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<H1 align=center><FONT color=#00006a>Computing Health Expectancies using
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| <html>
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IMaCh</FONT></H1>
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<H1 align=center><FONT color=#00006a size=5>(a Maximum Likelihood Computer
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| <head>
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Program using Interpolation of Markov Chains)</FONT></H1>
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<P align=center> </P>
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<P align=center><A href="http://www.ined.fr/"><IMG border=0 height=76
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| <title>IMaCh</title>
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src="Computing Health Expectancies using IMaCh_fichiers/logo-ined.gif"
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width=151></P>
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<H3 align=center><A href="http://www.ined.fr/"><FONT
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| <hr size="3" color="#EC5E5E">
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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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| <h1 align="center"><font color="#00006A">Computing Health
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<P align=center><FONT color=#00006a size=4><STRONG>Version 0.97, June
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| Expectancies using IMaCh</font></h1>
|
2004</STRONG></FONT></P>
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|
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<HR color=#ec5e5e SIZE=3>
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| <h1 align="center"><font color="#00006A" size="5">(a Maximum
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|
| Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
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<P align=center><FONT color=#00006a><STRONG>Authors of the program:
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|
|
</STRONG></FONT><A href="http://sauvy.ined.fr/brouard"><FONT
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| <p align="center"> </p>
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color=#00006a><STRONG>Nicolas Brouard</STRONG></FONT></A><FONT
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|
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color=#00006a><STRONG>, senior researcher at the </STRONG></FONT><A
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| <p align="center"><a href="http://www.ined.fr/"><img
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href="http://www.ined.fr/"><FONT color=#00006a><STRONG>Institut National
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| src="logo-ined.gif" border="0" width="151" height="76"></a><img
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d'Etudes Démographiques</STRONG></FONT></A><FONT color=#00006a><STRONG> (INED,
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| src="euroreves2.gif" width="151" height="75"></p>
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Paris) in the "Mortality, Health and Epidemiology" Research Unit
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</STRONG></FONT></P>
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| <h3 align="center"><a href="http://www.ined.fr/"><font
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<P align=center><FONT color=#00006a><STRONG>and Agnès Lièvre<BR
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| color="#00006A">INED</font></a><font color="#00006A"> and </font><a
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clear=left></STRONG></FONT></P>
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| href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
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<H4><FONT color=#00006a>Contribution to the mathematics: C. R. Heathcote
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|
|
</FONT><FONT color=#00006a size=2>(Australian National University,
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| <p align="center"><font color="#00006A" size="4"><strong>Version
|
Canberra).</FONT></H4>
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| 0.8a, May 2002</strong></font></p>
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<H4><FONT color=#00006a>Contact: Agnès Lièvre (</FONT><A
|
|
|
href="mailto:lievre@ined.fr"><FONT
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| <hr size="3" color="#EC5E5E">
|
color=#00006a><I>lievre@ined.fr</I></FONT></A><FONT color=#00006a>) </FONT></H4>
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|
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<HR>
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| <p align="center"><font color="#00006A"><strong>Authors of the
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|
| program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
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<UL>
|
| color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
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<LI><A
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| color="#00006A"><strong>, senior researcher at the </strong></font><a
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href="http://euroreves.ined.fr/imach/doc/imach.htm#intro">Introduction</A>
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| href="http://www.ined.fr"><font color="#00006A"><strong>Institut
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#data">On what kind
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| National d'Etudes Démographiques</strong></font></a><font
|
of data can it be used?</A>
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| color="#00006A"><strong> (INED, Paris) in the "Mortality,
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#datafile">The data
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| Health and Epidemiology" Research Unit </strong></font></p>
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file</A>
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|
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#biaspar">The
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| <p align="center"><font color="#00006A"><strong>and Agnès
|
parameter file</A>
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| Lièvre<br clear="left">
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#running">Running
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| </strong></font></p>
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Imach</A>
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|
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#output">Output files
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| <h4><font color="#00006A">Contribution to the mathematics: C. R.
|
and graphs</A>
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| Heathcote </font><font color="#00006A" size="2">(Australian
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<LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#example">Exemple</A>
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| National University, Canberra).</font></h4>
|
</LI></UL>
|
|
|
<HR>
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| <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
|
|
| href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
|
<H2><A name=intro><FONT color=#00006a>Introduction</FONT></A></H2>
|
| color="#00006A">) </font></h4>
|
<P>This program computes <B>Healthy Life Expectancies</B> from
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|
|
<B>cross-longitudinal data</B> using the methodology pioneered by Laditka and
|
| <hr>
|
Wolf (1). Within the family of Health Expectancies (HE), disability-free life
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|
|
expectancy (DFLE) is probably the most important index to monitor. In low
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| <ul>
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mortality countries, there is a fear that when mortality declines (and therefore total life expectancy improves), the increase will not be as great, leading to an <EM>Expansion of morbidity</EM>. Most of the data collected today,
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| <li><a href="#intro">Introduction</a> </li>
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in particular by the international <A href="http://www.reves.org/">REVES</A>
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| <li><a href="#data">On what kind of data can it be used?</a></li>
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network on Health Expectancy and the disability process, and most HE indices based on these data, are
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| <li><a href="#datafile">The data file</a> </li>
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<EM>cross-sectional</EM>. This means that the information collected comes from a
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| <li><a href="#biaspar">The parameter file</a> </li>
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single cross-sectional survey: people from a variety of ages (but often old people)
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| <li><a href="#running">Running Imach</a> </li>
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are surveyed on their health status at a single date. The proportion of people
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| <li><a href="#output">Output files and graphs</a> </li>
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disabled at each age can then be estimated at that date. This age-specific
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| <li><a href="#example">Exemple</a> </li>
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prevalence curve is used to distinguish, within the stationary population
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| </ul>
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(which, by definition, is the life table estimated from the vital statistics on
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|
|
mortality at the same date), the disabled population from the disability-free
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| <hr>
|
population. Life expectancy (LE) (or total population divided by the yearly
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|
|
number of births or deaths of this stationary population) is then decomposed
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| <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
|
into disability-free life expectancy (DFLE) and disability life
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|
|
expectancy (DLE). This method of computing HE is usually called the Sullivan
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| <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
|
method (after the author who first described it).</P>
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| data</b> using the methodology pioneered by Laditka and Wolf (1).
|
<P>The age-specific proportions of people disabled (prevalence of disability) are
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| Within the family of Health Expectancies (HE), Disability-free
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dependent upon the historical flows from entering disability and recovering in the past. The age-specific forces (or incidence rates) of entering
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| life expectancy (DFLE) is probably the most important index to
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disability or recovering a good health, estimated over a recent period of time (as period forces of mortality), are reflecting current conditions and
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| monitor. In low mortality countries, there is a fear that when
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therefore can be used at each age to forecast the future of this cohort <EM>if
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| mortality declines, the increase in DFLE is not proportionate to
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nothing changes in the future</EM>, i.e to forecast the prevalence of disability of each cohort. Our finding (2) is that the period prevalence of disability
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| the increase in total Life expectancy. This case is called the <em>Expansion
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(computed from period incidences) is lower than the cross-sectional prevalence.
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| of morbidity</em>. Most of the data collected today, in
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For example if a country is improving its technology of prosthesis, the
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| particular by the international <a href="http://www.reves.org">REVES</a>
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incidence of recovering the ability to walk will be higher at each (old) age,
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| network on Health expectancy, and most HE indices based on these
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but the prevalence of disability will only slightly reflect an improvement because
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| data, are <em>cross-sectional</em>. It means that the information
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the prevalence is mostly affected by the history of the cohort and not by recent
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| collected comes from a single cross-sectional survey: people from
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period effects. To measure the period improvement we have to simulate the future
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| various ages (but mostly old people) are surveyed on their health
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of a cohort of new-borns entering or leaving the disability state or
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| status at a single date. Proportion of people disabled at each
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dying at each age according to the incidence rates measured today on different cohorts. The
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| age, can then be measured at that date. This age-specific
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proportion of people disabled at each age in this simulated cohort will be much
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| prevalence curve is then used to distinguish, within the
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lower that the proportions observed at each age in a cross-sectional survey.
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| stationary population (which, by definition, is the life table
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This new prevalence curve introduced in a life table will give a more realistic
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| estimated from the vital statistics on mortality at the same
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HE level than the Sullivan method which mostly reflects the history of health
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| date), the disable population from the disability-free
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conditions in a country.</P>
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| population. Life expectancy (LE) (or total population divided by
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<P>Therefore, the main question is how can we measure incidence rates from
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| the yearly number of births or deaths of this stationary
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cross-longitudinal surveys? This is the goal of the IMaCH program. From your
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| population) is then decomposed into DFLE and DLE. This method of
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data and using IMaCH you can estimate period HE as well as the Sullivan HE. In addition the standard errors of the HE are computed.</P>
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| computing HE is usually called the Sullivan method (from the name
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<P>A cross-longitudinal survey consists of a first survey ("cross") where
|
| of the author who first described it).</p>
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individuals of different ages are interviewed about their health status or degree
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|
|
of disability. At least a second wave of interviews ("longitudinal") should
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| <p>Age-specific proportions of people disable are very difficult
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measure each individual new health status. Health expectancies are computed from
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| to forecast because each proportion corresponds to historical
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the transitions observed between waves (interviews) and are computed for each degree of
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| conditions of the cohort and it is the result of the historical
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severity of disability (number of health states). The more degrees of severity considered, the more
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| flows from entering disability and recovering in the past until
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time is necessary to reach the Maximum Likelihood of the parameters involved in
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| today. The age-specific intensities (or incidence rates) of
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the model. Considering only two states of disability (disabled and healthy) is
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| entering disability or recovering a good health, are reflecting
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generally enough but the computer program works also with more health
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| actual conditions and therefore can be used at each age to
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states.<BR><BR>The simplest model for the transition probabilities is the multinomial logistic model where
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| forecast the future of this cohort. For example if a country is
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<I>pij</I> is the probability to be observed in state <I>j</I> at the second
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| improving its technology of prosthesis, the incidence of
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wave conditional to be observed in state <EM>i</EM> at the first wave. Therefore
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| recovering the ability to walk will be higher at each (old) age,
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a simple model is: log<EM>(pij/pii)= aij + bij*age+ cij*sex,</EM> where
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| but the prevalence of disability will only slightly reflect an
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'<I>age</I>' is age and '<I>sex</I>' is a covariate. The advantage that this
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| improve because the prevalence is mostly affected by the history
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computer program claims, is that if the delay between waves is not
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| of the cohort and not by recent period effects. To measure the
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identical for each individual, or if some individual missed an interview, the
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| period improvement we have to simulate the future of a cohort of
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information is not rounded or lost, but taken into account using an
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| new-borns entering or leaving at each age the disability state or
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interpolation or extrapolation. <I>hPijx</I> is the probability to be observed
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| dying according to the incidence rates measured today on
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in state <I>i</I> at age <I>x+h</I> conditional on the observed state <I>i</I>
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| different cohorts. The proportion of people disabled at each age
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at age <I>x</I>. The delay '<I>h</I>' can be split into an exact number
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| in this simulated cohort will be much lower (using the exemple of
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(<I>nh*stepm</I>) of unobserved intermediate states. This elementary transition
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| an improvement) that the proportions observed at each age in a
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(by month or quarter, trimester, semester or year) is modeled as the above multinomial
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| cross-sectional survey. This new prevalence curve introduced in a
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logistic. The <I>hPx</I> matrix is simply the matrix product of <I>nh*stepm</I>
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| life table will give a much more actual and realistic HE level
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elementary matrices and the contribution of each individual to the likelihood is
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| than the Sullivan method which mostly measured the History of
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simply <I>hPijx</I>. <BR></P>
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| health conditions in this country.</p>
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<P>The program presented in this manual is a general program named
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|
|
<STRONG>IMaCh</STRONG> (for <STRONG>I</STRONG>nterpolated
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| <p>Therefore, the main question is how to measure incidence rates
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<STRONG>MA</STRONG>rkov <STRONG>CH</STRONG>ain), designed to analyse transitions from longitudinal surveys. The first step is the estimation of the set of the parameters of a model for the
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| from cross-longitudinal surveys? This is the goal of the IMaCH
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transition probabilities between an initial state and a final state.
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| program. From your data and using IMaCH you can estimate period
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From there, the computer program produces indicators such as the observed and
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| HE and not only Sullivan's HE. Also the standard errors of the HE
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stationary prevalence, life expectancies and their variances both numerically and graphically. Our
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| are computed.</p>
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transition model consists of absorbing and non-absorbing states assuming the
|
|
|
possibility of return across the non-absorbing states. The main advantage of
|
| <p>A cross-longitudinal survey consists in a first survey
|
this package, compared to other programs for the analysis of transition data
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| ("cross") where individuals from different ages are
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(for example: Proc Catmod of SAS<SUP>®</SUP>) is that the whole individual
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| interviewed on their health status or degree of disability. At
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information is used even if an interview is missing, a state or a date is
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| least a second wave of interviews ("longitudinal")
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unknown or when the delay between waves is not identical for each individual.
