is a smaller file of 3,000 |
prevalence of disability</em>. In order to get the stationary
|
| people but still with 4 waves. </p> |
prevalence at age 70 we should start the process at an earlier
|
| |
age, i.e.50. If the disability state is defined by severe
|
| <p>Click on the imach.exe icon to open a window. Answer to the |
disability criteria with only a few chance to recover, then the
|
| question:'<strong>Enter the parameter file name:'</strong></p> |
incidence of recovery is low and the time to convergence is
|
| |
probably longer. But we don't have experience yet.</p>
|
| <table border="1"> |
|
| <tr> |
<h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
|
| <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter |
and initial health status</b></font><b>: </b><a
|
| the parameter file name: ..\mytry\imachpar.txt</strong></p> |
href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
|
| </td> |
|
| </tr> |
<pre># Health expectancies
|
| </table> |
# Age 1-1 1-2 2-1 2-2
|
| |
70 10.9226 3.0401 5.6488 6.2122
|
| <p>Most of the data files or image files generated, will use the |
71 10.4384 3.0461 5.2477 6.1599
|
| 'imachpar' string into their name. The running time is about 2-3 |
72 9.9667 3.0502 4.8663 6.1025
|
| minutes on a Pentium III. If the execution worked correctly, the |
73 9.5077 3.0524 4.5044 6.0401 </pre>
|
| outputs files are created in the current directory, and should be |
|
| the same as the mypar files initially included in the directory <font |
<pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
|
| size="2" face="Courier New">mytry</font>.</p> |
e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
|
| |
|
| <ul> |
<pre><img src="expbiaspar21.gif" width="400" height="300"><img
|
| <li><pre><u>Output on the screen</u> The output screen looks like <a |
src="expbiaspar11.gif" width="400" height="300"></pre>
|
| href="imachrun.LOG">this Log file</a> |
|
| # |
<p>For example, life expectancy of a healthy individual at age 70
|
| |
is 10.42 in the healthy state and 3.04 in the disability state
|
| title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 |
(=13.46 years). If he was disable at age 70, his life expectancy
|
| ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
will be shorter, 5.64 in the healthy state and 5.71 in the
|
| </li> |
disability state (=11.35 years). The total life expectancy is a
|
| <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 |
weighted mean of both, 13.46 and 11.35; weight is the proportion
|
| |
of people disabled at age 70. In order to get a pure period index
|
| Warning, no any valid information for:126 line=126 |
(i.e. based only on incidences) we use the <a
|
| Warning, no any valid information for:2307 line=2307 |
href="#Stationary prevalence in each state">computed or
|
| Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 |
stationary prevalence</a> at age 70 (i.e. computed from
|
| <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font> |
incidences at earlier ages) instead of the <a
|
| Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 |
href="#Observed prevalence in each state">observed prevalence</a>
|
| prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 |
(for example at first exam) (<a href="#Health expectancies">see
|
| Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> |
below</a>).</p>
|
| </li> |
|
| </ul> |
<h5><font color="#EC5E5E" size="3"><b>- Variances of life
|
| |
expectancies by age and initial health status</b></font><b>: </b><a
|
| <p> </p> |
href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
|
| |
|
| <ul> |
<p>For example, the covariances of life expectancies Cov(ei,ej)
|
| <li>Maximisation with the Powell algorithm. 8 directions are |
at age 50 are (line 3) </p>
|
| given corresponding to the 8 parameters. this can be |
|
| rather long to get convergence.<br> |
<pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
|
| <font size="1" face="Courier New"><br> |
|
| Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 |
<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
| 0.000000000000 3<br> |
name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
|
| 0.000000000000 4 0.000000000000 5 0.000000000000 6 |
expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
|
| 0.000000000000 7 <br> |
with standard errors in parentheses</b></font><b>: </b><a
|
| 0.000000000000 8 0.000000000000<br> |
href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
|
| 1..........2.................3..........4.................5.........<br> |
|
| 6................7........8...............<br> |
<pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
|
| Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 |
|
| <br> |
<pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
|
| 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br> |
|
| 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br> |
<p>Thus, at age 70 the total life expectancy, e..=13.26 years is
|
| 8 0.051272038506<br> |
the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
|
| 1..............2...........3..............4...........<br> |
prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
|
| 5..........6................7...........8.........<br> |
state 2, respectively (the sum is equal to one). e.1=9.95 is the
|
| #Number of iterations = 23, -2 Log likelihood = |
Disability-free life expectancy at age 70 (it is again a weighted
|
| 6744.954042573691<br> |
mean of e11 and e21). e.2=3.30 is also the life expectancy at age
|
| # Parameters<br> |
70 to be spent in the disability state.</p>
|
| 12 -12.966061 0.135117 <br> |
|
| 13 -7.401109 0.067831 <br> |
<h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
|
| 21 -0.672648 -0.006627 <br> |
age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
|
| 23 -5.051297 0.051271 </font><br> |
</b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
|
| </li> |
|
| <li><pre><font size="2">Calculation of the hessian matrix. Wait... |
<p>This figure represents the health expectancies and the total
|
| 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 |
life expectancy with the confident interval in dashed curve. </p>
|
| |
|
| Inverting the hessian to get the covariance matrix. Wait... |
<pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
|
| |
|
| #Hessian matrix# |
<p>Standard deviations (obtained from the information matrix of
|
| 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 |
the model) of these quantities are very useful.
|
| 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 |
Cross-longitudinal surveys are costly and do not involve huge
|
| -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 |
samples, generally a few thousands; therefore it is very
|
| -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 |
important to have an idea of the standard deviation of our
|
| -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 |
estimates. It has been a big challenge to compute the Health
|
| -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 |
Expectancy standard deviations. Don't be confuse: life expectancy
|
| 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 |
is, as any expected value, the mean of a distribution; but here
|
| 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 |
we are not computing the standard deviation of the distribution,
|
| # Scales |
but the standard deviation of the estimate of the mean.</p>
|
| 12 1.00000e-004 1.00000e-006 |
|
| 13 1.00000e-004 1.00000e-006 |
<p>Our health expectancies estimates vary according to the sample
|
| 21 1.00000e-003 1.00000e-005 |
size (and the standard deviations give confidence intervals of
|
| 23 1.00000e-004 1.00000e-005 |
the estimate) but also according to the model fitted. Let us
|
| # Covariance |
explain it in more details.</p>
|
| 1 5.90661e-001 |
|
| 2 -7.26732e-003 8.98810e-005 |
<p>Choosing a model means ar least two kind of choices. First we
|
| 3 8.80177e-002 -1.12706e-003 5.15824e-001 |
have to decide the number of disability states. Second we have to
|
| 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 |
design, within the logit model family, the model: variables,
|
| 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 |
covariables, confonding factors etc. to be included.</p>
|
| 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 |
|
| 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 |
<p>More disability states we have, better is our demographical
|
| 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 |
approach of the disability process, but smaller are the number of
|
| # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). |
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
|
| agemin=70 agemax=100 bage=50 fage=100 |
important to say that even if we had huge and unbiased samples,
|
| Computing prevalence limit: result on file 'plrmypar.txt' |
the total life expectancy computed from a cross-longitudinal
|
| Computing pij: result on file 'pijrmypar.txt' |
survey, varies with the number of states. If we define only two
|
| Computing Health Expectancies: result on file 'ermypar.txt' |
states, alive or dead, we find the usual life expectancy where it
|
| Computing Variance-covariance of DFLEs: file 'vrmypar.txt' |
is assumed that at each age, people are at the same risk to die.
