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| <title>Computing Health Expectancies using IMaCh</title> |
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| <h1 align="center"><font color="#00006A">Computing Health |
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| Expectancies using IMaCh</font></h1> |
<h1 align="center"><font color="#00006A">Computing Health
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Expectancies using IMaCh</font></h1>
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| <h1 align="center"><font color="#00006A" size="5">(a Maximum |
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| Likelihood Computer Program using Interpolation of Markov Chains)</font></h1> |
<h1 align="center"><font color="#00006A" size="5">(a Maximum
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Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
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| <p align="center"> </p> |
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<p align="center"> </p>
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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 |
<p align="center"><a href="http://www.ined.fr/"><img
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| src="euroreves2.gif" width="151" height="75"></p> |
src="logo-ined.gif" border="0" width="151" height="76"></a><img
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src="euroreves2.gif" width="151" height="75"></p>
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| <h3 align="center"><a href="http://www.ined.fr/"><font |
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| color="#00006A">INED</font></a><font color="#00006A"> and </font><a |
<h3 align="center"><a href="http://www.ined.fr/"><font
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| href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3> |
color="#00006A">INED</font></a><font color="#00006A"> and </font><a
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href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
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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"><font color="#00006A" size="4"><strong>Version
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64b, May 2001</strong></font></p>
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| <hr size="3" color="#EC5E5E"> |
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<hr size="3" color="#EC5E5E">
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| <p align="center"><font color="#00006A"><strong>Authors of the |
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| program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font |
<p align="center"><font color="#00006A"><strong>Authors of the
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| color="#00006A"><strong>Nicolas Brouard</strong></font></a><font |
program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
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| color="#00006A"><strong>, senior researcher at the </strong></font><a |
color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
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| href="http://www.ined.fr"><font color="#00006A"><strong>Institut |
color="#00006A"><strong>, senior researcher at the </strong></font><a
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| National d'Etudes Démographiques</strong></font></a><font |
href="http://www.ined.fr"><font color="#00006A"><strong>Institut
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| color="#00006A"><strong> (INED, Paris) in the "Mortality, |
National d'Etudes Démographiques</strong></font></a><font
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| Health and Epidemiology" Research Unit </strong></font></p> |
color="#00006A"><strong> (INED, Paris) in the "Mortality,
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Health and Epidemiology" Research Unit </strong></font></p>
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| <p align="center"><font color="#00006A"><strong>and Agnès |
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| Lièvre<br clear="left"> |
<p align="center"><font color="#00006A"><strong>and Agnès
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| </strong></font></p> |
Lièvre<br clear="left">
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</strong></font></p>
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| <h4><font color="#00006A">Contribution to the mathematics: C. R. |
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| Heathcote </font><font color="#00006A" size="2">(Australian |
<h4><font color="#00006A">Contribution to the mathematics: C. R.
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| National University, Canberra).</font></h4> |
Heathcote </font><font color="#00006A" size="2">(Australian
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National University, Canberra).</font></h4>
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| <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a |
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| href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font |
<h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
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| color="#00006A">) </font></h4> |
href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
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color="#00006A">) </font></h4>
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| <hr> |
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<hr>
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| <ul> |
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| <li><a href="#intro">Introduction</a> </li> |
<ul>
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| <li>The detailed statistical model (<a href="docmath.pdf">PDF |
<li><a href="#intro">Introduction</a> </li>
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| version</a>),(<a href="docmath.ps">ps version</a>) </li> |
<li>The detailed statistical model (<a href="docmath.pdf">PDF
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| <li><a href="#data">On what kind of data can it be used?</a></li> |
version</a>),(<a href="docmath.ps">ps version</a>) </li>
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| <li><a href="#datafile">The data file</a> </li> |
<li><a href="#data">On what kind of data can it be used?</a></li>
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| <li><a href="#biaspar">The parameter file</a> </li> |
<li><a href="#datafile">The data file</a> </li>
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| <li><a href="#running">Running Imach</a> </li> |
<li><a href="#biaspar">The parameter file</a> </li>
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| <li><a href="#output">Output files and graphs</a> </li> |
<li><a href="#running">Running Imach</a> </li>
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| <li><a href="#example">Exemple</a> </li> |
<li><a href="#output">Output files and graphs</a> </li>
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| </ul> |
<li><a href="#example">Exemple</a> </li>
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</ul>
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| <hr> |
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<hr>
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| <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2> |
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<h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
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| <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal |
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| data</b>. Within the family of Health Expectancies (HE), |
<p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
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| Disability-free life expectancy (DFLE) is probably the most |
data</b> using the methodology pioneered by Laditka and Wolf (1).
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| important index to monitor. In low mortality countries, there is |
Within the family of Health Expectancies (HE), Disability-free
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| a fear that when mortality declines, the increase in DFLE is not |
life expectancy (DFLE) is probably the most important index to
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| proportionate to the increase in total Life expectancy. This case |
monitor. In low mortality countries, there is a fear that when
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| is called the <em>Expansion of morbidity</em>. Most of the data |
mortality declines, the increase in DFLE is not proportionate to
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| collected today, in particular by the international <a |
the increase in total Life expectancy. This case is called the <em>Expansion
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| href="http://euroreves/reves">REVES</a> network on Health |
of morbidity</em>. Most of the data collected today, in
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| expectancy, and most HE indices based on these data, are <em>cross-sectional</em>. |
particular by the international <a href="http://euroreves/reves">REVES</a>
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| It means that the information collected comes from a single |
network on Health expectancy, and most HE indices based on these
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| cross-sectional survey: people from various ages (but mostly old |
data, are <em>cross-sectional</em>. It means that the information
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| people) are surveyed on their health status at a single date. |
collected comes from a single cross-sectional survey: people from
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| Proportion of people disabled at each age, can then be measured |
various ages (but mostly old people) are surveyed on their health
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| at that date. This age-specific prevalence curve is then used to |
status at a single date. Proportion of people disabled at each
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| distinguish, within the stationary population (which, by |
age, can then be measured at that date. This age-specific
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| definition, is the life table estimated from the vital statistics |
prevalence curve is then used to distinguish, within the
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| on mortality at the same date), the disable population from the |
stationary population (which, by definition, is the life table
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| disability-free population. Life expectancy (LE) (or total |
estimated from the vital statistics on mortality at the same
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| population divided by the yearly number of births or deaths of |
date), the disable population from the disability-free
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| this stationary population) is then decomposed into DFLE and DLE. |
population. Life expectancy (LE) (or total population divided by
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| This method of computing HE is usually called the Sullivan method |
the yearly number of births or deaths of this stationary
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| (from the name of the author who first described it).</p> |
population) is then decomposed into DFLE and DLE. This method of
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computing HE is usually called the Sullivan method (from the name
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| <p>Age-specific proportions of people disable are very difficult |
of the author who first described it).</p>
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| to forecast because each proportion corresponds to historical |
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| conditions of the cohort and it is the result of the historical |
<p>Age-specific proportions of people disable are very difficult
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| flows from entering disability and recovering in the past until |
to forecast because each proportion corresponds to historical
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| today. The age-specific intensities (or incidence rates) of |
conditions of the cohort and it is the result of the historical
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| entering disability or recovering a good health, are reflecting |
flows from entering disability and recovering in the past until
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| actual conditions and therefore can be used at each age to |
today. The age-specific intensities (or incidence rates) of
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| forecast the future of this cohort. For example if a country is |
entering disability or recovering a good health, are reflecting
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| improving its technology of prosthesis, the incidence of |
actual conditions and therefore can be used at each age to
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| recovering the ability to walk will be higher at each (old) age, |
forecast the future of this cohort. For example if a country is
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| but the prevalence of disability will only slightly reflect an |
improving its technology of prosthesis, the incidence of
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| improve because the prevalence is mostly affected by the history |
recovering the ability to walk will be higher at each (old) age,
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| of the cohort and not by recent period effects. To measure the |
but the prevalence of disability will only slightly reflect an
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| period improvement we have to simulate the future of a cohort of |
improve because the prevalence is mostly affected by the history
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| new-borns entering or leaving at each age the disability state or |
of the cohort and not by recent period effects. To measure the
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| dying according to the incidence rates measured today on |
period improvement we have to simulate the future of a cohort of
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| different cohorts. The proportion of people disabled at each age |
new-borns entering or leaving at each age the disability state or
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| in this simulated cohort will be much lower (using the exemple of |
dying according to the incidence rates measured today on
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| an improvement) that the proportions observed at each age in a |
different cohorts. The proportion of people disabled at each age
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| cross-sectional survey. This new prevalence curve introduced in a |
in this simulated cohort will be much lower (using the exemple of
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| life table will give a much more actual and realistic HE level |
an improvement) that the proportions observed at each age in a
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| than the Sullivan method which mostly measured the History of |
cross-sectional survey. This new prevalence curve introduced in a
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| health conditions in this country.</p> |
life table will give a much more actual and realistic HE level
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| |
than the Sullivan method which mostly measured the History of
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| <p>Therefore, the main question is how to measure incidence rates |
health conditions in this country.</p>
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| from cross-longitudinal surveys? This is the goal of the IMaCH |
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| program. From your data and using IMaCH you can estimate period |
<p>Therefore, the main question is how to measure incidence rates
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| HE and not only Sullivan's HE. Also the standard errors of the HE |
from cross-longitudinal surveys? This is the goal of the IMaCH
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| are computed.</p> |
program. From your data and using IMaCH you can estimate period
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| |
HE and not only Sullivan's HE. Also the standard errors of the HE
|
| <p>A cross-longitudinal survey consists in a first survey |
are computed.</p>
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| ("cross") where individuals from different ages are |
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| interviewed on their health status or degree of disability. At |
<p>A cross-longitudinal survey consists in a first survey
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| least a second wave of interviews ("longitudinal") |
("cross") where individuals from different ages are
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| should measure each new individual health status. Health |
interviewed on their health status or degree of disability. At
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| expectancies are computed from the transitions observed between |