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| should measure each new individual health status. Health
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The program is dependent upon a set of parameters inputted by the user: selection of a sub-sample,
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| expectancies are computed from the transitions observed between
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number of absorbing and non-absorbing states, number of waves to be taken in account , a tolerance level for the
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| waves and are computed for each degree of severity of disability
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maximization function, the periodicity of the transitions (we can compute
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| (number of life states). More degrees you consider, more time is
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annual, quarterly or monthly transitions), covariates in the model. IMaCh works on
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| necessary to reach the Maximum Likelihood of the parameters
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Windows or on Unix platform.<BR></P>
|
| involved in the model. Considering only two states of disability
|
<HR>
|
| (disable and healthy) is generally enough but the computer
|
|
| program works also with more health statuses.<br>
|
<P>(1) Laditka S. B. and Wolf, D. (1998), New Methods for Analyzing
|
| <br>
|
Active Life Expectancy. <I>Journal of Aging and Health</I>. Vol 10, No. 2. </P>
|
| The simplest model is the multinomial logistic model where <i>pij</i>
|
<P>(2) <A
|
| is the probability to be observed in state <i>j</i> at the second
|
href="http://taylorandfrancis.metapress.com/app/home/contribution.asp?wasp=1f99bwtvmk5yrb7hlhw3&referrer=parent&backto=issue,1,2;journal,2,5;linkingpublicationresults,1:300265,1">Lièvre
|
| wave conditional to be observed in state <em>i</em> at the first
|
A., Brouard N. and Heathcote Ch. (2003) Estimating Health Expectancies from
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| wave. Therefore a simple model is: log<em>(pij/pii)= aij +
|
Cross-longitudinal surveys. <EM>Mathematical Population Studies</EM>.- 10(4),
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| bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
|
pp. 211-248</A>
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| is a covariate. The advantage that this computer program claims,
|
<HR>
|
| comes from that if the delay between waves is not identical for
|
|
| each individual, or if some individual missed an interview, the
|
<H2><A name=data><FONT color=#00006a>What kind of data is required?</FONT></A></H2>
|
| information is not rounded or lost, but taken into account using
|
<P>The minimum data required for a transition model is the recording of a set of
|
| an interpolation or extrapolation. <i>hPijx</i> is the
|
individuals interviewed at a first date and interviewed once more. From the observations of an individual, we obtain a follow-up over
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| probability to be observed in state <i>i</i> at age <i>x+h</i>
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time of the occurrence of a specific event. In this documentation, the event is
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| conditional to the observed state <i>i</i> at age <i>x</i>. The
|
related to health state, but the program can be applied to many
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| delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
|
longitudinal studies with different contexts. To build the data file
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| of unobserved intermediate states. This elementary transition (by
|
as explained
|
| month or quarter trimester, semester or year) is modeled as a
|
in the next section, you must have the month and year of each interview and
|
| multinomial logistic. The <i>hPx</i> matrix is simply the matrix
|
the corresponding health state. In order to get age, date of birth (month
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| product of <i>nh*stepm</i> elementary matrices and the
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and year) are required (missing values are allowed for month). Date of death
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| contribution of each individual to the likelihood is simply <i>hPijx</i>.
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(month and year) is an important information also required if the individual is
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| <br>
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dead. Shorter steps (i.e. a month) will more closely take into account the
|
| </p>
|
survival time after the last interview.</P>
|
|
|
<HR>
|
| <p>The program presented in this manual is a quite general
|
|
| program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
|
<H2><A name=datafile><FONT color=#00006a>The data file</FONT></A></H2>
|
| <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
|
<P>In this example, 8,000 people have been interviewed in a cross-longitudinal
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| analyse transition data from longitudinal surveys. The first step
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survey of 4 waves (1984, 1986, 1988, 1990). Some people missed 1, 2 or 3
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| is the parameters estimation of a transition probabilities model
|
interviews. Health states are healthy (1) and disabled (2). The survey is not a
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| between an initial status and a final status. From there, the
|
real one but a simulation of the American Longitudinal Survey on Aging. The
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| computer program produces some indicators such as observed and
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disability state is defined as dependence in at least one of four ADLs (Activities
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| stationary prevalence, life expectancies and their variances and
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of daily living, like bathing, eating, walking). Therefore, even if the
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| graphs. Our transition model consists in absorbing and
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individuals interviewed in the sample are virtual, the information in
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| non-absorbing states with the possibility of return across the
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this sample is close to reality for the United States. Sex is not recorded
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| non-absorbing states. The main advantage of this package,
|
is this sample. The LSOA survey is biased in the sense that people
|
| compared to other programs for the analysis of transition data
|
living in an institution were not included in the first interview in
|
| (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
|
1984. Thus the prevalence of disability observed in 1984 is lower than
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| individual information is used even if an interview is missing, a
|
the true prevalence at old ages. However when people moved into an
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| status or a date is unknown or when the delay between waves is
|
institution, they were interviewed there in 1986, 1988 and 1990. Thus
|
| not identical for each individual. The program can be executed
|
the incidences of disabilities are not biased. Cross-sectional
|
| according to parameters: selection of a sub-sample, number of
|
prevalences of disability at old ages are thus artificially increasing in 1986,
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| absorbing and non-absorbing states, number of waves taken in
|
1988 and 1990 because of a greater proportion of the sample
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| account (the user inputs the first and the last interview), a
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institutionalized. Our article (Lièvre A., Brouard N. and Heathcote
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| tolerance level for the maximization function, the periodicity of
|
Ch. (2003)) shows the opposite: the period prevalence based on the
|
| the transitions (we can compute annual, quarterly or monthly
|
incidences is lower at old
|
| transitions), covariates in the model. It works on Windows or on
|
ages than the adjusted cross-sectional prevalence illustrating that
|
| Unix.<br>
|
there has been significant progress against disability.</P>
|
| </p>
|
<P>Each line of the data set (named <A
|
|
|
href="http://euroreves.ined.fr/imach/doc/data1.txt">data1.txt</A> in this first
|
| <hr>
|
example) is an individual record. Fields are separated by blanks: </P>
|
|
|
<UL>
|
| <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
|
<LI><B>Index number</B>: positive number (field 1)
|
| Methods for Analyzing Active Life Expectancy". <i>Journal of
|
<LI><B>First covariate</B> positive number (field 2)
|
| Aging and Health</i>. Vol 10, No. 2. </p>
|
<LI><B>Second covariate</B> positive number (field 3)
|
|
|
<LI><A name=Weight><B>Weight</B></A>: positive number (field 4) . In most
|
| <hr>
|
surveys individuals are weighted to account for stratification of the
|
|
|
sample.
|
| <h2><a name="data"><font color="#00006A">On what kind of data can
|
<LI><B>Date of birth</B>: coded as mm/yyyy. Missing dates are coded as 99/9999
|
| it be used?</font></a></h2>
|
(field 5)
|
|
|
<LI><B>Date of death</B>: coded as mm/yyyy. Missing dates are coded as 99/9999
|
| <p>The minimum data required for a transition model is the
|
(field 6)
|
| recording of a set of individuals interviewed at a first date and
|
<LI><B>Date of first interview</B>: coded as mm/yyyy. Missing dates are coded
|
| interviewed again at least one another time. From the
|
as 99/9999 (field 7)
|
| observations of an individual, we obtain a follow-up over time of
|
<LI><B>Status at first interview</B>: positive number. Missing values ar coded
|
| the occurrence of a specific event. In this documentation, the
|
-1. (field 8)
|
| event is related to health status at older ages, but the program
|
<LI><B>Date of second interview</B>: coded as mm/yyyy. Missing dates are coded
|
| can be applied on a lot of longitudinal studies in different
|
as 99/9999 (field 9)
|
| contexts. To build the data file explained into the next section,
|
<LI><STRONG>Status at second interview</STRONG> positive number. Missing
|
| you must have the month and year of each interview and the
|
values ar coded -1. (field 10)
|
| corresponding health status. But in order to get age, date of
|
<LI><B>Date of third interview</B>: coded as mm/yyyy. Missing dates are coded
|
| birth (month and year) is required (missing values is allowed for
|
as 99/9999 (field 11)
|
| month). Date of death (month and year) is an important
|
<LI><STRONG>Status at third interview</STRONG> positive number. Missing values
|
| information also required if the individual is dead. Shorter
|
ar coded -1. (field 12)
|
| steps (i.e. a month) will more closely take into account the
|
<LI><B>Date of fourth interview</B>: coded as mm/yyyy. Missing dates are coded
|
| survival time after the last interview.</p>
|
as 99/9999 (field 13)
|
|
|
<LI><STRONG>Status at fourth interview</STRONG> positive number. Missing
|
| <hr>
|
values are coded -1. (field 14)
|
|
|
<LI>etc </LI></UL>
|
| <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
|
<P> </P>
|
|
|
<P>If you do not wish to include information on weights or
|
| <p>In this example, 8,000 people have been interviewed in a
|
covariates, you must fill the column with a number (e.g. 1) since all
|
| cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
|
fields must be present.</P>
|
| Some people missed 1, 2 or 3 interviews. Health statuses are
|
<HR>
|
| healthy (1) and disable (2). The survey is not a real one. It is
|
|
| a simulation of the American Longitudinal Survey on Aging. The
|
<H2><FONT color=#00006a>Your first example parameter file</FONT><A
|
| disability state is defined if the individual missed one of four
|
href="http://euroreves.ined.fr/imach"></A><A name=uio></A></H2>
|
| ADL (Activity of daily living, like bathing, eating, walking).
|
<H2><A name=biaspar></A>#Imach version 0.97b, June 2004, INED-EUROREVES </H2>
|
| Therefore, even is the individuals interviewed in the sample are
|
<P>This first line was a comment. Comments line start with a '#'.</P>
|
| virtual, the information brought with this sample is close to the
|
<H4><FONT color=#ff0000>First uncommented line</FONT></H4><PRE>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</PRE>
|
| situation of the United States. Sex is not recorded is this
|
<UL>
|
| sample.</p>
|
<LI><B>title=</B> 1st_example is title of the run.
|
|
|
<LI><B>datafile=</B> data1.txt is the name of the data set. Our example is a
|
| <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
|
six years follow-up survey. It consists of a baseline followed by 3
|
| in this first example) is an individual record which fields are: </p>
|
reinterviews.
|
|
|
<LI><B>lastobs=</B> 8600 the program is able to run on a subsample where the
|
| <ul>
|
last observation number is lastobs. It can be set a bigger number than the
|
| <li><b>Index number</b>: positive number (field 1) </li>
|
real number of observations (e.g. 100000). In this example, maximisation will
|
| <li><b>First covariate</b> positive number (field 2) </li>
|
be done on the first 8600 records.
|
| <li><b>Second covariate</b> positive number (field 3) </li>
|
<LI><B>firstpass=1</B> , <B>lastpass=4 </B>If there are more than two interviews
|
| <li><a name="Weight"><b>Weight</b></a>: positive number
|
in the survey, the program can be run on selected transitions periods.
|
| (field 4) . In most surveys individuals are weighted
|
firstpass=1 means the first interview included in the calculation is the
|
| according to the stratification of the sample.</li>
|
baseline survey. lastpass=4 means that the last interview to be
|
| <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
|
included will be by the 4th. </LI></UL>
|
| coded as 99/9999 (field 5) </li>
|
<P> </P>
|
| <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
|
<H4><A name=biaspar-2><FONT color=#ff0000>Second uncommented
|
| coded as 99/9999 (field 6) </li>
|
line</FONT></A></H4><PRE>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</PRE>
|
| <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
|
<UL>
|
| dates are coded as 99/9999 (field 7) </li>
|
<LI><B>ftol=1e-8</B> Convergence tolerance on the function value in the
|
| <li><b>Status at first interview</b>: positive number.
|
maximisation of the likelihood. Choosing a correct value for ftol is
|
| Missing values ar coded -1. (field 8) </li>
|
difficult. 1e-8 is the correct value for a 32 bit computer.
|
| <li><b>Date of second interview</b>: coded as mm/yyyy.
|
<LI><B>stepm=1</B> The time unit in months for interpolation. Examples:
|
| Missing dates are coded as 99/9999 (field 9) </li>
|
<UL>
|
| <li><strong>Status at second interview</strong> positive
|
<LI>If stepm=1, the unit is a month
|
| number. Missing values ar coded -1. (field 10) </li>
|
<LI>If stepm=4, the unit is a trimester
|
| <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
|
<LI>If stepm=12, the unit is a year
|
| dates are coded as 99/9999 (field 11) </li>
|
<LI>If stepm=24, the unit is two years
|
| <li><strong>Status at third interview</strong> positive
|
<LI>... </LI></UL>
|
| number. Missing values ar coded -1. (field 12) </li>
|
<LI><B>ncovcol=2</B> Number of covariate columns included in the datafile
|
| <li><b>Date of fourth interview</b>: coded as mm/yyyy.
|
before the column for the date of birth. You can include covariates
|
| Missing dates are coded as 99/9999 (field 13) </li>
|
that will not be used in the model as this number is not the number of covariates that will
|
| <li><strong>Status at fourth interview</strong> positive
|
be specified by the model. The 'model' syntax describes the covariates to be
|
| number. Missing values are coded -1. (field 14) </li>
|
taken into account during the run.
|
| <li>etc</li>
|
<LI><B>nlstate=2</B> Number of non-absorbing (alive) states. Here we have two
|
| </ul>
|
alive states: disability-free is coded 1 and disability is coded 2.
|
|
|
<LI><B>ndeath=1</B> Number of absorbing states. The absorbing state death is
|
| <p> </p>
|
coded 3.
|
|
|
<LI><B>maxwav=4</B> Number of waves in the datafile.
|
| <p>If your longitudinal survey do not include information about
|
<LI><A name=mle><B>mle</B></A><B>=1</B> Option for the Maximisation Likelihood
|
| weights or covariates, you must fill the column with a number
|
Estimation.
|
| (e.g. 1) because a missing field is not allowed.</p>
|
<UL>
|
|
|
<LI>If mle=1 the program does the maximisation and the calculation of health
|
| <hr>
|
expectancies
|
|
|
<LI>If mle=0 the program only does the calculation of the health
|
| <h2><font color="#00006A">Your first example parameter file</font><a
|
expectancies and other indices and graphs but without the maximization.
|
| href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
|
There are also other possible values:
|
|
|
<UL>
|
| <h2><a name="biaspar"></a>#Imach version 0.8a, May 2002,
|
<LI>If mle=-1 you get a template for the number of parameters
|
| INED-EUROREVES </h2>
|
and the size of the variance-covariance matrix. This is useful if the model is
|
|
|
complex with many covariates.
|
| <p>This is a comment. Comments start with a '#'.</p>
|
<LI>If mle=-3 IMaCh computes the mortality but without any health status
|
|
|
(May 2004)
|
| <h4><font color="#FF0000">First uncommented line</font></h4>
|
<LI>If mle=2 IMach likelihood corresponds to a linear interpolation
|
|
|
<LI>If mle=3 IMach likelihood corresponds to an exponential
|
| <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
|
inter-extrapolation
|
|
|
<LI>If mle=4 IMach likelihood corresponds to no inter-extrapolation, thus biasing the results.
|
| <ul>
|
<LI>If mle=5 IMach likelihood corresponds to no inter-extrapolation, and
|
| <li><b>title=</b> 1st_example is title of the run. </li>
|
before the correction of the Jackson's bug (avoid this). </LI></UL></LI></UL>
|
| <li><b>datafile=</b> data1.txt is the name of the data set.