|
| Computing Total LEs with variances: file 'trmypar.txt' |
If we are differentiating the alive state into healthy and
|
| Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' |
disable, and as the mortality from the disability state is higher
|
| End of Imach |
than the mortality from the healthy state, we are introducing
|
| </font></pre> |
heterogeneity in the risk of dying. The total mortality at each
|
| </li> |
age is the weighted mean of the mortality in each state by the
|
| </ul> |
prevalence in each state. Therefore if the proportion of people
|
| |
at each age and in each state is different from the stationary
|
| <p><font size="3">Once the running is finished, the program |
equilibrium, there is no reason to find the same total mortality
|
| requires a caracter:</font></p> |
at a particular age. Life expectancy, even if it is a very useful
|
| |
tool, has a very strong hypothesis of homogeneity of the
|
| <table border="1"> |
population. Our main purpose is not to measure differential
|
| <tr> |
mortality but to measure the expected time in a healthy or
|
| <td width="100%"><strong>Type g for plotting (available |
disability state in order to maximise the former and minimize the
|
| if mle=1), e to edit output files, c to start again,</strong><p><strong>and |
latter. But the differential in mortality complexifies the
|
| q for exiting:</strong></p> |
measurement.</p>
|
| </td> |
|
| </tr> |
<p>Incidences of disability or recovery are not affected by the
|
| </table> |
number of states if these states are independant. But incidences
|
| |
estimates are dependant on the specification of the model. More
|
| <p><font size="3">First you should enter <strong>g</strong> to |
covariates we added in the logit model better is the model, but
|
| make the figures and then you can edit all the results by typing <strong>e</strong>. |
some covariates are not well measured, some are confounding
|
| </font></p> |
factors like in any statistical model. The procedure to "fit
|
| |
the best model' is similar to logistic regression which itself is
|
| <ul> |
similar to regression analysis. We haven't yet been sofar because
|
| <li><u>Outputs files</u> <br> |
we also have a severe limitation which is the speed of the
|
| - index.htm, this file is the master file on which you |
convergence. On a Pentium III, 500 MHz, even the simplest model,
|
| should click first.<br> |
estimated by month on 8,000 people may take 4 hours to converge.
|
| - Observed prevalence in each state: <a |
Also, the program is not yet a statistical package, which permits
|
| href="..\mytry\prmypar.txt">mypar.txt</a> <br> |
a simple writing of the variables and the model to take into
|
| - Estimated parameters and the covariance matrix: <a |
account in the maximisation. The actual program allows only to
|
| href="..\mytry\rmypar.txt">rmypar.txt</a> <br> |
add simple variables like age+sex or age+sex+ age*sex but will
|
| - Stationary prevalence in each state: <a |
never be general enough. But what is to remember, is that
|
| href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br> |
incidences or probability of change from one state to another is
|
| - Transition probabilities: <a |
affected by the variables specified into the model.</p>
|
| href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br> |
|
| - Copy of the parameter file: <a |
<p>Also, the age range of the people interviewed has a link with
|
| href="..\mytry\ormypar.txt">ormypar.txt</a> <br> |
the age range of the life expectancy which can be estimated by
|
| - Life expectancies by age and initial health status: <a |
extrapolation. If your sample ranges from age 70 to 95, you can
|
| href="..\mytry\ermypar.txt">ermypar.txt</a> <br> |
clearly estimate a life expectancy at age 70 and trust your
|
| - Variances of life expectancies by age and initial |
confidence interval which is mostly based on your sample size,
|
| health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> |
but if you want to estimate the life expectancy at age 50, you
|
| <br> |
should rely in your model, but fitting a logistic model on a age
|
| - Health expectancies with their variances: <a |
range of 70-95 and estimating probabilties of transition out of
|
| href="..\mytry\trmypar.txt">trmypar.txt</a> <br> |
this age range, say at age 50 is very dangerous. At least you
|
| - Standard deviation of stationary prevalence: <a |
should remember that the confidence interval given by the
|
| href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br> |
standard deviation of the health expectancies, are under the
|
| <br> |
strong assumption that your model is the 'true model', which is
|
| </li> |
probably not the case.</p>
|
| <li><u>Graphs</u> <br> |
|
| <br> |
<h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
|
| -<a href="..\mytry\vmypar1.gif">Observed and stationary |
file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
|
| prevalence in state (1) with the confident interval</a> <br> |
|