least a second wave of interviews ("longitudinal")
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| waves and are computed for each degree of severity of disability |
should measure each new individual health status. Health
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| (number of life states). More degrees you consider, more time is |
expectancies are computed from the transitions observed between
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| necessary to reach the Maximum Likelihood of the parameters |
waves and are computed for each degree of severity of disability
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| involved in the model. Considering only two states of disability |
(number of life states). More degrees you consider, more time is
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| (disable and healthy) is generally enough but the computer |
necessary to reach the Maximum Likelihood of the parameters
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| program works also with more health statuses.<br> |
involved in the model. Considering only two states of disability
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| <br> |
(disable and healthy) is generally enough but the computer
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| The simplest model is the multinomial logistic model where <i>pij</i> |
program works also with more health statuses.<br>
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| is the probability to be observed in state <i>j</i> at the second |
<br>
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| wave conditional to be observed in state <em>i</em> at the first |
The simplest model is the multinomial logistic model where <i>pij</i>
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| wave. Therefore a simple model is: log<em>(pij/pii)= aij + |
is the probability to be observed in state <i>j</i> at the second
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| bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>' |
wave conditional to be observed in state <em>i</em> at the first
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| is a covariate. The advantage that this computer program claims, |
wave. Therefore a simple model is: log<em>(pij/pii)= aij +
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| comes from that if the delay between waves is not identical for |
bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
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| each individual, or if some individual missed an interview, the |
is a covariate. The advantage that this computer program claims,
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| information is not rounded or lost, but taken into account using |
comes from that if the delay between waves is not identical for
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| an interpolation or extrapolation. <i>hPijx</i> is the |
each individual, or if some individual missed an interview, the
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| probability to be observed in state <i>i</i> at age <i>x+h</i> |
information is not rounded or lost, but taken into account using
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| conditional to the observed state <i>i</i> at age <i>x</i>. The |
an interpolation or extrapolation. <i>hPijx</i> is the
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| delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>) |
probability to be observed in state <i>i</i> at age <i>x+h</i>
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| of unobserved intermediate states. This elementary transition (by |
conditional to the observed state <i>i</i> at age <i>x</i>. The
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| month or quarter trimester, semester or year) is modeled as a |
delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
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| multinomial logistic. The <i>hPx</i> matrix is simply the matrix |
of unobserved intermediate states. This elementary transition (by
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| product of <i>nh*stepm</i> elementary matrices and the |
month or quarter trimester, semester or year) is modeled as a
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| contribution of each individual to the likelihood is simply <i>hPijx</i>. |
multinomial logistic. The <i>hPx</i> matrix is simply the matrix
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| <br> |
product of <i>nh*stepm</i> elementary matrices and the
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| </p> |
contribution of each individual to the likelihood is simply <i>hPijx</i>.
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| |
<br>
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| <p>The program presented in this manual is a quite general |
</p>
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| program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated |
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| <strong>MA</strong>rkov <strong>CH</strong>ain), designed to |
<p>The program presented in this manual is a quite general
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| analyse transition data from longitudinal surveys. The first step |
program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
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| is the parameters estimation of a transition probabilities model |
<strong>MA</strong>rkov <strong>CH</strong>ain), designed to
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| between an initial status and a final status. From there, the |
analyse transition data from longitudinal surveys. The first step
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| computer program produces some indicators such as observed and |
is the parameters estimation of a transition probabilities model
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| stationary prevalence, life expectancies and their variances and |
between an initial status and a final status. From there, the
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| graphs. Our transition model consists in absorbing and |
computer program produces some indicators such as observed and
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| non-absorbing states with the possibility of return across the |
stationary prevalence, life expectancies and their variances and
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| non-absorbing states. The main advantage of this package, |
graphs. Our transition model consists in absorbing and
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| compared to other programs for the analysis of transition data |
non-absorbing states with the possibility of return across the
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| (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole |
non-absorbing states. The main advantage of this package,
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| individual information is used even if an interview is missing, a |
compared to other programs for the analysis of transition data
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| status or a date is unknown or when the delay between waves is |
(For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
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| not identical for each individual. The program can be executed |
individual information is used even if an interview is missing, a
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| according to parameters: selection of a sub-sample, number of |
status or a date is unknown or when the delay between waves is
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| absorbing and non-absorbing states, number of waves taken in |
not identical for each individual. The program can be executed
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| account (the user inputs the first and the last interview), a |
according to parameters: selection of a sub-sample, number of
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| tolerance level for the maximization function, the periodicity of |
absorbing and non-absorbing states, number of waves taken in
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| the transitions (we can compute annual, quaterly or monthly |
account (the user inputs the first and the last interview), a
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| transitions), covariates in the model. It works on Windows or on |
tolerance level for the maximization function, the periodicity of
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| Unix.<br> |
the transitions (we can compute annual, quaterly or monthly
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| </p> |
transitions), covariates in the model. It works on Windows or on
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| |
Unix.<br>
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| <hr> |
</p>
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| |
|
| <h2><a name="data"><font color="#00006A">On what kind of data can |
<hr>
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| it be used?</font></a></h2> |
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| |
<p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
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| <p>The minimum data required for a transition model is the |
Methods for Analyzing Active Life Expectancy". <i>Journal of
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| recording of a set of individuals interviewed at a first date and |
Aging and Health</i>. Vol 10, No. 2. </p>
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| interviewed again at least one another time. From the |
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| observations of an individual, we obtain a follow-up over time of |
<hr>
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| the occurrence of a specific event. In this documentation, the |
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| event is related to health status at older ages, but the program |
<h2><a name="data"><font color="#00006A">On what kind of data can
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| can be applied on a lot of longitudinal studies in different |
it be used?</font></a></h2>
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| contexts. To build the data file explained into the next section, |
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| you must have the month and year of each interview and the |
<p>The minimum data required for a transition model is the
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| corresponding health status. But in order to get age, date of |
recording of a set of individuals interviewed at a first date and
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| birth (month and year) is required (missing values is allowed for |
interviewed again at least one another time. From the
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| month). Date of death (month and year) is an important |
observations of an individual, we obtain a follow-up over time of
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| information also required if the individual is dead. Shorter |
the occurrence of a specific event. In this documentation, the
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| steps (i.e. a month) will more closely take into account the |
event is related to health status at older ages, but the program
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| survival time after the last interview.</p> |
can be applied on a lot of longitudinal studies in different
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| |
contexts. To build the data file explained into the next section,
|
| <hr> |
you must have the month and year of each interview and the
|
| |
corresponding health status. But in order to get age, date of
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| <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2> |
birth (month and year) is required (missing values is allowed for
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| |
month). Date of death (month and year) is an important
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| <p>In this example, 8,000 people have been interviewed in a |
information also required if the individual is dead. Shorter
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| cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). |
steps (i.e. a month) will more closely take into account the
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| Some people missed 1, 2 or 3 interviews. Health statuses are |
survival time after the last interview.</p>
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| healthy (1) and disable (2). The survey is not a real one. It is |
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| a simulation of the American Longitudinal Survey on Aging. The |
<hr>
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| disability state is defined if the individual missed one of four |
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| ADL (Activity of daily living, like bathing, eating, walking). |
<h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
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| Therefore, even is the individuals interviewed in the sample are |
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| virtual, the information brought with this sample is close to the |
<p>In this example, 8,000 people have been interviewed in a
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| situation of the United States. Sex is not recorded is this |
cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
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| sample.</p> |
Some people missed 1, 2 or 3 interviews. Health statuses are
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| |
healthy (1) and disable (2). The survey is not a real one. It is
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| <p>Each line of the data set (named <a href="data1.txt">data1.txt</a> |
a simulation of the American Longitudinal Survey on Aging. The
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| in this first example) is an individual record which fields are: </p> |
disability state is defined if the individual missed one of four
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| |
ADL (Activity of daily living, like bathing, eating, walking).
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| <ul> |
Therefore, even is the individuals interviewed in the sample are
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| <li><b>Index number</b>: positive number (field 1) </li> |
virtual, the information brought with this sample is close to the
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| <li><b>First covariate</b> positive number (field 2) </li> |
situation of the United States. Sex is not recorded is this
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| <li><b>Second covariate</b> positive number (field 3) </li> |
sample.</p>
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| <li><a name="Weight"><b>Weight</b></a>: positive number |
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| (field 4) . In most surveys individuals are weighted |
<p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
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| according to the stratification of the sample.</li> |
in this first example) is an individual record which fields are: </p>
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| <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are |
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| coded as 99/9999 (field 5) </li> |
<ul>
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| <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are |
<li><b>Index number</b>: positive number (field 1) </li>
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| coded as 99/9999 (field 6) </li> |
<li><b>First covariate</b> positive number (field 2) </li>
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| <li><b>Date of first interview</b>: coded as mm/yyyy. Missing |
<li><b>Second covariate</b> positive number (field 3) </li>
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| dates are coded as 99/9999 (field 7) </li> |
<li><a name="Weight"><b>Weight</b></a>: positive number
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| <li><b>Status at first interview</b>: positive number. |
(field 4) . In most surveys individuals are weighted
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| Missing values ar coded -1. (field 8) </li> |
according to the stratification of the sample.</li>
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| <li><b>Date of second interview</b>: coded as mm/yyyy. |
<li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
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| Missing dates are coded as 99/9999 (field 9) </li> |
coded as 99/9999 (field 5) </li>
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| <li><strong>Status at second interview</strong> positive |
<li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
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| number. Missing values ar coded -1. (field 10) </li> |
coded as 99/9999 (field 6) </li>
|
| <li><b>Date of third interview</b>: coded as mm/yyyy. Missing |
<li><b>Date of first interview</b>: coded as mm/yyyy. Missing
|
| dates are coded as 99/9999 (field 11) </li> |
dates are coded as 99/9999 (field 7) </li>
|
| <li><strong>Status at third interview</strong> positive |
<li><b>Status at first interview</b>: positive number.