|
<LI><B>weight=0</B> Provides the possibility of adding weights.
|
| Our example is a six years follow-up survey. It consists
|
<UL>
|
| in a baseline followed by 3 reinterviews. </li>
|
<LI>If weight=0 no weights are included
|
| <li><b>lastobs=</b> 8600 the program is able to run on a
|
<LI>If weight=1 the maximisation integrates the weights which are in field
|
| subsample where the last observation number is lastobs.
|
<A href="http://euroreves.ined.fr/imach/doc/imach.htm#Weight">4</A>
|
| It can be set a bigger number than the real number of
|
</LI></UL></LI></UL>
|
| observations (e.g. 100000). In this example, maximisation
|
<H4><FONT color=#ff0000>Covariates</FONT></H4>
|
| will be done on the 8600 first records. </li>
|
<P>Intercept and age are automatically included in the model. Additional
|
| <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
|
covariates can be included with the command: </P><PRE>model=<EM>list of covariates</EM></PRE>
|
| than two interviews in the survey, the program can be run
|
<UL>
|
| on selected transitions periods. firstpass=1 means the
|
<LI>if<STRONG> model=. </STRONG>then no covariates are included
|
| first interview included in the calculation is the
|
<LI>if <STRONG>model=V1</STRONG> the model includes the first covariate (field
|
| baseline survey. lastpass=4 means that the information
|
2)
|
| brought by the 4th interview is taken into account.</li>
|
<LI>if <STRONG>model=V2 </STRONG>the model includes the second covariate
|
| </ul>
|
(field 3)
|
|
|
<LI>if <STRONG>model=V1+V2 </STRONG>the model includes the first and the
|
| <p> </p>
|
second covariate (fields 2 and 3)
|
|
|
<LI>if <STRONG>model=V1*V2 </STRONG>the model includes the product of the
|
| <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
|
first and the second covariate (fields 2 and 3)
|
| line</font></a></h4>
|
<LI>if <STRONG>model=V1+V1*age</STRONG> the model includes the product
|
|
|
covariate*age </LI></UL>
|
| <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
<P>In this example, we have two covariates in the data file (fields 2 and 3).
|
|
|
The number of covariates included in the data file between the id and the date
|
| <ul>
|
of birth is ncovcol=2 (it was named ncov in version prior to 0.8). If you have 3
|
| <li><b>ftol=1e-8</b> Convergence tolerance on the function
|
covariates in the datafile (fields 2, 3 and 4), you will set ncovcol=3. Then you
|
| value in the maximisation of the likelihood. Choosing a
|
can run the programme with a new parametrisation taking into account the third
|
| correct value for ftol is difficult. 1e-8 is a correct
|
covariate. For example, <STRONG>model=V1+V3 </STRONG>estimates a model with the
|
| value for a 32 bits computer.</li>
|
first and third covariates. More complicated models can be used, but this will
|
| <li><b>stepm=1</b> Time unit in months for interpolation.
|
take more time to converge. With a simple model (no covariates), the programme
|
| Examples:<ul>
|
estimates 8 parameters. Adding covariates increases the number of parameters :
|
| <li>If stepm=1, the unit is a month </li>
|
12 for <STRONG>model=V1, </STRONG>16 for <STRONG>model=V1+V1*age </STRONG>and 20
|
| <li>If stepm=4, the unit is a trimester</li>
|
for <STRONG>model=V1+V2+V3.</STRONG></P>
|
| <li>If stepm=12, the unit is a year </li>
|
<H4><FONT color=#ff0000>Guess values for optimization</FONT><FONT color=#00006a>
|
| <li>If stepm=24, the unit is two years</li>
|
</FONT></H4>
|
| <li>... </li>
|
<P>You must write the initial guess values of the parameters for optimization.
|
| </ul>
|
The number of parameters, <EM>N</EM> depends on the number of absorbing states
|
| </li>
|
and non-absorbing states and on the number of covariates in the model (ncovmodel). <BR><EM>N</EM> is
|
| <li><b>ncovcol=2</b> Number of covariate columns in the
|
given by the formula <EM>N</EM>=(<EM>nlstate</EM> +
|
| datafile which precede the date of birth. Here you can
|
<EM>ndeath</EM>-1)*<EM>nlstate</EM>*<EM>ncovmodel</EM> . <BR><BR>Thus in
|
| put variables that won't necessary be used during the
|
the simple case with 2 covariates in the model(the model is log (pij/pii) = aij + bij * age
|
| run. It is not the number of covariates that will be
|
where intercept and age are the two covariates), and 2 health states (1 for
|
| specified by the model. The 'model' syntax describe the
|
disability-free and 2 for disability) and 1 absorbing state (3), you must enter
|
| covariates to take into account. </li>
|
8 initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can start with
|
| <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
|
zeros as in this example, but if you have a more precise set (for example from
|
| Here we have two alive states: disability-free is coded 1
|
an earlier run) you can enter it and it will speed up the convergence<BR>Each of the four
|
| and disability is coded 2. </li>
|
lines starts with indices "ij": <B>ij aij bij</B> </P>
|
| <li><b>ndeath=1</b> Number of absorbing states. The absorbing
|
<BLOCKQUOTE><PRE># Guess values of aij and bij in log (pij/pii) = aij + bij * age
|
| state death is coded 3. </li>
|
|
| <li><b>maxwav=4</b> Number of waves in the datafile.</li>
|
|
| <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
|
|
| Maximisation Likelihood Estimation. <ul>
|
|
| <li>If mle=1 the program does the maximisation and
|
|
| the calculation of health expectancies </li>
|
|
| <li>If mle=0 the program only does the calculation of
|
|
| the health expectancies. </li>
|
|
| </ul>
|
|
| </li>
|
|
| <li><b>weight=0</b> Possibility to add weights. <ul>
|
|
| <li>If weight=0 no weights are included </li>
|
|
| <li>If weight=1 the maximisation integrates the
|
|
| weights which are in field <a href="#Weight">4</a></li>
|
|
| </ul>
|
|
| </li>
|
|
| </ul>
|
|
|
|
|
| <h4><font color="#FF0000">Covariates</font></h4>
|
|
|
|
|
| <p>Intercept and age are systematically included in the model.
|
|
| Additional covariates can be included with the command: </p>
|
|
|
|
|
| <pre>model=<em>list of covariates</em></pre>
|
|
|
|
|
| <ul>
|
|
| <li>if<strong> model=. </strong>then no covariates are
|
|
| included</li>
|
|
| <li>if <strong>model=V1</strong> the model includes the first
|
|
| covariate (field 2)</li>
|
|
| <li>if <strong>model=V2 </strong>the model includes the
|
|
| second covariate (field 3)</li>
|
|
| <li>if <strong>model=V1+V2 </strong>the model includes the
|
|
| first and the second covariate (fields 2 and 3)</li>
|
|
| <li>if <strong>model=V1*V2 </strong>the model includes the
|
|
| product of the first and the second covariate (fields 2
|
|
| and 3)</li>
|
|
| <li>if <strong>model=V1+V1*age</strong> the model includes
|
|
| the product covariate*age</li>
|
|
| </ul>
|
|
|
|
|
| <p>In this example, we have two covariates in the data file
|
|
| (fields 2 and 3). The number of covariates included in the data
|
|
| file between the id and the date of birth is ncovcol=2 (it was
|
|
| named ncov in version prior to 0.8). If you have 3 covariates in
|
|
| the datafile (fields 2, 3 and 4), you will set ncovcol=3. Then
|
|
| you can run the programme with a new parametrisation taking into
|
|
| account the third covariate. For example, <strong>model=V1+V3 </strong>estimates
|
|
| a model with the first and third covariates. More complicated
|
|
| models can be used, but it will takes more time to converge. With
|
|
| a simple model (no covariates), the programme estimates 8
|
|
| parameters. Adding covariates increases the number of parameters
|
|
| : 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
|
|
| </strong>and 20 for <strong>model=V1+V2+V3.</strong></p>
|
|
|
|
|
| <h4><font color="#FF0000">Guess values for optimization</font><font
|
|
| color="#00006A"> </font></h4>
|
|
|
|
|
| <p>You must write the initial guess values of the parameters for
|
|
| optimization. The number of parameters, <em>N</em> depends on the
|
|
| number of absorbing states and non-absorbing states and on the
|
|
| number of covariates. <br>
|
|
| <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
|
|
| <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncovmodel</em> . <br>
|
|
| <br>
|
|
| Thus in the simple case with 2 covariates (the model is log
|
|
| (pij/pii) = aij + bij * age where intercept and age are the two
|
|
| covariates), and 2 health degrees (1 for disability-free and 2
|
|
| for disability) and 1 absorbing state (3), you must enter 8
|
|
| initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
|
|
| start with zeros as in this example, but if you have a more
|
|
| precise set (for example from an earlier run) you can enter it
|
|
| and it will speed up them<br>
|
|
| Each of the four lines starts with indices "ij": <b>ij
|
|
| aij bij</b> </p>
|
|
|
|
|
| <blockquote>
|
|
| <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
|
|
| 12 -14.155633 0.110794
|
12 -14.155633 0.110794
|
| 13 -7.925360 0.032091
|
13 -7.925360 0.032091
|
| 21 -1.890135 -0.029473
|
21 -1.890135 -0.029473
|
| 23 -6.234642 0.022315 </pre>
|
23 -6.234642 0.022315 </PRE></BLOCKQUOTE>
|
| </blockquote>
|
<P>or, to simplify (in most of cases it converges but there is no warranty!):
|
|
|
</P>
|
| <p>or, to simplify (in most of cases it converges but there is no
|
<BLOCKQUOTE><PRE>12 0.0 0.0
|
| warranty!): </p>
|
|
|
|
|
| <blockquote>
|
|
| <pre>12 0.0 0.0
|
|
| 13 0.0 0.0
|
13 0.0 0.0
|
| 21 0.0 0.0
|
21 0.0 0.0
|
| 23 0.0 0.0</pre>
|
23 0.0 0.0</PRE></BLOCKQUOTE>
|
| </blockquote>
|
<P>In order to speed up the convergence you can make a first run with a large
|
|
|
stepm i.e stepm=12 or 24 and then decrease the stepm until stepm=1 month. If
|
| <p>In order to speed up the convergence you can make a first run
|
newstepm is the new shorter stepm and stepm can be expressed as a multiple of
|
| with a large stepm i.e stepm=12 or 24 and then decrease the stepm
|
newstepm, like newstepm=n stepm, then the following approximation holds: </P><PRE>aij(stepm) = aij(n . stepm) - ln(n)
|
| until stepm=1 month. If newstepm is the new shorter stepm and
|
</PRE>
|
| stepm can be expressed as a multiple of newstepm, like newstepm=n
|
<P>and </P><PRE>bij(stepm) = bij(n . stepm) .</PRE>
|
| stepm, then the following approximation holds: </p>
|
<P>For example if you already ran with stepm=6 (a 6 months interval) and got:<BR></P><PRE># Parameters
|
|
|
|
| <pre>aij(stepm) = aij(n . stepm) - ln(n)
|
|
| </pre>
|
|
|
|
|
| <p>and </p>
|
|
|
|
|
| <pre>bij(stepm) = bij(n . stepm) .</pre>
|
|
|
|
|
| <p>For example if you already ran for a 6 months interval and
|
|
| got:<br>
|
|
| </p>
|
|
|
|
|
| <pre># Parameters
|
|
| 12 -13.390179 0.126133
|
12 -13.390179 0.126133
|
| 13 -7.493460 0.048069
|
13 -7.493460 0.048069
|
| 21 0.575975 -0.041322
|
21 0.575975 -0.041322
|
| 23 -4.748678 0.030626
|
23 -4.748678 0.030626
|
| </pre>
|
</PRE>
|
|
|
<P>Then you now want to get the monthly estimates, you can guess the aij by
|
| <p>If you now want to get the monthly estimates, you can guess
|
subtracting ln(6)= 1.7917<BR>and running using<BR></P><PRE>12 -15.18193847 0.126133
|
| the aij by substracting ln(6)= 1,7917<br>
|
|
| and running<br>
|
|
| </p>
|
|
|
|
|
| <pre>12 -15.18193847 0.126133
|
|
| 13 -9.285219469 0.048069
|
13 -9.285219469 0.048069
|
| 21 -1.215784469 -0.041322
|
21 -1.215784469 -0.041322
|
| 23 -6.540437469 0.030626
|
23 -6.540437469 0.030626
|
| </pre>
|
</PRE>
|
|
|
<P>and get<BR></P><PRE>12 -15.029768 0.124347
|
| <p>and get<br>
|
|
| </p>
|
|
|
|
|
| <pre>12 -15.029768 0.124347
|
|
| 13 -8.472981 0.036599
|
13 -8.472981 0.036599
|
| 21 -1.472527 -0.038394
|
21 -1.472527 -0.038394
|
| 23 -6.553602 0.029856
|
23 -6.553602 0.029856
|
|
|
|
| which is closer to the results. The approximation is probably useful
|
<P>which is closer to the results. The approximation is probably useful
|
| only for very small intervals and we don't have enough experience to
|
only for very small intervals and we don't have enough experience to
|
| know if you will speed up the convergence or not.