| -<a href="..\mytry\vmypar2.gif">Observed and stationary |
<p>This copy of the parameter file can be useful to re-run the
|
| prevalence in state (2) with the confident interval</a> <br> |
program while saving the old output files. </p>
|
| -<a href="..\mytry\exmypar1.gif">Health life expectancies |
|
| by age and initial health state (1)</a> <br> |
<h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
|
| -<a href="..\mytry\exmypar2.gif">Health life expectancies |
</b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
|
| by age and initial health state (2)</a> <br> |
|
| -<a href="..\mytry\emypar.gif">Total life expectancy by |
<p
|
| age and health expectancies in states (1) and (2).</a> </li> |
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">First,
|
| </ul> |
we have estimated the observed prevalence between 1/1/1984 and
|
| |
1/6/1988. The mean date of interview (weighed average of the
|
| <p>This software have been partly granted by <a |
interviews performed between1/1/1984 and 1/6/1988) is estimated
|
| href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted |
to be 13/9/1985, as written on the top on the file. Then we
|
| action from the European Union. It will be copyrighted |
forecast the probability to be in each state. </p>
|
| identically to a GNU software product, i.e. program and software |
|
| can be distributed freely for non commercial use. Sources are not |
<p
|
| widely distributed today. You can get them by asking us with a |
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">Example,
|
| simple justification (name, email, institute) <a |
at date 1/1/1989 : </p>
|
| href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a |
|
| href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p> |
<pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
|
| |
# Forecasting at date 1/1/1989
|
| <p>Latest version (0.63 of 16 march 2000) can be accessed at <a |
73 0.807 0.078 0.115</pre>
|
| href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br> |
|
| </p> |
<p
|
| </body> |
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">Since
|
| </html> |
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.</p>
|
| |
|
| |
<h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
|
| |
</b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
|
| |
|
| |
<pre># Age P.1 P.2 P.3 [Population]
|
| |
# Forecasting at date 1/1/1989
|
| |
75 572685.22 83798.08
|
| |
74 621296.51 79767.99
|
| |
73 645857.70 69320.60 </pre>
|
| |
|
| |
<pre># Forecasting at date 1/1/19909
|
| |
76 442986.68 92721.14 120775.48
|
| |
75 487781.02 91367.97 121915.51
|
| |
74 512892.07 85003.47 117282.76 </pre>
|
| |
|
| |
<p>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.</p>
|
| |
|
| |
<hr>
|
| |
|
| |
<h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>
|
| |
|
| |
<p>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 <a
|
| |
href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of <font
|
| |
size="2" face="Courier New">mypar.imach</font> included in the
|
| |
subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
|
| |
Edit it to change the name of the data file to <font size="2"
|
| |
face="Courier New">..\data\mydata.txt</font> if you don't want to
|
| |
copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
|
| |
is a smaller file of 3,000 people but still with 4 waves. </p>
|
| |
|
| |
<p>Click on the imach.exe icon to open a window. Answer to the
|
| |
question:'<strong>Enter the parameter file name:'</strong></p>
|
| |
|
| |
<table border="1">
|
| |
<tr>
|
| |
<td width="100%"><strong>IMACH, Version 0.8</strong><p><strong>Enter
|
| |
the parameter file name: ..\mytry\imachpar.imach</strong></p>
|
| |
</td>
|
| |
</tr>
|
| |
</table>
|
| |
|
| |
<p>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 <font
|
| |
size="2" face="Courier New">mytry</font>.</p>
|
| |
|
| |
<ul>
|
| |
<li><pre><u>Output on the screen</u> The output screen looks like <a
|
| |
href="imachrun.LOG">this Log file</a>
|
| |
#
|
| |
|
| |
title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
|
| |
ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
| |
</li>
|
| |
<li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
|
| |
|
| |
Warning, no any valid information for:126 line=126
|
| |
Warning, no any valid information for:2307 line=2307
|
| |
Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
|
| |
<font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
|
| |
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
|
| |
Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
|
| |
</li>
|
| |
</ul>
|
| |
|
| |
<p> </p>
|
| |
|
| |
<ul>
|
| |
<li>Maximisation with the Powell algorithm. 8 directions are
|
| |
given corresponding to the 8 parameters. this can be
|
| |
rather long to get convergence.<br>
|
| |
<font size="1" face="Courier New"><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 </font><br>
|
| |
</li>
|
| |
<li><pre><font size="2">Calculation of the hessian matrix. Wait...