|
| number. Missing values ar coded -1. (field 12) </li> |
Missing values ar coded -1. (field 8) </li>
|
| <li><b>Date of fourth interview</b>: coded as mm/yyyy. |
<li><b>Date of second interview</b>: coded as mm/yyyy.
|
| Missing dates are coded as 99/9999 (field 13) </li> |
Missing dates are coded as 99/9999 (field 9) </li>
|
| <li><strong>Status at fourth interview</strong> positive |
<li><strong>Status at second interview</strong> positive
|
| number. Missing values are coded -1. (field 14) </li> |
number. Missing values ar coded -1. (field 10) </li>
|
| <li>etc</li> |
<li><b>Date of third interview</b>: coded as mm/yyyy. Missing
|
| </ul> |
dates are coded as 99/9999 (field 11) </li>
|
| |
<li><strong>Status at third interview</strong> positive
|
| <p> </p> |
number. Missing values ar coded -1. (field 12) </li>
|
| |
<li><b>Date of fourth interview</b>: coded as mm/yyyy.
|
| <p>If your longitudinal survey do not include information about |
Missing dates are coded as 99/9999 (field 13) </li>
|
| weights or covariates, you must fill the column with a number |
<li><strong>Status at fourth interview</strong> positive
|
| (e.g. 1) because a missing field is not allowed.</p> |
number. Missing values are coded -1. (field 14) </li>
|
| |
<li>etc</li>
|
| <hr> |
</ul>
|
| |
|
| <h2><font color="#00006A">Your first example parameter file</font><a |
<p> </p>
|
| href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> |
|
| |
<p>If your longitudinal survey do not include information about
|
| <h2><a name="biaspar"></a>#Imach version 0.63, February 2000, |
weights or covariates, you must fill the column with a number
|
| INED-EUROREVES </h2> |
(e.g. 1) because a missing field is not allowed.</p>
|
| |
|
| <p>This is a comment. Comments start with a '#'.</p> |
<hr>
|
| |
|
| <h4><font color="#FF0000">First uncommented line</font></h4> |
<h2><font color="#00006A">Your first example parameter file</font><a
|
| |
href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
|
| <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> |
|
| |
<h2><a name="biaspar"></a>#Imach version 0.64b, May 2001,
|
| <ul> |
INED-EUROREVES </h2>
|
| <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. |
<p>This is a comment. Comments start with a '#'.</p>
|
| Our example is a six years follow-up survey. It consists |
|
| in a baseline followed by 3 reinterviews. </li> |
<h4><font color="#FF0000">First uncommented line</font></h4>
|
| <li><b>lastobs=</b> 8600 the program is able to run on a |
|
| subsample where the last observation number is lastobs. |
<pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
|
| It can be set a bigger number than the real number of |
|
| observations (e.g. 100000). In this example, maximisation |
<ul>
|
| will be done on the 8600 first records. </li> |
<li><b>title=</b> 1st_example is title of the run. </li>
|
| <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more |
<li><b>datafile=</b>data1.txt is the name of the data set.
|
| than two interviews in the survey, the program can be run |
Our example is a six years follow-up survey. It consists
|
| on selected transitions periods. firstpass=1 means the |
in a baseline followed by 3 reinterviews. </li>
|
| first interview included in the calculation is the |
<li><b>lastobs=</b> 8600 the program is able to run on a
|
| baseline survey. lastpass=4 means that the information |
subsample where the last observation number is lastobs.
|
| brought by the 4th interview is taken into account.</li> |
It can be set a bigger number than the real number of
|
| </ul> |
observations (e.g. 100000). In this example, maximisation
|
| |
will be done on the 8600 first records. </li>
|
| <p> </p> |
<li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
|
| |
than two interviews in the survey, the program can be run
|
| <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented |
on selected transitions periods. firstpass=1 means the
|
| line</font></a></h4> |
first interview included in the calculation is the
|
| |
baseline survey. lastpass=4 means that the information
|
| <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
brought by the 4th interview is taken into account.</li>
|
| |
</ul>
|
| <ul> |
|
| <li><b>ftol=1e-8</b> Convergence tolerance on the function |
<p> </p>
|
| value in the maximisation of the likelihood. Choosing a |
|
| correct value for ftol is difficult. 1e-8 is a correct |
<h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
|
| value for a 32 bits computer.</li> |
line</font></a></h4>
|
| <li><b>stepm=1</b> Time unit in months for interpolation. |
|
| Examples:<ul> |
<pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
| <li>If stepm=1, the unit is a month </li> |
|
| <li>If stepm=4, the unit is a trimester</li> |
<ul>
|
| <li>If stepm=12, the unit is a year </li> |
<li><b>ftol=1e-8</b> Convergence tolerance on the function
|
| <li>If stepm=24, the unit is two years</li> |
value in the maximisation of the likelihood. Choosing a
|
| <li>... </li> |
correct value for ftol is difficult. 1e-8 is a correct
|
| </ul> |
value for a 32 bits computer.</li>
|
| </li> |
<li><b>stepm=1</b> Time unit in months for interpolation.
|
| <li><b>ncov=2</b> Number of covariates to be add to the |
Examples:<ul>
|
| model. The intercept and the age parameter are counting |
<li>If stepm=1, the unit is a month </li>
|
| for 2 covariates. For example, if you want to add gender |
<li>If stepm=4, the unit is a trimester</li>
|
| in the covariate vector you must write ncov=3 else |
<li>If stepm=12, the unit is a year </li>
|
| ncov=2. </li> |
<li>If stepm=24, the unit is two years</li>
|
| <li><b>nlstate=2</b> Number of non-absorbing (live) states. |
<li>... </li>
|
| Here we have two alive states: disability-free is coded 1 |
</ul>
|
| and disability is coded 2. </li> |
</li>
|
| <li><b>ndeath=1</b> Number of absorbing states. The absorbing |
<li><b>ncov=2</b> Number of covariates in the datafile. The
|
| state death is coded 3. </li> |
intercept and the age parameter are counting for 2
|
| <li><b>maxwav=4</b> Maximum number of waves. The program can |
covariates.</li>
|
| not include more than 4 interviews. </li> |
<li><b>nlstate=2</b> Number of non-absorbing (alive) states.
|
| <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the |
Here we have two alive states: disability-free is coded 1
|
| Maximisation Likelihood Estimation. <ul> |
and disability is coded 2. </li>
|
| <li>If mle=1 the program does the maximisation and |
<li><b>ndeath=1</b> Number of absorbing states. The absorbing
|
| the calculation of heath expectancies </li> |
state death is coded 3. </li>
|
| <li>If mle=0 the program only does the calculation of |
<li><b>maxwav=4</b> Number of waves in the datafile.</li>
|
| the health expectancies. </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>weight=0</b> Possibility to add weights. <ul> |
the calculation of health expectancies </li>
|
| <li>If weight=0 no weights are included </li> |
<li>If mle=0 the program only does the calculation of
|
| <li>If weight=1 the maximisation integrates the |
the health expectancies. </li>
|
| weights which are in field <a href="#Weight">4</a></li> |
</ul>
|
| </ul> |
</li>
|
| </li> |
<li><b>weight=0</b> Possibility to add weights. <ul>
|
| </ul> |
<li>If weight=0 no weights are included </li>
|
| |
<li>If weight=1 the maximisation integrates the
|
| <h4><font color="#FF0000">Guess values for optimization</font><font |
weights which are in field <a href="#Weight">4</a></li>
|
| color="#00006A"> </font></h4> |
</ul>
|
| |
</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 |
|
| number of absorbing states and non-absorbing states and on the |
<h4><font color="#FF0000">Covariates</font></h4>
|
| number of covariates. <br> |
|
| <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> + |
<p>Intercept and age are systematically included in the model.