|
know if you will speed up the convergence or not.<BR></P>
|
| </pre>
|
</PRE><PRE> -ln(12)= -2.484
|
|
|
|
| <pre> -ln(12)= -2.484
|
|
| -ln(6/1)=-ln(6)= -1.791
|
-ln(6/1)=-ln(6)= -1.791
|
| -ln(3/1)=-ln(3)= -1.0986
|
-ln(3/1)=-ln(3)= -1.0986
|
| -ln(12/6)=-ln(2)= -0.693
|
-ln(12/6)=-ln(2)= -0.693
|
| </pre>
|
</PRE>In version 0.9 and higher you can still have valuable results even if your
|
|
|
stepm parameter is bigger than a month. The idea is to run with bigger stepm in
|
| <h4><font color="#FF0000">Guess values for computing variances</font></h4>
|
order to have a quicker convergence at the price of a small bias. Once you know
|
|
|
which model you want to fit, you can put stepm=1 and wait hours or days to get
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
the convergence! To get unbiased results even with large stepm we introduce the
|
| used as an input to get the various output data files (Health
|
idea of pseudo likelihood by interpolating two exact likelihoods. In
|
| expectancies, stationary prevalence etc.) and figures without
|
more detail:
|
| rerunning the rather long maximisation phase (mle=0). </p>
|
<P>If the interval of <EM>d</EM> months between two waves is not a multiple of
|
|
|
'stepm', but is between <EM>(n-1) stepm</EM> and <EM>n stepm</EM> then
|
| <p>The scales are small values for the evaluation of numerical
|
both exact likelihoods are computed (the contribution to the likelihood at <EM>n
|
| derivatives. These derivatives are used to compute the hessian
|
stepm</EM> requires one matrix product more) (let us remember that we are
|
| matrix of the parameters, that is the inverse of the covariance
|
modelling the probability to be observed in a particular state after <EM>d</EM>
|
| matrix, and the variances of health expectancies. Each line
|
months being observed at a particular state at 0). The distance, (<EM>bh</EM> in
|
| consists in indices "ij" followed by the initial scales
|
the program), from the month of interview to the rounded date of <EM>n
|
| (zero to simplify) associated with aij and bij. </p>
|
stepm</EM> is computed. It can be negative (interview occurs before <EM>n
|
|
|
stepm</EM>) or positive if the interview occurs after <EM>n stepm</EM> (and
|
| <ul>
|
before <EM>(n+1)stepm</EM>). <BR>Then the final contribution to the total
|
| <li>If mle=1 you can enter zeros:</li>
|
likelihood is a weighted average of these two exact likelihoods at <EM>n
|
| <li><blockquote>
|
stepm</EM> (out) and at <EM>(n-1)stepm</EM>(savm). We did not want to compute
|
| <pre># Scales (for hessian or gradient estimation)
|
the third likelihood at <EM>(n+1)stepm</EM> because it is too costly in time, so
|
| |
we used an extrapolation if <EM>bh</EM> is positive. <BR>The formula
|
| |
for the inter/extrapolation may vary according to the value of parameter mle: <PRE>mle=1 lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
|
| |
|
| |
mle=2 lli= (savm[s1][s2]>(double)1.e-8 ? \
|
| |
log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])): \
|
| |
log((1.+bbh)*out[s1][s2])); /* linear interpolation */
|
| |
mle=3 lli= (savm[s1][s2]>1.e-8 ? \
|
| |
(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]): \
|
| |
log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
|
| |
|
| |
mle=4 lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* No interpolation */
|
| |
no need to save previous likelihood into memory.
|
| |
</PRE>
|
| |
<P>If the death occurs between the first and second pass, and for example more
|
| |
precisely between <EM>n stepm</EM> and <EM>(n+1)stepm</EM> the contribution of
|
| |
these people to the likelihood is simply the difference between the probability
|
| |
of dying before <EM>n stepm</EM> and the probability of dying before
|
| |
<EM>(n+1)stepm</EM>. There was a bug in version 0.8 and death was treated as any
|
| |
other state, i.e. as if it was an observed death at second pass. This was not
|
| |
precise but correct, although when information on the precise month of
|
| |
death came (death occuring prior to second pass) we did not change the
|
| |
likelihood accordingly. We thank Chris Jackson for correcting it. In earlier
|
| |
versions (fortunately before first publication) the total mortality
|
| |
was thus overestimated (people were dying too early) by about 10%. Version
|
| |
0.95 and higher are correct.
|
| |
|
| |
<P>Our suggested choice is mle=1 . If stepm=1 there is no difference between
|
| |
various mle options (methods of interpolation). If stepm is big, like 12 or 24
|
| |
or 48 and mle=4 (no interpolation) the bias may be very important if the mean
|
| |
duration between two waves is not a multiple of stepm. See the appendix in our
|
| |
main publication concerning the sine curve of biases.
|
| |
<H4><FONT color=#ff0000>Guess values for computing variances</FONT></H4>
|
| |
<P>These values are output by the maximisation of the likelihood <A
|
| |
href="http://euroreves.ined.fr/imach/doc/imach.htm#mle">mle</A>=1 and
|
| |
can be used as an input for a second run in order to get the various output data
|
| |
files (Health expectancies, period prevalence etc.) and figures without
|
| |
rerunning the long maximisation phase (mle=0). </P>
|
| |
<P>The 'scales' are small values needed for the computing of numerical
|
| |
derivatives. These derivatives are used to compute the hessian matrix of the
|
| |
parameters, that is the inverse of the covariance matrix. They are often used
|
| |
for estimating variances and confidence intervals. Each line consists of indices
|
| |
"ij" followed by the initial scales (zero to simplify) associated with aij and
|
| |
bij. </P>
|
| |
<UL>
|
| |
<LI>If mle=1 you can enter zeros:
|
| |
<LI>
|
| |
<BLOCKQUOTE><PRE># Scales (for hessian or gradient estimation)
|
| 12 0. 0.
|
12 0. 0.
|
| 13 0. 0.
|
13 0. 0.
|
| 21 0. 0.
|
21 0. 0.
|
| 23 0. 0. </pre>
|
23 0. 0. </PRE></BLOCKQUOTE>
|
| </blockquote>
|
<LI>If mle=0 (no maximisation of Likelihood) you must enter a covariance
|
| </li>
|
matrix (usually obtained from an earlier run). </LI></UL>
|
| <li>If mle=0 you must enter a covariance matrix (usually
|
<H4><FONT color=#ff0000>Covariance matrix of parameters</FONT></H4>
|
| obtained from an earlier run).</li>
|
<P>The covariance matrix is output if <A
|
| </ul>
|
href="http://euroreves.ined.fr/imach/doc/imach.htm#mle">mle</A>=1. But it can be
|
|
|
also be used as an input to get the various output data files (Health
|
| <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
|
expectancies, period prevalence etc.) and figures without rerunning
|
|
|
the maximisation phase (mle=0). <BR>Each line starts with indices
|
| <p>This is an output if <a href="#mle">mle</a>=1. But it can be
|
"ijk" followed by the covariances between aij and bij:<BR>
|
| used as an input to get the various output data files (Health
|
</P><PRE> 121 Var(a12)
|
| expectancies, stationary prevalence etc.) and figures without
|
|
| rerunning the rather long maximisation phase (mle=0). <br>
|
|
| Each line starts with indices "ijk" followed by the
|
|
| covariances between aij and bij:<br>
|
|
| </p>
|
|
|
|
|
| <pre>
|
|
| 121 Var(a12)
|
|
| 122 Cov(b12,a12) Var(b12)
|
122 Cov(b12,a12) Var(b12)
|
| ...
|
...
|
| 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
|
232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </PRE>
|
|
|
<UL>
|
| <ul>
|
<LI>If mle=1 you can enter zeros.
|
| <li>If mle=1 you can enter zeros. </li>
|
<LI><PRE># Covariance matrix
|
| <li><pre># Covariance matrix
|
|
| 121 0.
|
121 0.
|
| 122 0. 0.
|
122 0. 0.
|
| 131 0. 0. 0.
|
131 0. 0. 0.
|
|
Line 538 covariances between aij and bij:<br>
|
Line 470 covariances between aij and bij:<br>
|
| 211 0. 0. 0. 0. 0.
|
211 0. 0. 0. 0. 0.
|
| 212 0. 0. 0. 0. 0. 0.
|
212 0. 0. 0. 0. 0. 0.
|
| 231 0. 0. 0. 0. 0. 0. 0.
|
231 0. 0. 0. 0. 0. 0. 0.
|
| 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
|
232 0. 0. 0. 0. 0. 0. 0. 0.</PRE>
|
| </li>
|
<LI>If mle=0 you must enter a covariance matrix (usually obtained from an
|
| <li>If mle=0 you must enter a covariance matrix (usually
|
earlier run). </LI></UL>
|
| obtained from an earlier run). </li>
|
<H4><FONT color=#ff0000>Age range for calculation of stationary prevalences and
|
| </ul>
|
health expectancies</FONT></H4><PRE>agemin=70 agemax=100 bage=50 fage=100</PRE>
|
|
|
<P>Once we obtained the estimated parameters, the program is able to calculate
|
| <h4><font color="#FF0000">Age range for calculation of stationary
|
period prevalence, transitions probabilities and life expectancies at any age.
|
| prevalences and health expectancies</font></h4>
|
Choice of the age range is useful for extrapolation. In this example,
|
|
|
the age of people interviewed varies from 69 to 102 and the model is
|
| <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
|
estimated using their exact ages. But if you are interested in the
|
|
|
age-specific period prevalence you can start the simulation at an
|
| <pre>
|
exact age like 70 and stop at 100. Then the program will draw at
|
| Once we obtained the estimated parameters, the program is able
|
least two curves describing the forecasted prevalences of two cohorts,
|
| to calculated stationary prevalence, transitions probabilities
|
one for healthy people at age 70 and the second for disabled people at
|
| and life expectancies at any age. Choice of age range is useful
|
the same initial age. And according to the mixing property
|
| for extrapolation. In our data file, ages varies from age 70 to
|
(ergodicity) and because of recovery, both prevalences will tend to be
|
| 102. It is possible to get extrapolated stationary prevalence by
|
identical at later ages. Thus if you want to compute the prevalence at
|
| age ranging from agemin to agemax.
|
age 70, you should enter a lower agemin value.
|
|
|
<P>Setting bage=50 (begin age) and fage=100 (final age), let the program compute
|
|
|
life expectancy from age 'bage' to age 'fage'. As we use a model, we can
|
| Setting bage=50 (begin age) and fage=100 (final age), makes
|
interessingly compute life expectancy on a wider age range than the age range
|
| the program computing life expectancy from age 'bage' to age
|
from the data. But the model can be rather wrong on much larger intervals.
|
| 'fage'. As we use a model, we can interessingly compute life
|
Program is limited to around 120 for upper age! <PRE></PRE>
|
| expectancy on a wider age range than the age range from the data.
|
<UL>
|
| But the model can be rather wrong on much larger intervals.
|
<LI><B>agemin=</B> Minimum age for calculation of the period prevalence
|
| Program is limited to around 120 for upper age!
|
<LI><B>agemax=</B> Maximum age for calculation of the period prevalence
|
| </pre>
|
<LI><B>bage=</B> Minimum age for calculation of the health expectancies
|
|
|
<LI><B>fage=</B> Maximum age for calculation of the health expectancies
|
| <ul>
|
</LI></UL>
|
| <li><b>agemin=</b> Minimum age for calculation of the
|
<H4><A name=Computing><FONT color=#ff0000>Computing</FONT></A><FONT
|
| stationary prevalence </li>
|
color=#ff0000> the cross-sectional prevalence</FONT></H4><PRE>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</PRE>
|
| <li><b>agemax=</b> Maximum age for calculation of the
|
<P>Statements 'begin-prev-date' and 'end-prev-date' allow the user to
|
| stationary prevalence </li>
|
select the period in which the observed prevalences in each state. In
|
| <li><b>bage=</b> Minimum age for calculation of the health
|
this example, the prevalences are calculated on data survey collected
|
| expectancies </li>
|
between 1 January 1984 and 1 June 1988. </P>
|
| <li><b>fage=</b> Maximum age for calculation of the health
|
<UL>
|
| expectancies </li>
|
<LI><STRONG>begin-prev-date= </STRONG>Starting date (day/month/year)
|
| </ul>
|
<LI><STRONG>end-prev-date= </STRONG>Final date (day/month/year)
|
|
|
<LI><STRONG>estepm= </STRONG>Unit (in months).We compute the life expectancy
|
| <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
|
from trapezoids spaced every estepm months. This is mainly to measure the
|
| color="#FF0000"> the observed prevalence</font></h4>
|
difference between two models: for example if stepm=24 months pijx are given
|
|
|
only every 2 years and by summing them we are calculating an estimate of the
|
| <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</pre>
|
Life Expectancy assuming a linear progression inbetween and thus
|
|
|
overestimating or underestimating according to the curvature of the survival
|
| <pre>
|
function. If, for the same date, we estimate the model with stepm=1 month, we
|
| Statements 'begin-prev-date' and 'end-prev-date' allow to
|
can keep estepm to 24 months to compare the new estimate of Life expectancy
|
| select the period in which we calculate the observed prevalences
|
with the same linear hypothesis. A more precise result, taking into account a
|
| in each state. In this example, the prevalences are calculated on
|
more precise curvature will be obtained if estepm is as small as stepm.
|
| data survey collected between 1 january 1984 and 1 june 1988.
|
</LI></UL>
|
| </pre>
|
<H4><FONT color=#ff0000>Population- or status-based health
|
|
|
expectancies</FONT></H4><PRE>pop_based=0</PRE>
|
| <ul>
|
<P>The program computes status-based health expectancies, i.e health
|
| <li><strong>begin-prev-date= </strong>Starting date
|
expectancies which depend on the initial health state. If you are healthy, your
|
| (day/month/year)</li>
|
healthy life expectancy (e11) is higher than if you were disabled (e21, with e11
|
| <li><strong>end-prev-date= </strong>Final date
|
> e21).<BR>To compute a healthy life expectancy 'independent' of the initial
|
| (day/month/year)</li>
|
status we have to weight e11 and e21 according to the probability of
|
| <li><strong>estepm= </strong>Unit (in months).We compute the
|
being in each state at initial age which correspond to the proportions
|
| life expectancy from trapezoids spaced every estepm
|
of people in each health state (cross-sectional prevalences).
|
| months. This is mainly to measure the difference between
|
<P>We could also compute e12 and e12 and get e.2 by weighting them according to
|
| two models: for example if stepm=24 months pijx are given
|
the observed cross-sectional prevalences at initial age.
|
| only every 2 years and by summing them we are calculating
|
<P>In a similar way we could compute the total life expectancy by summing e.1
|
| an estimate of the Life Expectancy assuming a linear
|
and e.2 . <BR>The main difference between 'population based' and 'implied' or
|
| progression inbetween and thus overestimating or
|
'period' is in the weights used. 'Usually', cross-sectional prevalences of
|
| underestimating according to the curvature of the
|
disability are higher than period prevalences particularly at old ages. This is
|
| survival function. If, for the same date, we estimate the
|
true if the country is improving its health system by teaching people how to
|
| model with stepm=1 month, we can keep estepm to 24 months
|
prevent disability by promoting better screening, for example of people
|
| to compare the new estimate of Life expectancy with the
|
needing cataract surgery. Then the proportion of disabled people at
|
| same linear hypothesis. A more precise result, taking
|
age 90 will be lower than the current observed proportion.