|
| |
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
|
| |
|
| |
Inverting the hessian to get the covariance matrix. Wait...
|
| |
|
| |
#Hessian matrix#
|
| |
3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
|
| |
2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
|
| |
-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
|
| |
-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
|
| |
-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
|
| |
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
|
| |
# Scales
|
| |
12 1.00000e-004 1.00000e-006
|
| |
13 1.00000e-004 1.00000e-006
|
| |
21 1.00000e-003 1.00000e-005
|
| |
23 1.00000e-004 1.00000e-005
|
| |
# Covariance
|
| |
1 5.90661e-001
|
| |
2 -7.26732e-003 8.98810e-005
|
| |
3 8.80177e-002 -1.12706e-003 5.15824e-001
|
| |
4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
|
| |
5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
|
| |
6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
|
| |
7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
|
| |
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
|
| |
# agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
|
| |
|
| |
|
| |
agemin=70 agemax=100 bage=50 fage=100
|
| |
Computing prevalence limit: result on file 'plrmypar.txt'
|
| |
Computing pij: result on file 'pijrmypar.txt'
|
| |
Computing Health Expectancies: result on file 'ermypar.txt'
|
| |
Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
|
| |
Computing Total LEs with variances: file 'trmypar.txt'
|
| |
Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
|
| |
End of Imach
|
| |
</font></pre>
|
| |
</li>
|
| |
</ul>
|
| |
|
| |
<p><font size="3">Once the running is finished, the program
|
| |
requires a caracter:</font></p>
|
| |
|
| |
<table border="1">
|
| |
<tr>
|
| |
<td width="100%"><strong>Type e to edit output files, c
|
| |
to start again, and q for exiting:</strong></td>
|
| |
</tr>
|
| |
</table>
|
| |
|
| |
<p><font size="3">First you should enter <strong>e </strong>to
|
| |
edit the master file mypar.htm. </font></p>
|
| |
|
| |
<ul>
|
| |
<li><u>Outputs files</u> <br>
|
| |
<br>
|
| |
- Observed prevalence in each state: <a
|
| |
href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
|
| |
- Estimated parameters and the covariance matrix: <a
|
| |
href="..\mytry\rmypar.txt">rmypar.imach</a> <br>
|
| |
- Stationary prevalence in each state: <a
|
| |
href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
|
| |
- Transition probabilities: <a
|
| |
href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
|
| |
- Copy of the parameter file: <a
|
| |
href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
|
| |
- Life expectancies by age and initial health status: <a
|
| |
href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
|
| |
- Variances of life expectancies by age and initial
|
| |
health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
|
| |
<br>
|
| |
- Health expectancies with their variances: <a
|
| |
href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
|
| |
- Standard deviation of stationary prevalence: <a
|
| |
href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
|
| |
- Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
|
| |
<br>
|
| |
- Population forecasting (if popforecast=1): <a
|
| |
href="poprmypar.txt">poprmypar.txt</a> <br>
|
| |
</li>
|
| |
<li><u>Graphs</u> <br>
|
| |
<br>
|
| |
-<a href="../mytry/pemypar1.gif">One-step transition probabilities</a><br>
|
| |
-<a href="../mytry/pmypar11.gif">Convergence to the stationary prevalence</a><br>
|
| |
-<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> <br>
|
| |
-<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> <br>
|
| |
-<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> <br>
|
| |
-<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> <br>
|
| |
-<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li>
|
| |
</ul>
|
| |
|
| |
<p>This software have been partly granted by <a
|
| |
href="http://euroreves.ined.fr">Euro-REVES</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) <a
|
| |
href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
|
| |
href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
|
| |
|
| |
<p>Latest version (0.8 of March 2002) can be accessed at <a
|
| |
href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
|
| |
</p>
|
| |
</body>
|
| |
</html>
|
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