|
| <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br> |
Additional covariates can be included with the command </p>
|
| <br> |
|
| Thus in the simple case with 2 covariates (the model is log |
<pre>model=<em>list of covariates</em></pre>
|
| (pij/pii) = aij + bij * age where intercept and age are the two |
|
| covariates), and 2 health degrees (1 for disability-free and 2 |
<ul>
|
| for disability) and 1 absorbing state (3), you must enter 8 |
<li>if<strong> model=. </strong>then no covariates are
|
| initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can |
included</li>
|
| start with zeros as in this example, but if you have a more |
<li>if <strong>model=V1</strong> the model includes the first
|
| precise set (for example from an earlier run) you can enter it |
covariate (field 2)</li>
|
| and it will speed up them<br> |
<li>if <strong>model=V2 </strong>the model includes the
|
| Each of the four lines starts with indices "ij": <br> |
second covariate (field 3)</li>
|
| <br> |
<li>if <strong>model=V1+V2 </strong>the model includes the
|
| <b>ij aij bij</b> </p> |
first and the second covariate (fields 2 and 3)</li>
|
| |
<li>if <strong>model=V1*V2 </strong>the model includes the
|
| <blockquote> |
product of the first and the second covariate (fields 2
|
| <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age |
and 3)</li>
|
| 12 -14.155633 0.110794 |
<li>if <strong>model=V1+V1*age</strong> the model includes
|
| 13 -7.925360 0.032091 |
the product covariate*age</li>
|
| 21 -1.890135 -0.029473 |
</ul>
|
| 23 -6.234642 0.022315 </pre> |
|
| </blockquote> |
<h4><font color="#FF0000">Guess values for optimization</font><font
|
| |
color="#00006A"> </font></h4>
|
| <p>or, to simplify: </p> |
|
| |
<p>You must write the initial guess values of the parameters for
|
| <blockquote> |
optimization. The number of parameters, <em>N</em> depends on the
|
| <pre>12 0.0 0.0 |
number of absorbing states and non-absorbing states and on the
|
| 13 0.0 0.0 |
number of covariates. <br>
|
| 21 0.0 0.0 |
<em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
|
| 23 0.0 0.0</pre> |
<em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br>
|
| </blockquote> |
<br>
|
| |
Thus in the simple case with 2 covariates (the model is log
|
| <h4><font color="#FF0000">Guess values for computing variances</font></h4> |
(pij/pii) = aij + bij * age where intercept and age are the two
|
| |
covariates), and 2 health degrees (1 for disability-free and 2
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
for disability) and 1 absorbing state (3), you must enter 8
|
| used as an input to get the vairous output data files (Health |
initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
|
| expectancies, stationary prevalence etc.) and figures without |
start with zeros as in this example, but if you have a more
|
| rerunning the rather long maximisation phase (mle=0). </p> |
precise set (for example from an earlier run) you can enter it
|
| |
and it will speed up them<br>
|
| <p>The scales are small values for the evaluation of numerical |
Each of the four lines starts with indices "ij": <br>
|
| derivatives. These derivatives are used to compute the hessian |
<br>
|
| matrix of the parameters, that is the inverse of the covariance |
<b>ij aij bij</b> </p>
|
| matrix, and the variances of health expectancies. Each line |
|
| consists in indices "ij" followed by the initial scales |
<blockquote>
|
| (zero to simplify) associated with aij and bij. </p> |
<pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
|
| |
12 -14.155633 0.110794
|
| <ul> |
13 -7.925360 0.032091
|
| <li>If mle=1 you can enter zeros:</li> |
21 -1.890135 -0.029473
|
| </ul> |
23 -6.234642 0.022315 </pre>
|
| |
</blockquote>
|
| <blockquote> |
|
| <pre># Scales (for hessian or gradient estimation) |
<p>or, to simplify: </p>
|
| 12 0. 0. |
|
| 13 0. 0. |
<blockquote>
|
| 21 0. 0. |
<pre>12 0.0 0.0
|
| 23 0. 0. </pre> |
13 0.0 0.0
|
| </blockquote> |
21 0.0 0.0
|
| |
23 0.0 0.0</pre>
|
| <ul> |
</blockquote>
|
| <li>If mle=0 you must enter a covariance matrix (usually |
|
| obtained from an earlier run).</li> |
<h4><font color="#FF0000">Guess values for computing variances</font></h4>
|
| </ul> |
|
| |
<p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
| <h4><font color="#FF0000">Covariance matrix of parameters</font></h4> |
used as an input to get the vairous output data files (Health
|
| |
expectancies, stationary prevalence etc.) and figures without
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be |
rerunning the rather long maximisation phase (mle=0). </p>
|
| used as an input to get the vairous output data files (Health |
|
| expectancies, stationary prevalence etc.) and figures without |
<p>The scales are small values for the evaluation of numerical
|
| rerunning the rather long maximisation phase (mle=0). </p> |
derivatives. These derivatives are used to compute the hessian
|
| |
matrix of the parameters, that is the inverse of the covariance
|
| <p>Each line starts with indices "ijk" followed by the |
matrix, and the variances of health expectancies. Each line
|
| covariances between aij and bij: </p> |
consists in indices "ij" followed by the initial scales
|
| |
(zero to simplify) associated with aij and bij. </p>
|
| <pre> |
|
| 121 Var(a12) |
<ul>
|
| 122 Cov(b12,a12) Var(b12) |
<li>If mle=1 you can enter zeros:</li>
|
| ... |
</ul>
|
| 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> |
|
| |
<blockquote>
|
| <ul> |
<pre># Scales (for hessian or gradient estimation)
|
| <li>If mle=1 you can enter zeros. </li> |
12 0. 0.
|
| </ul> |
13 0. 0.
|
| |
21 0. 0.
|
| <blockquote> |
23 0. 0. </pre>
|
| <pre># Covariance matrix |
</blockquote>
|
| 121 0. |
|
| 122 0. 0. |
<ul>
|
| 131 0. 0. 0. |
<li>If mle=0 you must enter a covariance matrix (usually
|
| 132 0. 0. 0. 0. |
obtained from an earlier run).</li>
|
| 211 0. 0. 0. 0. 0. |
</ul>
|
| 212 0. 0. 0. 0. 0. 0. |
|
| 231 0. 0. 0. 0. 0. 0. 0. |
<h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
|
| 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> |
|
| </blockquote> |
<p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
| |
used as an input to get the vairous output data files (Health
|
| <ul> |
expectancies, stationary prevalence etc.) and figures without
|
| <li>If mle=0 you must enter a covariance matrix (usually |
rerunning the rather long maximisation phase (mle=0). </p>
|
| obtained from an earlier run).<br> |
|
| </li> |
<p>Each line starts with indices "ijk" followed by the
|
| </ul> |
covariances between aij and bij: </p>
|
| |
|
| <h4><a name="biaspar-l"></a><font color="#FF0000">last |
<pre>
|
| uncommented line</font></h4> |
121 Var(a12)
|
| |
122 Cov(b12,a12) Var(b12)
|
| <pre>agemin=70 agemax=100 bage=50 fage=100</pre> |
...
|
| |
232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
|
| <p>Once we obtained the estimated parameters, the program is able |
|
| to calculated stationary prevalence, transitions probabilities |
<ul>
|
| and life expectancies at any age. Choice of age ranges is useful |
<li>If mle=1 you can enter zeros. </li>
|
| for extrapolation. In our data file, ages varies from age 70 to |
</ul>
|
| 102. Setting bage=50 and fage=100, makes the program computing |
|
| life expectancy from age bage to age fage. As we use a model, we |
<blockquote>
|
| can compute life expectancy on a wider age range than the age |
<pre># Covariance matrix
|
| range from the data. But the model can be rather wrong on big |
121 0.
|
| intervals.</p> |
122 0. 0.
|
| |
131 0. 0. 0.
|
| <p>Similarly, it is possible to get extrapolated stationary |
132 0. 0. 0. 0.
|
| prevalence by age raning from agemin to agemax. </p> |
211 0. 0. 0. 0. 0.
|
| |
212 0. 0. 0. 0. 0. 0.
|
| <ul> |
231 0. 0. 0. 0. 0. 0. 0.
|
| <li><b>agemin=</b> Minimum age for calculation of the |
232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
|
| stationary prevalence </li> |
</blockquote>
|
| <li><b>agemax=</b> Maximum age for calculation of the |
|
| stationary prevalence </li> |
<ul>
|
| <li><b>bage=</b> Minimum age for calculation of the health |
<li>If mle=0 you must enter a covariance matrix (usually
|
| expectancies </li> |
obtained from an earlier run).<br>
|
| <li><b>fage=</b> Maximum ages for calculation of the health |
</li>
|
| expectancies </li> |
</ul>
|
| </ul> |
|
| |
<h4><a name="biaspar-l"></a><font color="#FF0000">last
|
| <hr> |
uncommented line</font></h4>
|
| |
|
| <h2><a name="running"></a><font color="#00006A">Running Imach |
<pre>agemin=70 agemax=100 bage=50 fage=100</pre>
|
| with this example</font></h2> |
|
| |
<p>Once we obtained the estimated parameters, the program is able
|
| <p>We assume that you entered your <a href="biaspar.txt">1st_example |
to calculated stationary prevalence, transitions probabilities
|
| parameter file</a> as explained <a href="#biaspar">above</a>. To |
and life expectancies at any age. Choice of age ranges is useful
|
| run the program you should click on the imach.exe icon and enter |
for extrapolation. In our data file, ages varies from age 70 to
|
| the name of the parameter file which is for example <a |
102. Setting bage=50 and fage=100, makes the program computing
|
| href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a> |
life expectancy from age bage to age fage. As we use a model, we
|
| (you also can click on the biaspar.txt icon located in <br> |
can compute life expectancy on a wider age range than the age
|
| <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with |
range from the data. But the model can be rather wrong on big
|
| the mouse on the imach window).<br> |
intervals.</p>
|
| </p> |
|
| |
<p>Similarly, it is possible to get extrapolated stationary
|
| <p>The time to converge depends on the step unit that you used (1 |
prevalence by age raning from agemin to agemax. </p>
|
| month is cpu consuming), on the number of cases, and on the |
|
| number of variables.</p> |
<ul>
|
| |
<li><b>agemin=</b> Minimum age for calculation of the
|
| <p>The program outputs many files. Most of them are files which |
stationary prevalence </li>
|
| will be plotted for better understanding.</p> |
<li><b>agemax=</b> Maximum age for calculation of the
|
| |
stationary prevalence </li>
|
| <hr> |
<li><b>bage=</b> Minimum age for calculation of the health
|
| |
expectancies </li>
|
| <h2><a name="output"><font color="#00006A">Output of the program |
<li><b>fage=</b> Maximum ages for calculation of the health
|
| and graphs</font> </a></h2> |
expectancies </li>
|
| |
</ul>
|
| <p>Once the optimization is finished, some graphics can be made |