|
| into account a more precise curvature will be obtained if
|
<P>Thus a better Health Expectancy and even a better Life Expectancy value is
|
| estepm is as small as stepm.</li>
|
given by forecasting not only the current lower mortality at all ages but also a
|
| </ul>
|
lower incidence of disability and higher recovery. <BR>Using the period
|
|
|
prevalences as weight instead of the cross-sectional prevalences we are
|
| <h4><font color="#FF0000">Population- or status-based health
|
computing indices which are more specific to the current situations and
|
| expectancies</font></h4>
|
therefore more useful to predict improvements or regressions in the future as to
|
|
|
compare different policies in various countries.
|
| <pre>pop_based=0</pre>
|
<UL>
|
|
|
<LI><STRONG>popbased= 0 </STRONG>Health expectancies are computed at each age
|
| <p>The program computes status-based health expectancies, i.e
|
from period prevalences 'expected' at this initial age.
|
| health expectancies which depends on your initial health state.
|
<LI><STRONG>popbased= 1 </STRONG>Health expectancies are computed at each age
|
| If you are healthy your healthy life expectancy (e11) is higher
|
from cross-sectional 'observed' prevalence at the initial age. As all the
|
| than if you were disabled (e21, with e11 > e21).<br>
|
population is not observed at the same exact date we define a short period
|
| To compute a healthy life expectancy independant of the initial
|
where the observed prevalence can be computed as follows:<BR>we simply sum all people
|
| status we have to weight e11 and e21 according to the probability
|
surveyed within these two exact dates who belong to a particular age group
|
| to be in each state at initial age or, with other word, according
|
(single year) at the date of interview and are in a particular health state.
|
| to the proportion of people in each state.<br>
|
Then it is easy to get the proportion of people in a particular
|
| We prefer computing a 'pure' period healthy life expectancy based
|
health state as a percentage of all people of the same age group.<BR>If both dates are spaced and are
|
| only on the transtion forces. Then the weights are simply the
|
covering two waves or more, people being interviewed twice or more are counted
|
| stationnary prevalences or 'implied' prevalences at the initial
|
twice or more. The program takes into account the selection of individuals
|
| age.<br>
|
interviewed between firstpass and lastpass too (we don't know if
|
| Some other people would like to use the cross-sectional
|
this is useful). </LI></UL>
|
| prevalences (the "Sullivan prevalences") observed at
|
<H4><FONT color=#ff0000>Prevalence forecasting (Experimental)</FONT></H4><PRE>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </PRE>
|
| the initial age during a period of time <a href="#Computing">defined
|
<P>Prevalence and population projections are only available if the interpolation
|
| just above</a>. <br>
|
unit is a month, i.e. stepm=1 and if there are no covariate. The programme
|
| </p>
|
estimates the prevalence in each state at a precise date expressed in
|
|
|
day/month/year. The programme computes one forecasted prevalence a year from a
|
| <ul>
|
starting date (1 January 1989 in this example) to a final date (1 January
|
| <li><strong>popbased= 0 </strong>Health expectancies are
|
1992). The statement mov_average allows computation of smoothed forecasted
|
| computed at each age from stationary prevalences
|
prevalences with a five-age moving average centered at the mid-age of the
|
| 'expected' at this initial age.</li>
|
fiveyear-age period. <BR></P>
|
| <li><strong>popbased= 1 </strong>Health expectancies are
|
<H4><FONT color=#ff0000>Population forecasting (Experimental)</FONT></H4>
|
| computed at each age from cross-sectional 'observed'
|
<UL>
|
| prevalence at this initial age. As all the population is
|
<LI><STRONG>starting-proj-date</STRONG>= starting date (day/month/year) of
|
| not observed at the same exact date we define a short
|
forecasting
|
| period were the observed prevalence is computed.</li>
|
<LI><STRONG>final-proj-date= </STRONG>final date (day/month/year) of
|
| </ul>
|
forecasting
|
|
|
<LI><STRONG>mov_average</STRONG>= smoothing with a five-age moving average
|
| <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
|
centered at the mid-age of the fiveyear-age period. The command<STRONG>
|
|
|
mov_average</STRONG> takes value 1 if the prevalences are smoothed and 0
|
| <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
|
otherwise. </LI></UL>
|
|
|
<UL type=disc>
|
| <p>Prevalence and population projections are only available if
|
<LI><B>popforecast= 0 </B>Option for population forecasting. If popforecast=1,
|
| the interpolation unit is a month, i.e. stepm=1 and if there are
|
the programme does the forecasting<B>.</B>
|
| no covariate. The programme estimates the prevalence in each
|
<LI><B>popfile= </B>name of the population file
|
| state at a precise date expressed in day/month/year. The
|
<LI><B>popfiledate=</B> date of the population population
|
| programme computes one forecasted prevalence a year from a
|
<LI><B>last-popfiledate</B>= date of the last population projection
|
| starting date (1 january of 1989 in this example) to a final date
|
</LI></UL>
|
| (1 january 1992). The statement mov_average allows to compute
|
<HR>
|
| smoothed forecasted prevalences with a five-age moving average
|
|
| centered at the mid-age of the five-age period. <br>
|
<H2><A name=running></A><FONT color=#00006a>Running Imach with this
|
| </p>
|
example</FONT></H2>
|
|
|
<P>We assume that you have already typed your <A
|
| <ul>
|
href="http://euroreves.ined.fr/imach/doc/biaspar.imach">1st_example parameter
|
| <li><strong>starting-proj-date</strong>= starting date
|
file</A> as explained <A
|
| (day/month/year) of forecasting</li>
|
href="http://euroreves.ined.fr/imach/doc/imach.htm#biaspar">above</A>. To run
|
| <li><strong>final-proj-date= </strong>final date
|
the program under Windows you should either: </P>
|
| (day/month/year) of forecasting</li>
|
<UL>
|
| <li><strong>mov_average</strong>= smoothing with a five-age
|
<LI>click on the imach.exe icon and either:
|
| moving average centered at the mid-age of the five-age
|
<UL>
|
| period. The command<strong> mov_average</strong> takes
|
<LI>enter the name of the parameter file which is for example
|
| value 1 if the prevalences are smoothed and 0 otherwise.</li>
|
<TT>C:\home\myname\lsoa\biaspar.imach</TT>
|
| </ul>
|
<LI>or locate the biaspar.imach icon in your folder such as
|
|
|
<TT>C:\home\myname\lsoa</TT> and drag it, with your mouse, on the already
|
| <h4><font color="#FF0000">Last uncommented line : Population
|
open imach window. </LI></UL>
|
| forecasting </font></h4>
|
<LI>With version (0.97b) if you ran setup at installation, Windows is supposed
|
|
|
to understand the ".imach" extension and you can right click the biaspar.imach
|
| <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
|
icon and either edit with wordpad (better than notepad) the parameter file or
|
|
|
execute it with IMaCh. </LI></UL>
|
| <p>This command is available if the interpolation unit is a
|
<P>The time to converge depends on the step unit used (1 month is more
|
| month, i.e. stepm=1 and if popforecast=1. From a data file
|
precise but more cpu time consuming), on the number of cases, and on the number of
|
| including age and number of persons alive at the precise date
|
variables (covariates).
|
| ‘popfiledate’, you can forecast the number of persons
|
<P>The program outputs many files. Most of them are files which will be plotted
|
| in each state until date ‘last-popfiledate’. In this
|
for better understanding. </P>To run under Linux is mostly the same.
|
| example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
|
<P>It is no more difficult to run IMaCh on a MacIntosh.
|
| includes real data which are the Japanese population in 1989.<br>
|
<HR>
|
| </p>
|
|
|
|
<H2><A name=output><FONT color=#00006a>Output of the program and graphs</FONT>
|
| <ul type="disc">
|
</A></H2>
|
| <li class="MsoNormal"
|
<P>Once the optimization is finished (once the convergence is reached), many
|
| style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
|
tables and graphics are produced.
|
| 0 </b>Option for population forecasting. If
|
<P>The IMaCh program will create a subdirectory with the same name as your
|
| popforecast=1, the programme does the forecasting<b>.</b></li>
|
parameter file (here mypar) where all the tables and figures will be
|
| <li class="MsoNormal"
|
stored.<BR>Important files like the log file and the output parameter file
|
| style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
|
(the latter contains the maximum likelihood estimates) are stored at
|
| </b>name of the population file</li>
|
the main level not in this subdirectory. Files with extension .log and
|
| <li class="MsoNormal"
|
.txt can be edited with a standard editor like wordpad or notepad or
|
| style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
|
even can be viewed with a browser like Internet Explorer or Mozilla.
|
| date of the population population</li>
|
<P>The main html file is also named with the same name <A
|
| <li class="MsoNormal"
|
href="http://euroreves.ined.fr/imach/doc/biaspar.htm">biaspar.htm</A>. You can
|
| style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
|
click on it by holding your shift key in order to open it in another window
|
| date of the last population projection </li>
|
(Windows).
|
| </ul>
|
<P>Our grapher is Gnuplot, an interactive plotting program (GPL) which can
|
|
|
also work in batch mode. A gnuplot reference manual is available <A
|
| <hr>
|
href="http://www.gnuplot.info/">here</A>. <BR>When the run is finished, and in
|
|
|
order that the window doesn't disappear, the user should enter a character like
|
| <h2><a name="running"></a><font color="#00006A">Running Imach
|
<TT>q</TT> for quitting. <BR>These characters are:<BR></P>
|
| with this example</font></h2>
|
<UL>
|
|
|
<LI>'e' for opening the main result html file <A
|
| <pre>We assume that you typed in your <a href="biaspar.imach">1st_example
|
href="http://euroreves.ined.fr/imach/doc/biaspar.htm"><STRONG>biaspar.htm</STRONG></A>
|
| parameter file</a> as explained <a href="#biaspar">above</a>.
|
file to edit the output files and graphs.
|
|
|
<LI>'g' to graph again
|
| To run the program you should either:
|
<LI>'c' to start again the program from the beginning.
|
| </pre>
|
<LI>'q' for exiting. </LI></UL>The main gnuplot file is named
|
|
|
<TT>biaspar.gp</TT> and can be edited (right click) and run again.
|
| <ul>
|
<P>Gnuplot is easy and you can use it to make more complex graphs. Just click on
|
| <li>click on the imach.exe icon and enter the name of the
|
gnuplot and type plot sin(x) to see how easy it is.
|
| parameter file which is for example <a
|
<H5><FONT size=4><STRONG>Results files </STRONG></FONT><BR><BR><FONT
|
| href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
|
color=#ec5e5e size=3><STRONG>- </STRONG></FONT><A
|
| </li>
|
name="cross-sectional prevalence in each state"><FONT color=#ec5e5e
|
| <li>You also can locate the biaspar.imach icon in <a
|
size=3><STRONG>cross-sectional prevalence in each state</STRONG></FONT></A><FONT
|
| href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your
|
color=#ec5e5e size=3><STRONG> (and at first pass)</STRONG></FONT><B>: </B><A
|
| mouse and drag it with the mouse on the imach window). </li>
|
href="http://euroreves.ined.fr/imach/doc/biaspar/prbiaspar.txt"><B>biaspar/prbiaspar.txt</B></A><BR></H5>
|
| <li>With latest version (0.7 and higher) if you setup windows
|
<P>The first line is the title and displays each field of the file. First column
|
| in order to understand ".imach" extension you
|
corresponds to age. Fields 2 and 6 are the proportion of individuals in states 1
|
| can right click the biaspar.imach icon and either edit
|
and 2 respectively as observed at first exam. Others fields are the numbers of
|
| with notepad the parameter file or execute it with imach
|
people in states 1, 2 or more. The number of columns increases if the number of
|
| or whatever. </li>
|
states is higher than 2.<BR>The header of the file is </P><PRE># Age Prev(1) N(1) N Age Prev(2) N(2) N
|
| </ul>
|
|
|
|
|
| <pre>The time to converge depends on the step unit that you used (1
|
|
| month is cpu consuming), on the number of cases, and on the
|
|
| number of variables.
|
|
|
|
|
|
|
|
| The program outputs many files. Most of them are files which
|
|
| will be plotted for better understanding.
|
|
|
|
|
| </pre>
|
|
|
|
|
| <hr>
|
|
|
|
|
| <h2><a name="output"><font color="#00006A">Output of the program
|
|
| and graphs</font> </a></h2>
|
|
|
|
|
| <p>Once the optimization is finished, some graphics can be made
|
|
| with a grapher. We use Gnuplot which is an interactive plotting
|
|
| program copyrighted but freely distributed. A gnuplot reference
|
|
| manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
|
|
| When the running is finished, the user should enter a caracter
|
|
| for plotting and output editing. <br>
|
|
| These caracters are:<br>
|
|
| </p>
|
|
|
|
|
| <ul>
|
|
| <li>'c' to start again the program from the beginning.</li>
|
|
| <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
|
|
| file to edit the output files and graphs. </li>
|
|
| <li>'g' to graph again</li>
|
|
| <li>'q' for exiting.</li>
|
|
| </ul>
|
|
|
|
|
| <h5><font size="4"><strong>Results files </strong></font><br>
|
|
| <br>
|
|
| <font color="#EC5E5E" size="3"><strong>- </strong></font><a
|
|
| name="Observed prevalence in each state"><font color="#EC5E5E"
|
|
| size="3"><strong>Observed prevalence in each state</strong></font></a><font
|
|
| color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
|
|
| </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
|
|
| </h5>
|
|
|
|
|
| <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
|
|
| proportion of individuals in states 1 and 2 respectively as
|
|
| observed during the first exam. Others fields are the numbers of
|
|
| people in states 1, 2 or more. The number of columns increases if
|
|
| the number of states is higher than 2.<br>
|
|
| The header of the file is </p>
|
|
|
|
|
| <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
|
|
| 70 1.00000 631 631 70 0.00000 0 631
|
70 1.00000 631 631 70 0.00000 0 631
|
| 71 0.99681 625 627 71 0.00319 2 627
|
71 0.99681 625 627 71 0.00319 2 627
|
| 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
|
72 0.97125 1115 1148 72 0.02875 33 1148 </PRE>
|
|
|
<P>It means that at age 70 (between 70 and 71), the prevalence in state 1 is
|
| <p>It means that at age 70, the prevalence in state 1 is 1.000
|
1.000 and in state 2 is 0.00 . At age 71 the number of individuals in state 1 is
|
| and in state 2 is 0.00 . At age 71 the number of individuals in
|
625 and in state 2 is 2, hence the total number of people aged 71 is 625+2=627.
|
| state 1 is 625 and in state 2 is 2, hence the total number of
|
<BR></P>
|
| people aged 71 is 625+2=627. <br>
|
<H5><FONT color=#ec5e5e size=3><B>- Estimated parameters and covariance
|
| </p>
|
matrix</B></FONT><B>: </B><A
|
|
|
href="http://euroreves.ined.fr/imach/doc/rbiaspar.txt"><B>rbiaspar.imach</B></A></H5>
|
| <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
|
<P>This file contains all the maximisation results: </P><PRE> -2 log likelihood= 21660.918613445392
|
| covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>
|
|
|
|
|
| <p>This file contains all the maximisation results: </p>
|
|
|
|
|
| <pre> -2 log likelihood= 21660.918613445392
|
|
| Estimated parameters: a12 = -12.290174 b12 = 0.092161
|
Estimated parameters: a12 = -12.290174 b12 = 0.092161
|
| a13 = -9.155590 b13 = 0.046627
|
a13 = -9.155590 b13 = 0.046627
|
| a21 = -2.629849 b21 = -0.022030
|
a21 = -2.629849 b21 = -0.022030
|
|
Line 804 covariance matrix</b></font><b>: </b><a
|
Line 679 covariance matrix</b></font><b>: </b><a
|
| Var(b21) = 1.29229e-004
|
Var(b21) = 1.29229e-004
|
| Var(a23) = 4.48405e-001
|
Var(a23) = 4.48405e-001
|
| Var(b23) = 5.85631e-005
|
Var(b23) = 5.85631e-005
|
| </pre>
|
</PRE>
|
|
|
<P>By substitution of these parameters in the regression model, we obtain the
|
| <p>By substitution of these parameters in the regression model,
|
elementary transition probabilities:</P>
|
| we obtain the elementary transition probabilities:</p>
|
<P><IMG height=300
|
|
|
src="Computing Health Expectancies using IMaCh_fichiers/pebiaspar11.png"
|
| <p><img src="pebiaspar1.gif" width="400" height="300"></p>
|
width=400></P>
|
|
|
<H5><FONT color=#ec5e5e size=3><B>- Transition probabilities</B></FONT><B>:
|
| <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
|
</B><A
|
| </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
|
href="http://euroreves.ined.fr/imach/doc/biaspar/pijrbiaspar.txt"><B>biaspar/pijrbiaspar.txt</B></A></H5>
|
|
|
<P>Here are the transitions probabilities Pij(x, x+nh). The second column is the
|
| <p>Here are the transitions probabilities Pij(x, x+nh) where nh
|
starting age x (from age 95 to 65), the third is age (x+nh) and the others are
|
| is a multiple of 2 years. The first column is the starting age x
|
the transition probabilities p11, p12, p13, p21, p22, p23. The first column
|
| (from age 50 to 100), the second is age (x+nh) and the others are
|
indicates the value of the covariate (without any other variable than age it is
|
| the transition probabilities p11, p12, p13, p21, p22, p23. For
|
equal to 1) For example, line 5 of the file is: </P><PRE>1 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </PRE>
|
| example, line 5 of the file is: </p>
|
<P>and this means: </P><PRE>p11(100,106)=0.02655
|
|
|
|
| <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
|
|
|
|
|
| <p>and this means: </p>
|
|
|
|
|
| <pre>p11(100,106)=0.02655
|
|
| p12(100,106)=0.17622
|
p12(100,106)=0.17622
|
| p13(100,106)=0.79722
|
p13(100,106)=0.79722
|
| p21(100,106)=0.01809
|
p21(100,106)=0.01809
|
| p22(100,106)=0.13678
|
p22(100,106)=0.13678
|
| p22(100,106)=0.84513 </pre>
|
p22(100,106)=0.84513 </PRE>
|
|
|
<H5><FONT color=#ec5e5e size=3><B>- </B></FONT><A
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
name="Period prevalence in each state"><FONT color=#ec5e5e size=3><B>Period
|
| name="Stationary prevalence in each state"><font color="#EC5E5E"
|
prevalence in each state</B></FONT></A><B>: </B><A
|
| size="3"><b>Stationary prevalence in each state</b></font></a><b>:
|
href="http://euroreves.ined.fr/imach/doc/biaspar/plrbiaspar.txt"><B>biaspar/plrbiaspar.txt</B></A></H5><PRE>#Prevalence
|
| </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
|
|
|
|
|
| <pre>#Prevalence
|
|
| #Age 1-1 2-2
|
#Age 1-1 2-2
|
|
|
|
| #************
|
#************
|
| 70 0.90134 0.09866
|
70 0.90134 0.09866
|
| 71 0.89177 0.10823
|
71 0.89177 0.10823
|
| 72 0.88139 0.11861
|
72 0.88139 0.11861
|
| 73 0.87015 0.12985 </pre>
|
73 0.87015 0.12985 </PRE>
|
|
|
<P>At age 70 the period prevalence is 0.90134 in state 1 and 0.09866 in state 2.
|
| <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
|
This period prevalence differs from the cross-sectional prevalence and
|
| 0.09866 in state 2. This stationary prevalence differs from
|
we explaining. The cross-sectional prevalence at age 70 results from
|
| observed prevalence. Here is the point. The observed prevalence
|
the incidence of disability, incidence of recovery and mortality which
|
| at age 70 results from the incidence of disability, incidence of
|
occurred in the past for the cohort. Period prevalence results from a
|
| recovery and mortality which occurred in the past of the cohort.
|
simulation with current incidences of disability, recovery and
|
| Stationary prevalence results from a simulation with actual
|
mortality estimated from this cross-longitudinal survey. It is a good
|
| incidences and mortality (estimated from this cross-longitudinal
|
prediction of the prevalence in the future if "nothing changes in the
|
| survey). It is the best predictive value of the prevalence in the
|
future". This is exactly what demographers do with a period life
|
| future if "nothing changes in the future". This is
|
table. Life expectancy is the expected mean survival time if current
|
| exactly what demographers do with a Life table. Life expectancy
|
mortality rates (age-specific incidences of mortality) "remain
|
| is the expected mean time to survive if observed mortality rates
|
constant" in the future.
|
| (incidence of mortality) "remains constant" in the
|
</P>
|
| future. </p>
|
<H5><FONT color=#ec5e5e size=3><B>- Standard deviation of period
|
|
|
prevalence</B></FONT><B>: </B><A
|
| <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
|
href="http://euroreves.ined.fr/imach/doc/biaspar/vplrbiaspar.txt"><B>biaspar/vplrbiaspar.txt</B></A></H5>
|
| stationary prevalence</b></font><b>: </b><a
|
<P>The period prevalence has to be compared with the cross-sectional prevalence.
|
| href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
|
But both are statistical estimates and therefore have confidence intervals.
|
|
|
<BR>For the cross-sectional prevalence we generally need information on the
|
| <p>The stationary prevalence has to be compared with the observed
|
design of the surveys. It is usually not enough to consider the number of people
|
| prevalence by age. But both are statistical estimates and
|
surveyed at a particular age and to estimate a Bernouilli confidence interval
|
| subjected to stochastic errors due to the size of the sample, the
|
based on the prevalence at that age. But you can do it to have an idea of the
|
| design of the survey, and, for the stationary prevalence to the
|
randomness. At least you can get a visual appreciation of the randomness by
|
| model used and fitted. It is possible to compute the standard
|
looking at the fluctuation over ages.
|
| deviation of the stationary prevalence at each age.</p>
|
<P>For the period prevalence it is possible to estimate the confidence interval
|
|
|
from the Hessian matrix (see the publication for details). We are supposing that
|
| <h5><font color="#EC5E5E" size="3">-Observed and stationary
|
the design of the survey will only alter the weight of each individual. IMaCh
|
| prevalence in state (2=disable) with confidence interval</font>:<b>
|
scales the weights of individuals-waves contributing to the likelihood by
|
| </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
|
making the sum of the weights equal to the sum of individuals-waves
|
|
|
contributing: a weighted survey doesn't increase or decrease the size of the
|
| <p>This graph exhibits the stationary prevalence in state (2)
|
survey, it only give more weight to some individuals and thus less to the
|
| with the confidence interval in red. The green curve is the
|
others.
|
| observed prevalence (or proportion of individuals in state (2)).
|
<H5><FONT color=#ec5e5e size=3>-cross-sectional and period prevalence in state
|
| Without discussing the results (it is not the purpose here), we
|
(2=disable) with confidence interval</FONT>:<B> </B><A
|
| observe that the green curve is rather below the stationary
|
href="http://euroreves.ined.fr/imach/doc/biaspar/vbiaspar21.htm"><B>biaspar/vbiaspar21.png</B></A></H5>
|
| prevalence. It suggests an increase of the disability prevalence
|
<P>This graph exhibits the period prevalence in state (2) with the confidence
|
| in the future.</p>
|
interval in red. The green curve is the observed prevalence (or proportion of
|
|
|
individuals in state (2)). Without discussing the results (it is not the purpose
|
| <p><img src="vbiaspar21.gif" width="400" height="300"></p>
|
here), we observe that the green curve is somewhat below the period
|
|
|
prevalence. If the data were not biased by the non inclusion of people
|
| <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
|
living in institutions we would have concluded that the prevalence of
|
| stationary prevalence of disability</b></font><b>: </b><a
|
disability will increase in the future (see the main publication if
|
| href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
|
you are interested in real data and results which are opposite).</P>
|
| <img src="pbiaspar11.gif" width="400" height="300"> </h5>
|
<P><IMG height=300
|
|
|
src="Computing Health Expectancies using IMaCh_fichiers/vbiaspar21.png"
|
| <p>This graph plots the conditional transition probabilities from
|
width=400></P>
|
| an initial state (1=healthy in red at the bottom, or 2=disable in
|
<H5><FONT color=#ec5e5e size=3><B>-Convergence to the period prevalence of
|
| green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
|
disability</B></FONT><B>: </B><A
|
| age <em>x+h. </em>Conditional means at the condition to be alive
|
href="Computing Health Expectancies using IMaCh_fichiers/pbiaspar11.png"><B>biaspar/pbiaspar11.png</B></A><BR><IMG
|
| at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
|
height=300
|
| curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
|
src="Computing Health Expectancies using IMaCh_fichiers/pbiaspar11.png"
|
| + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
|
width=400> </H5>
|
| prevalence of disability</em>. In order to get the stationary
|
<P>This graph plots the conditional transition probabilities from an initial
|
| prevalence at age 70 we should start the process at an earlier
|
state (1=healthy in red at the bottom, or 2=disabled in green on the top) at age
|
| age, i.e.50. If the disability state is defined by severe
|
<EM>x </EM>to the final state 2=disabled<EM> </EM>at age <EM>x+h
|
| disability criteria with only a few chance to recover, then the
|
</EM> where conditional means conditional on being alive at age <EM>x+h </EM>which is
|
| incidence of recovery is low and the time to convergence is
|
<I>hP12x</I> + <EM>hP22x</EM>. The curves <I>hP12x/(hP12x</I> + <EM>hP22x)
|
| probably longer. But we don't have experience yet.</p>
|
</EM>and <I>hP22x/(hP12x</I> + <EM>hP22x) </EM>converge with <EM>h, </EM>to the
|
|
|
<EM>period prevalence of disability</EM>. In order to get the period prevalence
|
| <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
|
at age 70 we should start the process at an earlier age, i.e.50. If the
|
| and initial health status with standard deviation</b></font><b>: </b><a
|
disability state is defined by severe disability criteria with only a
|
| href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
|
small chance of recovering, then the incidence of recovery is low and the time to convergence is
|
|
|
probably longer. But we don't have experience of this yet.</P>
|
| <pre># Health expectancies
|
<H5><FONT color=#ec5e5e size=3><B>- Life expectancies by age and initial health
|
| |
status with standard deviation</B></FONT><B>: </B><A
|
| |
href="http://euroreves.ined.fr/imach/doc/biaspar/erbiaspar.txt"><B>biaspar/erbiaspar.txt</B></A></H5><PRE># Health expectancies
|
| # Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)
|
# Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)
|
| 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366)
|
70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
|
| 71 9.9325 (0.1409) 3.0495 (0.4234) 5.2627 (0.1107) 5.6384 (0.3129)
|
71 10.4786 (0.1184) 3.2093 (0.3212) 4.3384 (0.0875) 4.4820 (0.2076)
|
| 72 9.4603 (0.1319) 3.0540 (0.3770) 4.8810 (0.1099) 5.5811 (0.2907)
|
72 9.9551 (0.1103) 3.2236 (0.2827) 4.0426 (0.0885) 4.4827 (0.1966)
|
| 73 9.0009 (0.1246) 3.0565 (0.3345) 4.5188 (0.1098) 5.5187 (0.2702)
|
73 9.4476 (0.1035) 3.2379 (0.2478) 3.7621 (0.0899) 4.4825 (0.1858)
|
| </pre>
|
74 8.9564 (0.0980) 3.2522 (0.2165) 3.4966 (0.0920) 4.4815 (0.1754)
|
|
|
75 8.4815 (0.0937) 3.2665 (0.1887) 3.2457 (0.0946) 4.4798 (0.1656)
|
| <pre>For example 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366) means:
|
76 8.0230 (0.0905) 3.2806 (0.1645) 3.0090 (0.0979) 4.4772 (0.1565)
|
| e11=10.4171 e12=3.0433 e21=5.6641 e22=5.6907 </pre>
|
77 7.5810 (0.0884) 3.2946 (0.1438) 2.7860 (0.1017) 4.4738 (0.1484)
|
|
|
78 7.1554 (0.0871) 3.3084 (0.1264) 2.5763 (0.1062) 4.4696 (0.1416)
|
| <pre><img src="expbiaspar21.gif" width="400" height="300"><img
|
79 6.7464 (0.0867) 3.3220 (0.1124) 2.3794 (0.1112) 4.4646 (0.1364)
|
| src="expbiaspar11.gif" width="400" height="300"></pre>
|
80 6.3538 (0.0868) 3.3354 (0.1014) 2.1949 (0.1168) 4.4587 (0.1331)
|
|
|
81 5.9775 (0.0873) 3.3484 (0.0933) 2.0222 (0.1230) 4.4520 (0.1320)
|
| <p>For example, life expectancy of a healthy individual at age 70
|
</PRE><PRE>For example 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
|
| is 10.42 in the healthy state and 3.04 in the disability state
|
means
|
| (=13.46 years). If he was disable at age 70, his life expectancy
|
e11=11.0180 e12=3.1950 e21=4.6500 e22=4.4807 </PRE><PRE><IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/expbiaspar21.png" width=400><IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/expbiaspar11.png" width=400></PRE>
|
| will be shorter, 5.66 in the healthy state and 5.69 in the
|
<P>For example, life expectancy of a healthy individual at age 70 is 11.0 in the
|
| disability state (=11.35 years). The total life expectancy is a
|
healthy state and 3.2 in the disability state (total of 14.2 years). If he was
|
| weighted mean of both, 13.46 and 11.35; weight is the proportion
|
disabled at age 70, his life expectancy will be shorter, 4.65 years in the
|
| of people disabled at age 70. In order to get a pure period index
|
healthy state and 4.5 in the disability state (=9.15 years). The total life
|
| (i.e. based only on incidences) we use the <a
|
expectancy is a weighted mean of both, 14.2 and 9.15. The weight is the
|
| href="#Stationary prevalence in each state">computed or
|
proportion of people disabled at age 70. In order to get a period index (i.e.