|
| with a grapher. We use Gnuplot which is an interactive plotting |
<hr>
|
| program copyrighted but freely distributed. Imach outputs the |
|
| source of a gnuplot file, named 'graph.gp', which can be directly |
<h2><a name="running"></a><font color="#00006A">Running Imach
|
| input into gnuplot.<br> |
with this example</font></h2>
|
| When the running is finished, the user should enter a caracter |
|
| for plotting and output editing. </p> |
<p>We assume that you entered your <a href="biaspar.txt">1st_example
|
| |
parameter file</a> as explained <a href="#biaspar">above</a>. To
|
| <p>These caracters are:</p> |
run the program you should click on the imach.exe icon and enter
|
| |
the name of the parameter file which is for example <a
|
| <ul> |
href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
|
| <li>'c' to start again the program from the beginning.</li> |
(you also can click on the biaspar.txt icon located in <br>
|
| <li>'g' to made graphics. The output graphs are in GIF format |
<a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
|
| and you have no control over which is produced. If you |
the mouse on the imach window).<br>
|
| want to modify the graphics or make another one, you |
</p>
|
| should modify the parameters in the file <b>graph.gp</b> |
|
| located in imach\bin. A gnuplot reference manual is |
<p>The time to converge depends on the step unit that you used (1
|
| available <a |
month is cpu consuming), on the number of cases, and on the
|
| href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>. |
number of variables.</p>
|
| </li> |
|
| <li>'e' opens the <strong>index.htm</strong> file to edit the |
<p>The program outputs many files. Most of them are files which
|
| output files and graphs. </li> |
will be plotted for better understanding.</p>
|
| <li>'q' for exiting.</li> |
|
| </ul> |
<hr>
|
| |
|
| <h5><font size="4"><strong>Results files </strong></font><br> |
<h2><a name="output"><font color="#00006A">Output of the program
|
| <br> |
and graphs</font> </a></h2>
|
| <font color="#EC5E5E" size="3"><strong>- </strong></font><a |
|
| name="Observed prevalence in each state"><font color="#EC5E5E" |
<p>Once the optimization is finished, some graphics can be made
|
| size="3"><strong>Observed prevalence in each state</strong></font></a><font |
with a grapher. We use Gnuplot which is an interactive plotting
|
| color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>: |
program copyrighted but freely distributed. A gnuplot reference
|
| </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br> |
manual is available <a href="http://www.gnuplot.org/">here</a>. <br>
|
| </h5> |
When the running is finished, the user should enter a caracter
|
| |
for plotting and output editing. </p>
|
| <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 |
<p>These caracters are:</p>
|
| proportion of individuals in states 1 and 2 respectively as |
|
| observed during the first exam. Others fields are the numbers of |
<ul>
|
| people in states 1, 2 or more. The number of columns increases if |
<li>'c' to start again the program from the beginning.</li>
|
| the number of states is higher than 2.<br> |
<li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
|
| The header of the file is </p> |
file to edit the output files and graphs. </li>
|
| |
<li>'q' for exiting.</li>
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
</ul>
|
| 70 1.00000 631 631 70 0.00000 0 631 |
|
| 71 0.99681 625 627 71 0.00319 2 627 |
<h5><font size="4"><strong>Results files </strong></font><br>
|
| 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> |
<br>
|
| |
<font color="#EC5E5E" size="3"><strong>- </strong></font><a
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N |
name="Observed prevalence in each state"><font color="#EC5E5E"
|
| 70 0.95721 604 631 70 0.04279 27 631</pre> |
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>It means that at age 70, the prevalence in state 1 is 1.000 |
</b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
|
| and in state 2 is 0.00 . At age 71 the number of individuals in |
</h5>
|
| state 1 is 625 and in state 2 is 2, hence the total number of |
|
| people aged 71 is 625+2=627. <br> |
<p>The first line is the title and displays each field of the
|
| </p> |
file. The first column is age. The fields 2 and 6 are the
|
| |
proportion of individuals in states 1 and 2 respectively as
|
| <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and |
observed during the first exam. Others fields are the numbers of
|
| covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5> |
people in states 1, 2 or more. The number of columns increases if
|
| |
the number of states is higher than 2.<br>
|
| <p>This file contains all the maximisation results: </p> |
The header of the file is </p>
|
| |
|
| <pre> Number of iterations=47 |
<pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
|
| -2 log likelihood=46553.005854373667 |
70 1.00000 631 631 70 0.00000 0 631
|
| Estimated parameters: a12 = -12.691743 b12 = 0.095819 |
71 0.99681 625 627 71 0.00319 2 627
|
| a13 = -7.815392 b13 = 0.031851 |
72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
|
| a21 = -1.809895 b21 = -0.030470 |
|
| a23 = -7.838248 b23 = 0.039490 |
<p>It means that at age 70, the prevalence in state 1 is 1.000
|
| Covariance matrix: Var(a12) = 1.03611e-001 |
and in state 2 is 0.00 . At age 71 the number of individuals in
|
| Var(b12) = 1.51173e-005 |
state 1 is 625 and in state 2 is 2, hence the total number of
|
| Var(a13) = 1.08952e-001 |
people aged 71 is 625+2=627. <br>
|
| Var(b13) = 1.68520e-005 |
</p>
|
| Var(a21) = 4.82801e-001 |
|
| Var(b21) = 6.86392e-005 |
<h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
|
| Var(a23) = 2.27587e-001 |
covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
|
| Var(b23) = 3.04465e-005 |
|
| </pre> |
<p>This file contains all the maximisation results: </p>
|
| |
|
| <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>: |
<pre> -2 log likelihood= 21660.918613445392
|
| </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5> |
Estimated parameters: a12 = -12.290174 b12 = 0.092161
|
| |
a13 = -9.155590 b13 = 0.046627
|
| <p>Here are the transitions probabilities Pij(x, x+nh) where nh |
a21 = -2.629849 b21 = -0.022030
|
| is a multiple of 2 years. The first column is the starting age x |
a23 = -7.958519 b23 = 0.042614
|
| (from age 50 to 100), the second is age (x+nh) and the others are |
Covariance matrix: Var(a12) = 1.47453e-001
|
| the transition probabilities p11, p12, p13, p21, p22, p23. For |
Var(b12) = 2.18676e-005
|
| example, line 5 of the file is: </p> |
Var(a13) = 2.09715e-001
|
| |
Var(b13) = 3.28937e-005
|
| <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre> |
Var(a21) = 9.19832e-001
|
| |
Var(b21) = 1.29229e-004
|
| <p>and this means: </p> |
Var(a23) = 4.48405e-001
|
| |
Var(b23) = 5.85631e-005
|
| <pre>p11(100,106)=0.03286 |
</pre>
|
| p12(100,106)=0.23512 |
|
| p13(100,106)=0.73202 |
<p>By substitution of these parameters in the regression model,
|
| p21(100,106)=0.02330 |
we obtain the elementary transition probabilities:</p>
|
| p22(100,106)=0.19210 |
|
| p22(100,106)=0.78460 </pre> |
<p><img src="pebiaspar1.gif" width="400" height="300"></p>
|
| |
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
<h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
|
| name="Stationary prevalence in each state"><font color="#EC5E5E" |
</b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
|
| size="3"><b>Stationary prevalence in each state</b></font></a><b>: |
|
| </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5> |
<p>Here are the transitions probabilities Pij(x, x+nh) where nh
|
| |
is a multiple of 2 years. The first column is the starting age x
|
| <pre>#Age 1-1 2-2 |
(from age 50 to 100), the second is age (x+nh) and the others are
|
| 70 0.92274 0.07726 |
the transition probabilities p11, p12, p13, p21, p22, p23. For
|
| 71 0.91420 0.08580 |
example, line 5 of the file is: </p>
|
| 72 0.90481 0.09519 |
|
| 73 0.89453 0.10547</pre> |
<pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
|
| |
|
| <p>At age 70 the stationary prevalence is 0.92274 in state 1 and |
<p>and this means: </p>
|
| 0.07726 in state 2. This stationary prevalence differs from |
|
| observed prevalence. Here is the point. The observed prevalence |
<pre>p11(100,106)=0.02655
|
| at age 70 results from the incidence of disability, incidence of |
p12(100,106)=0.17622
|
| recovery and mortality which occurred in the past of the cohort. |
p13(100,106)=0.79722
|
| Stationary prevalence results from a simulation with actual |
p21(100,106)=0.01809
|
| incidences and mortality (estimated from this cross-longitudinal |
p22(100,106)=0.13678
|
| survey). It is the best predictive value of the prevalence in the |
p22(100,106)=0.84513 </pre>
|
| future if "nothing changes in the future". This is |
|
| exactly what demographers do with a Life table. Life expectancy |
<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
| is the expected mean time to survive if observed mortality rates |
name="Stationary prevalence in each state"><font color="#EC5E5E"
|
| (incidence of mortality) "remains constant" in the |
size="3"><b>Stationary prevalence in each state</b></font></a><b>:
|
| future. </p> |
</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
|
| |
|
| <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of |
<pre>#Prevalence
|
| stationary prevalence</b></font><b>: </b><a |
#Age 1-1 2-2
|
| href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5> |
|
| |
#************
|
| <p>The stationary prevalence has to be compared with the observed |
70 0.90134 0.09866
|
| prevalence by age. But both are statistical estimates and |
71 0.89177 0.10823
|
| subjected to stochastic errors due to the size of the sample, the |
72 0.88139 0.11861
|
| design of the survey, and, for the stationary prevalence to the |
73 0.87015 0.12985 </pre>
|
| model used and fitted. It is possible to compute the standard |
|
| deviation of the stationary prevalence at each age.</p> |
<p>At age 70 the stationary prevalence is 0.90134 in state 1 and
|
| |
0.09866 in state 2. This stationary prevalence differs from
|
| <h6><font color="#EC5E5E" size="3">Observed and stationary |
observed prevalence. Here is the point. The observed prevalence
|
| prevalence in state (2=disable) with the confident interval</font>:<b> |
at age 70 results from the incidence of disability, incidence of
|
| vbiaspar2.gif</b></h6> |
recovery and mortality which occurred in the past of the cohort.