|
| stationary prevalence</a> at age 70 (i.e. computed from
|
based only on incidences) we use the <A
|
| incidences at earlier ages) instead of the <a
|
href="http://euroreves.ined.fr/imach/doc/imach.htm#Period prevalence in each state">stable
|
| href="#Observed prevalence in each state">observed prevalence</a>
|
or period prevalence</A> at age 70 (i.e. computed from incidences at earlier
|
| (for example at first exam) (<a href="#Health expectancies">see
|
ages) instead of the <A
|
| below</a>).</p>
|
href="http://euroreves.ined.fr/imach/doc/imach.htm#cross-sectional prevalence in each state">cross-sectional
|
|
|
prevalence</A> (observed for example at first interview) (<A
|
| <h5><font color="#EC5E5E" size="3"><b>- Variances of life
|
href="http://euroreves.ined.fr/imach/doc/imach.htm#Health expectancies">see
|
| expectancies by age and initial health status</b></font><b>: </b><a
|
below</A>).</P>
|
| href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
|
<H5><FONT color=#ec5e5e size=3><B>- Variances of life expectancies by age and
|
|
|
initial health status</B></FONT><B>: </B><A
|
| <p>For example, the covariances of life expectancies Cov(ei,ej)
|
href="http://euroreves.ined.fr/imach/doc/biaspar/vrbiaspar.txt"><B>biaspar/vrbiaspar.txt</B></A></H5>
|
| at age 50 are (line 3) </p>
|
<P>For example, the covariances of life expectancies Cov(ei,ej) at age 50 are
|
|
|
(line 3) </P><PRE> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</PRE>
|
| <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
|
<H5><FONT color=#ec5e5e size=3><B>-Variances of one-step probabilities
|
|
|
</B></FONT><B>: </B><A
|
| <h5><font color="#EC5E5E" size="3"><b>-Variances of one-step
|
href="http://euroreves.ined.fr/imach/doc/biaspar/probrbiaspar.txt"><B>biaspar/probrbiaspar.txt</B></A></H5>
|
| probabilities </b></font><b>: </b><a href="probrbiaspar.txt"><b>probrbiaspar.txt</b></a></h5>
|
<P>For example, at age 65</P><PRE> p11=9.960e-001 standard deviation of p11=2.359e-004</PRE>
|
|
|
<H5><FONT color=#ec5e5e size=3><B>- </B></FONT><A
|
| <p>For example, at age 65</p>
|
name="Health expectancies"><FONT color=#ec5e5e size=3><B>Health
|
|
|
expectancies</B></FONT></A><FONT color=#ec5e5e size=3><B> with standard errors
|
| <pre> p11=9.960e-001 standard deviation of p11=2.359e-004</pre>
|
in parentheses</B></FONT><B>: </B><A
|
|
|
href="http://euroreves.ined.fr/imach/doc/biaspar/trbiaspar.txt"><FONT
|
| <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
|
face="Courier New"><B>biaspar/trbiaspar.txt</B></FONT></A></H5><PRE>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </PRE><PRE>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </PRE>
|
| name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
|
<P>Thus, at age 70 the total life expectancy, e..=13.26 years is the weighted
|
| expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
|
mean of e1.=13.46 and e2.=11.35 by the period prevalences at age 70 which are
|
| with standard errors in parentheses</b></font><b>: </b><a
|
0.90134 in state 1 and 0.09866 in state 2 respectively (the sum is equal to
|
| href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
|
one). e.1=9.95 is the Disability-free life expectancy at age 70 (it is again a
|
|
|
weighted mean of e11 and e21). e.2=3.30 is also the life expectancy at age 70 to
|
| <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
|
be spent in the disability state.</P>
|
|
|
<H5><FONT color=#ec5e5e size=3><B>-Total life expectancy by age and health
|
| <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
|
expectancies in states (1=healthy) and (2=disable)</B></FONT><B>: </B><A
|
|
|
href="Computing Health Expectancies using IMaCh_fichiers/ebiaspar1.png"><B>biaspar/ebiaspar1.png</B></A></H5>
|
| <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
|
<P>This figure represents the health expectancies and the total life expectancy
|
| the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
|
with a confidence interval (dashed line). </P><PRE> <IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/ebiaspar1.png" width=400></PRE>
|
| prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
|
<P>Standard deviations (obtained from the information matrix of the model) of
|
| state 2, respectively (the sum is equal to one). e.1=9.95 is the
|
these quantities are very useful. Cross-longitudinal surveys are costly and do
|
| Disability-free life expectancy at age 70 (it is again a weighted
|
not involve huge samples, generally a few thousands; therefore it is very
|
| mean of e11 and e21). e.2=3.30 is also the life expectancy at age
|
important to have an idea of the standard deviation of our estimates. It has
|
| 70 to be spent in the disability state.</p>
|
been a big challenge to compute the Health Expectancy standard deviations. Don't
|
|
|
be confused: life expectancy is, as any expected value, the mean of a
|
| <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
|
distribution; but here we are not computing the standard deviation of the
|
| age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
|
distribution, but the standard deviation of the estimate of the mean.</P>
|
| </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
|
<P>Our health expectancy estimates vary according to the sample size (and the
|
|
|
standard deviations give confidence intervals of the estimates) but also
|
| <p>This figure represents the health expectancies and the total
|
according to the model fitted. We explain this in more detail.</P>
|
| life expectancy with the confident interval in dashed curve. </p>
|
<P>Choosing a model means at least two kind of choices. First we have to
|
|
|
decide the number of disability states. And second we have to design, within
|
| <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
|
the logit model family, the model itself: variables, covariates, confounding
|
|
|
factors etc. to be included.</P>
|
| <p>Standard deviations (obtained from the information matrix of
|
<P>The more disability states we have, the better is our demographical
|
| the model) of these quantities are very useful.
|
approximation of the disability process, but the smaller the number of
|
| Cross-longitudinal surveys are costly and do not involve huge
|
transitions between each state and the higher the noise in the
|
| samples, generally a few thousands; therefore it is very
|
measurement. We have not experimented enough with the various models
|
| important to have an idea of the standard deviation of our
|
to summarize the advantages and disadvantages, but it is important to
|
| estimates. It has been a big challenge to compute the Health
|
note that even if we had huge unbiased samples, the total life
|
| Expectancy standard deviations. Don't be confuse: life expectancy
|
expectancy computed from a cross-longitudinal survey would vary with
|
| is, as any expected value, the mean of a distribution; but here
|
the number of states. If we define only two states, alive or dead, we
|
| we are not computing the standard deviation of the distribution,
|
find the usual life expectancy where it is assumed that at each age,
|
| but the standard deviation of the estimate of the mean.</p>
|
people are at the same risk of dying. If we are differentiating the
|
|
|
alive state into healthy and disabled, and as mortality from the
|
| <p>Our health expectancies estimates vary according to the sample
|
disabled state is higher than mortality from the healthy state, we are
|
| size (and the standard deviations give confidence intervals of
|
introducing heterogeneity in the risk of dying. The total mortality at
|
| the estimate) but also according to the model fitted. Let us
|
each age is the weighted mean of the mortality from each state by the
|
| explain it in more details.</p>
|
prevalence of each state. Therefore if the proportion of people at each age and
|
|
|
in each state is different from the period equilibrium, there is no reason to
|
| <p>Choosing a model means ar least two kind of choices. First we
|
find the same total mortality at a particular age. Life expectancy, even if it
|
| have to decide the number of disability states. Second we have to
|
is a very useful tool, has a very strong hypothesis of homogeneity of the
|
| design, within the logit model family, the model: variables,
|
population. Our main purpose is not to measure differential mortality but to
|
| covariables, confonding factors etc. to be included.</p>
|
measure the expected time in a healthy or disabled state in order to maximise
|
|
|
the former and minimize the latter. But the differential in mortality
|
| <p>More disability states we have, better is our demographical
|
complicates the measurement.</P>
|
| approach of the disability process, but smaller are the number of
|
<P>Incidences of disability or recovery are not affected by the number of states
|
| transitions between each state and higher is the noise in the
|
if these states are independent. But incidence estimates are dependent on the
|
| measurement. We do not have enough experiments of the various
|
specification of the model. The more covariates we add in the logit
|
| models to summarize the advantages and disadvantages, but it is
|
model the better
|
| important to say that even if we had huge and unbiased samples,
|
is the model, but some covariates are not well measured, some are confounding
|
| the total life expectancy computed from a cross-longitudinal
|
factors like in any statistical model. The procedure to "fit the best model' is
|
| survey, varies with the number of states. If we define only two
|
similar to logistic regression which itself is similar to regression analysis.
|
| states, alive or dead, we find the usual life expectancy where it
|
We haven't yet been sofar because we also have a severe limitation which is the
|
| is assumed that at each age, people are at the same risk to die.
|
speed of the convergence. On a Pentium III, 500 MHz, even the simplest model,
|
| If we are differentiating the alive state into healthy and
|
estimated by month on 8,000 people may take 4 hours to converge. Also, the IMaCh
|
| disable, and as the mortality from the disability state is higher
|
program is not a statistical package, and does not allow sophisticated design
|
| than the mortality from the healthy state, we are introducing
|
variables. If you need sophisticated design variable you have to them your self
|
| heterogeneity in the risk of dying. The total mortality at each
|
and and add them as ordinary variables. IMaCh allows up to 8 variables. The
|
| age is the weighted mean of the mortality in each state by the
|
current version of this program allows only to add simple variables like age+sex
|
| prevalence in each state. Therefore if the proportion of people
|
or age+sex+ age*sex but will never be general enough. But what is to remember,
|
| at each age and in each state is different from the stationary
|
is that incidences or probability of change from one state to another is
|
| equilibrium, there is no reason to find the same total mortality
|
affected by the variables specified into the model.</P>
|
| at a particular age. Life expectancy, even if it is a very useful
|
<P>Also, the age range of the people interviewed is linked the age range of the
|
| tool, has a very strong hypothesis of homogeneity of the
|
life expectancy which can be estimated by extrapolation. If your sample ranges
|
| population. Our main purpose is not to measure differential
|
from age 70 to 95, you can clearly estimate a life expectancy at age 70 and
|
| mortality but to measure the expected time in a healthy or
|
trust your confidence interval because it is mostly based on your sample size,
|
| disability state in order to maximise the former and minimize the
|
but if you want to estimate the life expectancy at age 50, you should rely in
|
| latter. But the differential in mortality complexifies the
|
the design of your model. Fitting a logistic model on a age range of 70 to 95
|
| measurement.</p>
|
and estimating probabilties of transition out of this age range, say at age 50,
|
|
|
is very dangerous. At least you should remember that the confidence interval
|
| <p>Incidences of disability or recovery are not affected by the
|
given by the standard deviation of the health expectancies, are under the strong
|
| number of states if these states are independant. But incidences
|
assumption that your model is the 'true model', which is probably not the case
|
| estimates are dependant on the specification of the model. More
|
outside the age range of your sample.</P>
|
| covariates we added in the logit model better is the model, but
|
<H5><FONT color=#ec5e5e size=3><B>- Copy of the parameter file</B></FONT><B>:
|
| some covariates are not well measured, some are confounding
|
</B><A
|
| factors like in any statistical model. The procedure to "fit
|
href="http://euroreves.ined.fr/imach/doc/orbiaspar.txt"><B>orbiaspar.txt</B></A></H5>
|
| the best model' is similar to logistic regression which itself is
|
<P>This copy of the parameter file can be useful to re-run the program while
|
| similar to regression analysis. We haven't yet been sofar because
|
saving the old output files. </P>
|
| we also have a severe limitation which is the speed of the
|
<H5><FONT color=#ec5e5e size=3><B>- Prevalence forecasting</B></FONT><B>: </B><A
|
| convergence. On a Pentium III, 500 MHz, even the simplest model,
|
href="http://euroreves.ined.fr/imach/doc/biaspar/frbiaspar.txt"><B>biaspar/frbiaspar.txt</B></A></H5>
|
| estimated by month on 8,000 people may take 4 hours to converge.