|
| |
Stationary prevalence results from a simulation with actual
|
| <p><br> |
incidences and mortality (estimated from this cross-longitudinal
|
| This graph exhibits the stationary prevalence in state (2) with |
survey). It is the best predictive value of the prevalence in the
|
| the confidence interval in red. The green curve is the observed |
future if "nothing changes in the future". This is
|
| prevalence (or proportion of individuals in state (2)). Without |
exactly what demographers do with a Life table. Life expectancy
|
| discussing the results (it is not the purpose here), we observe |
is the expected mean time to survive if observed mortality rates
|
| that the green curve is rather below the stationary prevalence. |
(incidence of mortality) "remains constant" in the
|
| It suggests an increase of the disability prevalence in the |
future. </p>
|
| future.</p> |
|
| |
<h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
|
| <p><img src="vbiaspar2.gif" width="400" height="300"></p> |
stationary prevalence</b></font><b>: </b><a
|
| |
href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
|
| <h6><font color="#EC5E5E" size="3"><b>Convergence to the |
|
| stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br> |
<p>The stationary prevalence has to be compared with the observed
|
| <img src="pbiaspar1.gif" width="400" height="300"> </h6> |
prevalence by age. But both are statistical estimates and
|
| |
subjected to stochastic errors due to the size of the sample, the
|
| <p>This graph plots the conditional transition probabilities from |
design of the survey, and, for the stationary prevalence to the
|
| an initial state (1=healthy in red at the bottom, or 2=disable in |
model used and fitted. It is possible to compute the standard
|
| green on top) at age <em>x </em>to the final state 2=disable<em> </em>at |
deviation of the stationary prevalence at each age.</p>
|
| age <em>x+h. </em>Conditional means at the condition to be alive |
|
| at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The |
<h5><font color="#EC5E5E" size="3">-Observed and stationary
|
| curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i> |
prevalence in state (2=disable) with the confident interval</font>:<b>
|
| + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary |
</b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
|
| prevalence of disability</em>. In order to get the stationary |
|
| prevalence at age 70 we should start the process at an earlier |
<p>This graph exhibits the stationary prevalence in state (2)
|
| age, i.e.50. If the disability state is defined by severe |
with the confidence interval in red. The green curve is the
|
| disability criteria with only a few chance to recover, then the |
observed prevalence (or proportion of individuals in state (2)).
|
| incidence of recovery is low and the time to convergence is |
Without discussing the results (it is not the purpose here), we
|
| probably longer. But we don't have experience yet.</p> |
observe that the green curve is rather below the stationary
|
| |
prevalence. It suggests an increase of the disability prevalence
|
| <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age |
in the future.</p>
|
| and initial health status</b></font><b>: </b><a |
|
| href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5> |
<p><img src="vbiaspar21.gif" width="400" height="300"></p>
|
| |
|
| <pre># Health expectancies |
<h5><font color="#EC5E5E" size="3"><b>-Convergence to the
|
| # Age 1-1 1-2 2-1 2-2 |
stationary prevalence of disability</b></font><b>: </b><a
|
| 70 10.7297 2.7809 6.3440 5.9813 |
href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
|
| 71 10.3078 2.8233 5.9295 5.9959 |
<img src="pbiaspar11.gif" width="400" height="300"> </h5>
|
| 72 9.8927 2.8643 5.5305 6.0033 |
|
| 73 9.4848 2.9036 5.1474 6.0035 </pre> |
<p>This graph plots the conditional transition probabilities from
|
| |
an initial state (1=healthy in red at the bottom, or 2=disable in
|
| <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means: |
green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
|
| e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre> |
age <em>x+h. </em>Conditional means at the condition to be alive
|
| |
at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
|
| <pre><img src="exbiaspar1.gif" width="400" height="300"><img |
curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
|
| src="exbiaspar2.gif" width="400" height="300"></pre> |
+ <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
|
| |
prevalence of disability</em>. In order to get the stationary
|
| <p>For example, life expectancy of a healthy individual at age 70 |
prevalence at age 70 we should start the process at an earlier
|
| is 10.73 in the healthy state and 2.78 in the disability state |
age, i.e.50. If the disability state is defined by severe
|
| (=13.51 years). If he was disable at age 70, his life expectancy |
disability criteria with only a few chance to recover, then the
|
| will be shorter, 6.34 in the healthy state and 5.98 in the |
incidence of recovery is low and the time to convergence is
|
| disability state (=12.32 years). The total life expectancy is a |
probably longer. But we don't have experience yet.</p>
|
| 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 |
<h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
|
| (i.e. based only on incidences) we use the <a |
and initial health status</b></font><b>: </b><a
|
| href="#Stationary prevalence in each state">computed or |
href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
|
| stationary prevalence</a> at age 70 (i.e. computed from |
|
| incidences at earlier ages) instead of the <a |
<pre># Health expectancies
|
| href="#Observed prevalence in each state">observed prevalence</a> |
# Age 1-1 1-2 2-1 2-2
|
| (for example at first exam) (<a href="#Health expectancies">see |
70 10.9226 3.0401 5.6488 6.2122
|
| below</a>).</p> |
71 10.4384 3.0461 5.2477 6.1599
|
| |
72 9.9667 3.0502 4.8663 6.1025
|
| <h5><font color="#EC5E5E" size="3"><b>- Variances of life |
73 9.5077 3.0524 4.5044 6.0401 </pre>
|
| expectancies by age and initial health status</b></font><b>: </b><a |
|
| href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5> |
<pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:
|
| |
e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>
|
| <p>For example, the covariances of life expectancies Cov(ei,ej) |
|
| at age 50 are (line 3) </p> |
<pre><img src="expbiaspar21.gif" width="400" height="300"><img
|
| |
src="expbiaspar11.gif" width="400" height="300"></pre>
|
| <pre> Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183</pre> |
|
| |
<p>For example, life expectancy of a healthy individual at age 70
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a |
is 10.92 in the healthy state and 3.04 in the disability state
|
| name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health |
(=13.96 years). If he was disable at age 70, his life expectancy
|
| expectancies</b></font></a><font color="#EC5E5E" size="3"><b> |
will be shorter, 5.64 in the healthy state and 6.21 in the
|
| with standard errors in parentheses</b></font><b>: </b><a |
disability state (=11.85 years). The total life expectancy is a
|
| href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5> |
weighted mean of both, 13.96 and 11.85; weight is the proportion
|
| |
of people disabled at age 70. In order to get a pure period index
|
| <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> |
(i.e. based only on incidences) we use the <a
|
| |
href="#Stationary prevalence in each state">computed or
|
| <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> |
stationary prevalence</a> at age 70 (i.e. computed from
|
| |
incidences at earlier ages) instead of the <a
|
| <p>Thus, at age 70 the total life expectancy, e..=13.42 years is |
href="#Observed prevalence in each state">observed prevalence</a>
|
| the weighted mean of e1.=13.51 and e2.=12.32 by the stationary |
(for example at first exam) (<a href="#Health expectancies">see
|
| prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in |
below</a>).</p>
|
| state 2, respectively (the sum is equal to one). e.1=10.39 is the |
|
| Disability-free life expectancy at age 70 (it is again a weighted |
<h5><font color="#EC5E5E" size="3"><b>- Variances of life
|
| mean of e11 and e21). e.2=3.03 is also the life expectancy at age |
expectancies by age and initial health status</b></font><b>: </b><a
|
| 70 to be spent in the disability state.</p> |
href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
|
| |
|
| <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by |
<p>For example, the covariances of life expectancies Cov(ei,ej)
|
| age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>: |
at age 50 are (line 3) </p>
|
| ebiaspar.gif</b></h6> |
|
| |
<pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
|
| <p>This figure represents the health expectancies and the total |
|
| life expectancy with the confident interval in dashed curve. </p> |
<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
| |
name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
|
| <pre> <img src="ebiaspar.gif" width="400" height="300"></pre> |
expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
|
| |
with standard errors in parentheses</b></font><b>: </b><a
|
| <p>Standard deviations (obtained from the information matrix of |
href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
|
| the model) of these quantities are very useful. |
|
| Cross-longitudinal surveys are costly and do not involve huge |
<pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
|
| samples, generally a few thousands; therefore it is very |
|
| important to have an idea of the standard deviation of our |
<pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>
|
| estimates. It has been a big challenge to compute the Health |
|
| Expectancy standard deviations. Don't be confuse: life expectancy |
<p>Thus, at age 70 the total life expectancy, e..=13.76years is
|
| is, as any expected value, the mean of a distribution; but here |
the weighted mean of e1.=13.96 and e2.=11.85 by the stationary
|
| we are not computing the standard deviation of the distribution, |
prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
|
| but the standard deviation of the estimate of the mean.</p> |
state 2, respectively (the sum is equal to one). e.1=10.40 is the
|
| |
Disability-free life expectancy at age 70 (it is again a weighted
|
| <p>Our health expectancies estimates vary according to the sample |
mean of e11 and e21). e.2=3.35 is also the life expectancy at age
|
| size (and the standard deviations give confidence intervals of |
70 to be spent in the disability state.</p>
|
| the estimate) but also according to the model fitted. Let us |
|
| explain it in more details.</p> |
<h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
|
| |
age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
|
| <p>Choosing a model means ar least two kind of choices. First we |
</b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</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>This figure represents the health expectancies and the total
|
| covariables, confonding factors etc. to be included.</p> |
life expectancy with the confident interval in dashed curve. </p>
|
| |
|
| <p>More disability states we have, better is our demographical |
<pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
|
| approach of the disability process, but smaller are the number of |
|
| transitions between each state and higher is the noise in the |
<p>Standard deviations (obtained from the information matrix of
|
| measurement. We do not have enough experiments of the various |
the model) of these quantities are very useful.
|
| models to summarize the advantages and disadvantages, but it is |
Cross-longitudinal surveys are costly and do not involve huge
|
| important to say that even if we had huge and unbiased samples, |
samples, generally a few thousands; therefore it is very
|
| the total life expectancy computed from a cross-longitudinal |
important to have an idea of the standard deviation of our
|
| survey, varies with the number of states. If we define only two |
estimates. It has been a big challenge to compute the Health
|
| states, alive or dead, we find the usual life expectancy where it |
Expectancy standard deviations. Don't be confuse: life expectancy
|
| is assumed that at each age, people are at the same risk to die. |
is, as any expected value, the mean of a distribution; but here
|
| If we are differentiating the alive state into healthy and |
we are not computing the standard deviation of the distribution,
|
| disable, and as the mortality from the disability state is higher |
but the standard deviation of the estimate of the mean.</p>
|
| than the mortality from the healthy state, we are introducing |
|
| heterogeneity in the risk of dying. The total mortality at each |
<p>Our health expectancies estimates vary according to the sample
|
| age is the weighted mean of the mortality in each state by the |
size (and the standard deviations give confidence intervals of
|
| prevalence in each state. Therefore if the proportion of people |
the estimate) but also according to the model fitted. Let us
|
| at each age and in each state is different from the stationary |
explain it in more details.</p>
|
| equilibrium, there is no reason to find the same total mortality |
|
| at a particular age. Life expectancy, even if it is a very useful |
<p>Choosing a model means ar least two kind of choices. First we
|
| tool, has a very strong hypothesis of homogeneity of the |
have to decide the number of disability states. Second we have to
|
| population. Our main purpose is not to measure differential |
design, within the logit model family, the model: variables,
|
| mortality but to measure the expected time in a healthy or |
covariables, confonding factors etc. to be included.</p>
|
| disability state in order to maximise the former and minimize the |
|
| latter. But the differential in mortality complexifies the |
<p>More disability states we have, better is our demographical
|
| measurement.</p> |
approach of the disability process, but smaller are the number of
|
| |
transitions between each state and higher is the noise in the
|
| <p>Incidences of disability or recovery are not affected by the |
measurement. We do not have enough experiments of the various
|
| number of states if these states are independant. But incidences |
models to summarize the advantages and disadvantages, but it is
|
| estimates are dependant on the specification of the model. More |
important to say that even if we had huge and unbiased samples,
|
| covariates we added in the logit model better is the model, but |
the total life expectancy computed from a cross-longitudinal
|
| some covariates are not well measured, some are confounding |
survey, varies with the number of states. If we define only two
|
| factors like in any statistical model. The procedure to "fit |
states, alive or dead, we find the usual life expectancy where it
|
| the best model' is similar to logistic regression which itself is |
is assumed that at each age, people are at the same risk to die.
|
| similar to regression analysis. We haven't yet been sofar because |
If we are differentiating the alive state into healthy and
|
| we also have a severe limitation which is the speed of the |
disable, and as the mortality from the disability state is higher
|
| convergence. On a Pentium III, 500 MHz, even the simplest model, |
than the mortality from the healthy state, we are introducing
|
| estimated by month on 8,000 people may take 4 hours to converge. |
heterogeneity in the risk of dying. The total mortality at each
|
| Also, the program is not yet a statistical package, which permits |
age is the weighted mean of the mortality in each state by the
|
| a simple writing of the variables and the model to take into |
prevalence in each state. Therefore if the proportion of people
|
| account in the maximisation. The actual program allows only to |
at each age and in each state is different from the stationary
|
| add simple variables without covariations, like age+sex but |
equilibrium, there is no reason to find the same total mortality
|
| without age+sex+ age*sex . This can be done from the source code |
at a particular age. Life expectancy, even if it is a very useful
|
| (you have to change three lines in the source code) but will |
tool, has a very strong hypothesis of homogeneity of the
|
| never be general enough. But what is to remember, is that |
population. Our main purpose is not to measure differential
|
| incidences or probability of change from one state to another is |
mortality but to measure the expected time in a healthy or
|
| affected by the variables specified into the model.</p> |
disability state in order to maximise the former and minimize the
|
| |
latter. But the differential in mortality complexifies the
|
| <p>Also, the age range of the people interviewed has a link with |
measurement.</p>
|
| the age range of the life expectancy which can be estimated by |
|
| extrapolation. If your sample ranges from age 70 to 95, you can |
<p>Incidences of disability or recovery are not affected by the
|
| clearly estimate a life expectancy at age 70 and trust your |
number of states if these states are independant. But incidences
|
| confidence interval which is mostly based on your sample size, |
estimates are dependant on the specification of the model. More
|
| but if you want to estimate the life expectancy at age 50, you |
covariates we added in the logit model better is the model, but
|
| should rely in your model, but fitting a logistic model on a age |
some covariates are not well measured, some are confounding
|
| range of 70-95 and estimating probabilties of transition out of |
factors like in any statistical model. The procedure to "fit
|
| this age range, say at age 50 is very dangerous. At least you |
the best model' is similar to logistic regression which itself is
|
| should remember that the confidence interval given by the |
similar to regression analysis. We haven't yet been sofar because
|
| standard deviation of the health expectancies, are under the |
we also have a severe limitation which is the speed of the
|
| strong assumption that your model is the 'true model', which is |
convergence. On a Pentium III, 500 MHz, even the simplest model,
|
| probably not the case.</p> |
estimated by month on 8,000 people may take 4 hours to converge.
|
| |
Also, the program is not yet a statistical package, which permits
|
| <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter |
a simple writing of the variables and the model to take into
|
| file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5> |
account in the maximisation. The actual program allows only to
|
| |
add simple variables like age+sex or age+sex+ age*sex but will
|
| <p>This copy of the parameter file can be useful to re-run the |
never be general enough. But what is to remember, is that
|
| program while saving the old output files. </p> |
incidences or probability of change from one state to another is
|
| |
affected by the variables specified into the model.</p>
|
| <hr> |
|
| |
<p>Also, the age range of the people interviewed has a link with
|
| <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2> |
the age range of the life expectancy which can be estimated by
|
| |
extrapolation. If your sample ranges from age 70 to 95, you can
|
| <p>Since you know how to run the program, it is time to test it |
clearly estimate a life expectancy at age 70 and trust your
|
| on your own computer. Try for example on a parameter file named <a |
confidence interval which is mostly based on your sample size,
|
| href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a |
but if you want to estimate the life expectancy at age 50, you
|
| copy of <font size="2" face="Courier New">mypar.txt</font> |
should rely in your model, but fitting a logistic model on a age
|
| included in the subdirectory of imach, <font size="2" |
range of 70-95 and estimating probabilties of transition out of
|
| face="Courier New">mytry</font>. Edit it to change the name of |
this age range, say at age 50 is very dangerous. At least you
|
| the data file to <font size="2" face="Courier New">..\data\mydata.txt</font> |
should remember that the confidence interval given by the
|
| if you don't want to copy it on the same directory. The file <font |
standard deviation of the health expectancies, are under the
|
| face="Courier New">mydata.txt</font> is a smaller file of 3,000 |
strong assumption that your model is the 'true model', which is
|
| people but still with 4 waves. </p> |
probably not the case.</p>
|
| |
|
| <p>Click on the imach.exe icon to open a window. Answer to the |
<h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
|
| question:'<strong>Enter the parameter file name:'</strong></p> |
file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
|
| |
|
| <table border="1"> |
<p>This copy of the parameter file can be useful to re-run the
|
| <tr> |
program while saving the old output files. </p>
|
| <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter |
|
| the parameter file name: ..\mytry\imachpar.txt</strong></p> |
<hr>
|
| </td> |
|
| </tr> |
<h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
|
| </table> |
|
| |
<p>Since you know how to run the program, it is time to test it
|
| <p>Most of the data files or image files generated, will use the |
on your own computer. Try for example on a parameter file named <a
|
| 'imachpar' string into their name. The running time is about 2-3 |
href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
|
| minutes on a Pentium III. If the execution worked correctly, the |
size="2" face="Courier New">mypar.txt</font> included in the
|
| outputs files are created in the current directory, and should be |
subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
|
| the same as the mypar files initially included in the directory <font |
Edit it to change the name of the data file to <font size="2"
|
| size="2" face="Courier New">mytry</font>.</p> |
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>
|
| <ul> |
is a smaller file of 3,000 people but still with 4 waves. </p>
|
| <li><pre><u>Output on the screen</u> The output screen looks like <a |
|
| href="imachrun.LOG">this Log file</a> |
<p>Click on the imach.exe icon to open a window. Answer to the
|
| # |
question:'<strong>Enter the parameter file name:'</strong></p>
|
| |
|
| title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 |
<table border="1">
|
| ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> |
<tr>
|
| </li> |
<td width="100%"><strong>IMACH, Version 0.64b</strong><p><strong>Enter
|
| <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 |
the parameter file name: ..\mytry\imachpar.txt</strong></p>
|
| |
</td>
|
| Warning, no any valid information for:126 line=126 |
</tr>
|
| Warning, no any valid information for:2307 line=2307 |
</table>
|
| 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> |
<p>Most of the data files or image files generated, will use the
|
| Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 |
'imachpar' string into their name. The running time is about 2-3
|
| prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 |
minutes on a Pentium III. If the execution worked correctly, the
|
| Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> |
outputs files are created in the current directory, and should be
|
| </li> |
the same as the mypar files initially included in the directory <font
|
| </ul> |
size="2" face="Courier New">mytry</font>.</p>
|
| |
|
| <p> </p> |
<ul>
|
| |
<li><pre><u>Output on the screen</u> The output screen looks like <a
|
| <ul> |
href="imachrun.LOG">this Log file</a>
|
| <li>Maximisation with the Powell algorithm. 8 directions are |
#
|
| given corresponding to the 8 parameters. this can be |
|
| rather long to get convergence.<br> |
title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
|
| <font size="1" face="Courier New"><br> |
ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
| Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 |
</li>
|
| 0.000000000000 3<br> |
<li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
|
| 0.000000000000 4 0.000000000000 5 0.000000000000 6 |
|
| 0.000000000000 7 <br> |
Warning, no any valid information for:126 line=126
|
| 0.000000000000 8 0.000000000000<br> |
Warning, no any valid information for:2307 line=2307
|
| 1..........2.................3..........4.................5.........<br> |
Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
|
| 6................7........8...............<br> |
<font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
|
| Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 |
Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
|
| <br> |
prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
|
| 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br> |
Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
|
| 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br> |
</li>
|
| 8 0.051272038506<br> |
</ul>
|
| 1..............2...........3..............4...........<br> |
|
| 5..........6................7...........8.........<br> |
<p> </p>
|
| #Number of iterations = 23, -2 Log likelihood = |
|
| 6744.954042573691<br> |
<ul>
|
| # Parameters<br> |
<li>Maximisation with the Powell algorithm. 8 directions are
|
| 12 -12.966061 0.135117 <br> |
given corresponding to the 8 parameters. this can be
|
| 13 -7.401109 0.067831 <br> |
rather long to get convergence.<br>
|
| 21 -0.672648 -0.006627 <br> |
<font size="1" face="Courier New"><br>
|
| 23 -5.051297 0.051271 </font><br> |
Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
|
| </li> |
0.000000000000 3<br>
|
| <li><pre><font size="2">Calculation of the hessian matrix. Wait... |
0.000000000000 4 0.000000000000 5 0.000000000000 6
|
| 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 |
0.000000000000 7 <br>
|
| |
0.000000000000 8 0.000000000000<br>
|
| Inverting the hessian to get the covariance matrix. Wait... |
1..........2.................3..........4.................5.........<br>
|
| |
6................7........8...............<br>
|
| #Hessian matrix# |
Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
|
| 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 |
<br>
|
| 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 |
2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
|
| -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 |
5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
|
| -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 |
8 0.051272038506<br>
|
| -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..............2...........3..............4...........<br>
|
| -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 |
5..........6................7...........8.........<br>
|
| 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 |
#Number of iterations = 23, -2 Log likelihood =
|
| 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 |
6744.954042573691<br>
|
| # Scales |
# Parameters<br>
|
| 12 1.00000e-004 1.00000e-006 |
12 -12.966061 0.135117 <br>
|
| 13 1.00000e-004 1.00000e-006 |
13 -7.401109 0.067831 <br>
|
| 21 1.00000e-003 1.00000e-005 |
21 -0.672648 -0.006627 <br>
|
| 23 1.00000e-004 1.00000e-005 |
23 -5.051297 0.051271 </font><br>
|
| # Covariance |
</li>
|
| 1 5.90661e-001 |
<li><pre><font size="2">Calculation of the hessian matrix. Wait...
|
| 2 -7.26732e-003 8.98810e-005 |
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
|
| 3 8.80177e-002 -1.12706e-003 5.15824e-001 |
|
| 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 |
Inverting the hessian to get the covariance matrix. Wait...
|
| 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 |
#Hessian matrix#
|
| 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 |
3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
|
| 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 |
2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
|
| # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). |
-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
|
| agemin=70 agemax=100 bage=50 fage=100 |
-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
|
| Computing prevalence limit: result on file 'plrmypar.txt' |
3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
|
| Computing pij: result on file 'pijrmypar.txt' |
3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
|
| Computing Health Expectancies: result on file 'ermypar.txt' |
# Scales
|
| Computing Variance-covariance of DFLEs: file 'vrmypar.txt' |
12 1.00000e-004 1.00000e-006
|
| Computing Total LEs with variances: file 'trmypar.txt' |
13 1.00000e-004 1.00000e-006
|
| Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' |
21 1.00000e-003 1.00000e-005
|
| End of Imach |
23 1.00000e-004 1.00000e-005
|
| </font></pre> |
# Covariance
|
| </li> |
1 5.90661e-001
|
| </ul> |
2 -7.26732e-003 8.98810e-005
|
| |
3 8.80177e-002 -1.12706e-003 5.15824e-001
|
| <p><font size="3">Once the running is finished, the program |
4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
|
| requires a caracter:</font></p> |
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
|
| <table border="1"> |
7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
|
| <tr> |
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
|
| <td width="100%"><strong>Type g for plotting (available |
# agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
|
| if mle=1), e to edit output files, c to start again,</strong><p><strong>and |
|
| q for exiting:</strong></p> |
|
| </td> |
agemin=70 agemax=100 bage=50 fage=100
|
| </tr> |
Computing prevalence limit: result on file 'plrmypar.txt'
|
| </table> |
Computing pij: result on file 'pijrmypar.txt'
|
| |
Computing Health Expectancies: result on file 'ermypar.txt'
|
| <p><font size="3">First you should enter <strong>g</strong> to |
Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
|
| make the figures and then you can edit all the results by typing <strong>e</strong>. |
Computing Total LEs with variances: file 'trmypar.txt'
|
| </font></p> |
Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
|
| |
End of Imach
|
| <ul> |
</font></pre>
|
| <li><u>Outputs files</u> <br> |
</li>
|
| - index.htm, this file is the master file on which you |
</ul>
|
| should click first.<br> |
|
| - Observed prevalence in each state: <a |
<p><font size="3">Once the running is finished, the program
|
| href="..\mytry\prmypar.txt">mypar.txt</a> <br> |
requires a caracter:</font></p>
|
| - Estimated parameters and the covariance matrix: <a |
|
| href="..\mytry\rmypar.txt">rmypar.txt</a> <br> |
<table border="1">
|
| - Stationary prevalence in each state: <a |
<tr>
|
| href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br> |
<td width="100%"><strong>Type e to edit output files, c
|
| - Transition probabilities: <a |
to start again, and q for exiting:</strong></td>
|
| href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br> |
</tr>
|
| - Copy of the parameter file: <a |
</table>
|
| href="..\mytry\ormypar.txt">ormypar.txt</a> <br> |
|
| - Life expectancies by age and initial health status: <a |
<p><font size="3">First you should enter <strong>e </strong>to
|
| href="..\mytry\ermypar.txt">ermypar.txt</a> <br> |
edit the master file mypar.htm. </font></p>
|
| - Variances of life expectancies by age and initial |
|
| health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> |
<ul>
|
| <br> |
<li><u>Outputs files</u> <br>
|
| - Health expectancies with their variances: <a |
<br>
|
| href="..\mytry\trmypar.txt">trmypar.txt</a> <br> |
- Observed prevalence in each state: <a
|
| - Standard deviation of stationary prevalence: <a |
href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
|
| href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br> |
- Estimated parameters and the covariance matrix: <a
|
| <br> |
href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
|
| </li> |
- Stationary prevalence in each state: <a
|
| <li><u>Graphs</u> <br> |
href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
|
| <br> |
- Transition probabilities: <a
|
| -<a href="..\mytry\vmypar1.gif">Observed and stationary |
href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
|
| prevalence in state (1) with the confident interval</a> <br> |
- Copy of the parameter file: <a
|
| -<a href="..\mytry\vmypar2.gif">Observed and stationary |
href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
|
| prevalence in state (2) with the confident interval</a> <br> |
- Life expectancies by age and initial health status: <a
|
| -<a href="..\mytry\exmypar1.gif">Health life expectancies |
href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
|
| by age and initial health state (1)</a> <br> |
- Variances of life expectancies by age and initial
|
| -<a href="..\mytry\exmypar2.gif">Health life expectancies |
health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
|
| by age and initial health state (2)</a> <br> |
<br>
|
| -<a href="..\mytry\emypar.gif">Total life expectancy by |
- Health expectancies with their variances: <a
|
| age and health expectancies in states (1) and (2).</a> </li> |
href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
|
| </ul> |
- Standard deviation of stationary prevalence: <a
|
| |
href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>
|
| <p>This software have been partly granted by <a |
<br>
|
| href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted |
</li>
|
| action from the European Union. It will be copyrighted |
<li><u>Graphs</u> <br>
|
| identically to a GNU software product, i.e. program and software |
<br>
|
| can be distributed freely for non commercial use. Sources are not |
-<a href="../mytry/pemypar1.gif">One-step transition
|
| widely distributed today. You can get them by asking us with a |
probabilities</a><br>
|
| simple justification (name, email, institute) <a |
-<a href="../mytry/pmypar11.gif">Convergence to the
|
| href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a |
stationary prevalence</a><br>
|
| href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p> |
-<a href="..\mytry\vmypar11.gif">Observed and stationary
|
| |
prevalence in state (1) with the confident interval</a> <br>
|
| <p>Latest version (0.63 of 16 march 2000) can be accessed at <a |
-<a href="..\mytry\vmypar21.gif">Observed and stationary
|
| href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br> |
prevalence in state (2) with the confident interval</a> <br>
|
| </p> |
-<a href="..\mytry\expmypar11.gif">Health life
|
| </body> |
expectancies by age and initial health state (1)</a> <br>
|
| </html> |
-<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 (0.64b of may 2001) can be accessed at <a
|
| |
href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
|
| |
</p>
|
| |
</body>
|
| |
</html>
|
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