|
<P>First, we have estimated the observed prevalence between 1/1/1984 and
|
| Also, the program is not yet a statistical package, which permits
|
1/6/1988 (June, European syntax of dates). The mean date of all interviews
|
| a simple writing of the variables and the model to take into
|
(weighted average of the interviews performed between 1/1/1984 and 1/6/1988) is
|
| account in the maximisation. The actual program allows only to
|
estimated to be 13/9/1985, as written on the top on the file. Then we forecast
|
| add simple variables like age+sex or age+sex+ age*sex but will
|
the probability to be in each state. </P>
|
| never be general enough. But what is to remember, is that
|
<P>For example on 1/1/1989 : </P><PRE class=MsoNormal># StartingAge FinalAge P.1 P.2 P.3
|
| incidences or probability of change from one state to another is
|
|
| affected by the variables specified into the model.</p>
|
|
|
|
|
| <p>Also, the age range of the people interviewed has a link with
|
|
| the age range of the life expectancy which can be estimated by
|
|
| extrapolation. If your sample ranges from age 70 to 95, you can
|
|
| clearly estimate a life expectancy at age 70 and trust your
|
|
| confidence interval which is mostly based on your sample size,
|
|
| but if you want to estimate the life expectancy at age 50, you
|
|
| should rely in your model, but fitting a logistic model on a age
|
|
| range of 70-95 and estimating probabilties of transition out of
|
|
| this age range, say at age 50 is very dangerous. At least you
|
|
| should remember that the confidence interval given by the
|
|
| standard deviation of the health expectancies, are under the
|
|
| strong assumption that your model is the 'true model', which is
|
|
| probably not the case.</p>
|
|
|
|
|
| <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
|
|
| file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
|
|
|
|
|
| <p>This copy of the parameter file can be useful to re-run the
|
|
| program while saving the old output files. </p>
|
|
|
|
|
| <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
|
|
| </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
|
|
|
|
|
| <p
|
|
| style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,
|
|
| we have estimated the observed prevalence between 1/1/1984 and
|
|
| 1/6/1988. The mean date of interview (weighed average of the
|
|
| interviews performed between1/1/1984 and 1/6/1988) is estimated
|
|
| to be 13/9/1985, as written on the top on the file. Then we
|
|
| forecast the probability to be in each state. </p>
|
|
|
|
|
| <p
|
|
| style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,
|
|
| at date 1/1/1989 : </p>
|
|
|
|
|
| <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
|
|
| # Forecasting at date 1/1/1989
|
# Forecasting at date 1/1/1989
|
| 73 0.807 0.078 0.115</pre>
|
73 0.807 0.078 0.115</PRE>
|
|
|
<P>Since the minimum age is 70 on the 13/9/1985, the youngest forecasted age is
|
| <p
|
73. This means that at age a person aged 70 at 13/9/1989 has a probability to
|
| style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Since
|
enter state1 of 0.807 at age 73 on 1/1/1989. Similarly, the probability to be in
|
| the minimum age is 70 on the 13/9/1985, the youngest forecasted
|
state 2 is 0.078 and the probability to die is 0.115. Then, on the 1/1/1989, the
|
| age is 73. This means that at age a person aged 70 at 13/9/1989
|
prevalence of disability at age 73 is estimated to be 0.088.</P>
|
| has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
|
<H5><FONT color=#ec5e5e size=3><B>- Population forecasting</B></FONT><B>: </B><A
|
| Similarly, the probability to be in state 2 is 0.078 and the
|
href="http://euroreves.ined.fr/imach/doc/biaspar/poprbiaspar.txt"><B>biaspar/poprbiaspar.txt</B></A></H5><PRE># Age P.1 P.2 P.3 [Population]
|
| probability to die is 0.115. Then, on the 1/1/1989, the
|
|
| prevalence of disability at age 73 is estimated to be 0.088.</p>
|
|
|
|
|
| <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
|
|
| </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
|
|
|
|
|
| <pre># Age P.1 P.2 P.3 [Population]
|
|
| # Forecasting at date 1/1/1989
|
# Forecasting at date 1/1/1989
|
| 75 572685.22 83798.08
|
75 572685.22 83798.08
|
| 74 621296.51 79767.99
|
74 621296.51 79767.99
|
| 73 645857.70 69320.60 </pre>
|
73 645857.70 69320.60 </PRE><PRE># Forecasting at date 1/1/19909
|
|
|
|
| <pre># Forecasting at date 1/1/19909
|
|
| 76 442986.68 92721.14 120775.48
|
76 442986.68 92721.14 120775.48
|
| 75 487781.02 91367.97 121915.51
|
75 487781.02 91367.97 121915.51
|
| 74 512892.07 85003.47 117282.76 </pre>
|
74 512892.07 85003.47 117282.76 </PRE>
|
|
|
<P>From the population file, we estimate the number of people in each state. At
|
| <p>From the population file, we estimate the number of people in
|
age 73, 645857 persons are in state 1 and 69320 are in state 2. One year latter,
|
| each state. At age 73, 645857 persons are in state 1 and 69320
|
512892 are still in state 1, 85003 are in state 2 and 117282 died before
|
| are in state 2. One year latter, 512892 are still in state 1,
|
1/1/1990.</P>
|
| 85003 are in state 2 and 117282 died before 1/1/1990.</p>
|
<HR>
|
|
|
|
| <hr>
|
<H2><A name=example></A><FONT color=#00006a>Trying an example</FONT></H2>
|
|
|
<P>Since you know how to run the program, it is time to test it on your own
|
| <h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>
|
computer. Try for example on a parameter file named <A
|
|
|
href="http://euroreves.ined.fr/imach/doc/imachpar.imach">imachpar.imach</A>
|
| <p>Since you know how to run the program, it is time to test it
|
which is a copy of <FONT face="Courier New" size=2>mypar.imach</FONT> included
|
| on your own computer. Try for example on a parameter file named <a
|
in the subdirectory of imach, <FONT face="Courier New" size=2>mytry</FONT>. Edit
|
| href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy
|
it and change the name of the data file to <FONT face="Courier New"
|
| of <font size="2" face="Courier New">mypar.imach</font> included
|
size=2>mydata.txt</FONT> if you don't want to copy it on the same directory. The
|
| in the subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
|
file <FONT face="Courier New">mydata.txt</FONT> is a smaller file of 3,000
|
| Edit it to change the name of the data file to <font size="2"
|
people but still with 4 waves. </P>
|
| face="Courier New">..\data\mydata.txt</font> if you don't want to
|
<P>Right click on the .imach file and a window will popup with the string
|
| copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
|
'<STRONG>Enter the parameter file name:'</STRONG></P>
|
| is a smaller file of 3,000 people but still with 4 waves. </p>
|
<TABLE border=1>
|
|
|
<TBODY>
|
| <p>Click on the imach.exe icon to open a window. Answer to the
|
<TR>
|
| question:'<strong>Enter the parameter file name:'</strong></p>
|
<TD width="100%"><STRONG>IMACH, Version 0.97b</STRONG>
|
|
|
<P><STRONG>Enter the parameter file name:
|
| <table border="1">
|
imachpar.imach</STRONG></P></TD></TR></TBODY></TABLE>
|
| <tr>
|
<P>Most of the data files or image files generated, will use the 'imachpar'
|
| <td width="100%"><strong>IMACH, Version 0.8a</strong><p><strong>Enter
|
string into their name. The running time is about 2-3 minutes on a Pentium III.
|
| the parameter file name: ..\mytry\imachpar.imach</strong></p>
|
If the execution worked correctly, the outputs files are created in the current
|
| </td>
|
directory, and should be the same as the mypar files initially included in the
|
| </tr>
|
directory <FONT face="Courier New" size=2>mytry</FONT>.</P>
|
| </table>
|
<UL>
|
|
|
<LI><PRE><U>Output on the screen</U> The output screen looks like <A href="http://euroreves.ined.fr/imach/doc/biaspar.log">biaspar.log</A>
|
| <p>Most of the data files or image files generated, will use the
|
|
| 'imachpar' string into their name. The running time is about 2-3
|
|
| minutes on a Pentium III. If the execution worked correctly, the
|
|
| outputs files are created in the current directory, and should be
|
|
| the same as the mypar files initially included in the directory <font
|
|
| size="2" face="Courier New">mytry</font>.</p>
|
|
|
|
|
| <ul>
|
|
| <li><pre><u>Output on the screen</u> The output screen looks like <a
|
|
| href="imachrun.LOG">this Log file</a>
|
|
| #
|
#
|
|
|
title=MLE datafile=mydaiata.txt lastobs=3000 firstpass=1 lastpass=3
|
| title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
|
ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</PRE>
|
| ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
|
<LI><PRE>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
|
| </li>
|
|
| <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
|
|
|
|
|
| Warning, no any valid information for:126 line=126
|
Warning, no any valid information for:126 line=126
|
| Warning, no any valid information for:2307 line=2307
|
Warning, no any valid information for:2307 line=2307
|
| Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
|
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>
|
<FONT face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</FONT>
|
| Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
|
Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
|
| prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
|
prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
|
| Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
|
Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </PRE></LI></UL>It
|
| </li>
|
includes some warnings or errors which are very important for you. Be careful
|
| </ul>
|
with such warnings because your results may be biased if, for example, you have
|
|
|
people who accepted to be interviewed at first pass but never after. Or if you
|
| <p> </p>
|
don't have the exact month of death. In such cases IMaCh doesn't take any
|
|
|
initiative, it does only warn you. It is up to you to decide what to do with
|
| <ul>
|
these people. Excluding them is usually a wrong decision. It is better to decide
|
| <li>Maximisation with the Powell algorithm. 8 directions are
|
that the month of death is at the mid-interval between the last two waves for
|
| given corresponding to the 8 parameters. this can be
|
example.
|
| rather long to get convergence.<br>
|
<P>If you survey suffers from severe attrition, you have to analyse the
|
| <font size="1" face="Courier New"><br>
|
characteristics of the lost people and overweight people with same
|
| Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
|
characteristics for example.
|
| 0.000000000000 3<br>
|
<P>By default, IMaCH warns and excludes these problematic people, but you have
|
| 0.000000000000 4 0.000000000000 5 0.000000000000 6
|
to be careful with such results.
|
| 0.000000000000 7 <br>
|
<P> </P>
|
| 0.000000000000 8 0.000000000000<br>
|
<UL>
|
| 1..........2.................3..........4.................5.........<br>
|
<LI>Maximisation with the Powell algorithm. 8 directions are given
|
| 6................7........8...............<br>
|
corresponding to the 8 parameters. this can be rather long to get
|
| Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
|
convergence.<BR><FONT face="Courier New" size=1><BR>Powell iter=1
|
| <br>
|
-2*LL=11531.405658264877 1 0.000000000000 2 0.000000000000 3<BR>0.000000000000
|
| 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
|
4 0.000000000000 5 0.000000000000 6 0.000000000000 7 <BR>0.000000000000 8
|
| 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
|
0.000000000000<BR>1..........2.................3..........4.................5.........<BR>6................7........8...............<BR>Powell
|
| 8 0.051272038506<br>
|
iter=23 -2*LL=6744.954108371555 1 -12.967632334283 <BR>2 0.135136681033 3
|
| 1..............2...........3..............4...........<br>
|
-7.402109728262 4 0.067844593326 <BR>5 -0.673601538129 6 -0.006615504377 7
|
| 5..........6................7...........8.........<br>
|
-5.051341616718 <BR>8
|
| #Number of iterations = 23, -2 Log likelihood =
|
0.051272038506<BR>1..............2...........3..............4...........<BR>5..........6................7...........8.........<BR>#Number
|
| 6744.954042573691<br>
|
of iterations = 23, -2 Log likelihood = 6744.954042573691<BR>#
|
| # Parameters<br>
|
Parameters<BR>12 -12.966061 0.135117 <BR>13 -7.401109 0.067831 <BR>21
|
| 12 -12.966061 0.135117 <br>
|
-0.672648 -0.006627 <BR>23 -5.051297 0.051271 </FONT><BR>
|
| 13 -7.401109 0.067831 <br>
|
<LI><PRE><FONT size=2>Calculation of the hessian matrix. Wait...
|
| 21 -0.672648 -0.006627 <br>
|
|
| 23 -5.051297 0.051271 </font><br>
|
|
| </li>
|
|
| <li><pre><font size="2">Calculation of the hessian matrix. Wait...
|
|
| 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78
|
12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78
|
|
|
|
| Inverting the hessian to get the covariance matrix. Wait...
|
Inverting the hessian to get the covariance matrix. Wait...
|
|
Line 1232 Computing Variance-covariance of DFLEs:
|
Line 1036 Computing Variance-covariance of DFLEs:
|
| Computing Total LEs with variances: file 'trmypar.txt'
|
Computing Total LEs with variances: file 'trmypar.txt'
|
| Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
|
Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
|
| End of Imach
|
End of Imach
|
| </font></pre>
|
</FONT></PRE></LI></UL>
|
| </li>
|
<P><FONT size=3>Once the running is finished, the program requires a
|
| </ul>
|
character:</FONT></P>
|
|
|
<TABLE border=1>
|
| <p><font size="3">Once the running is finished, the program
|
<TBODY>
|
| requires a caracter:</font></p>
|
<TR>
|
|
|
<TD width="100%"><STRONG>Type e to edit output files, g to graph again, c
|
| <table border="1">
|
to start again, and q for exiting:</STRONG></TD></TR></TBODY></TABLE>In order to
|
| <tr>
|
have an idea of the time needed to reach convergence, IMaCh gives an estimation
|
| <td width="100%"><strong>Type e to edit output files, g
|
if the convergence needs 10, 20 or 30 iterations. It might be useful.
|
| to graph again, c to start again, and q for exiting:</strong></td>
|
<P><FONT size=3>First you should enter <STRONG>e </STRONG>to edit the master
|
| </tr>
|
file mypar.htm. </FONT></P>
|
| </table>
|
<UL>
|
|
|
<LI><U>Outputs files</U> <BR><BR>- Copy of the parameter file: <A
|
| <p><font size="3">First you should enter <strong>e </strong>to
|
href="http://euroreves.ined.fr/imach/doc/ormypar.txt">ormypar.txt</A><BR>-
|
| edit the master file mypar.htm. </font></p>
|
Gnuplot file name: <A
|
|
|
href="http://euroreves.ined.fr/imach/doc/mypar.gp.txt">mypar.gp.txt</A><BR>-
|
| <ul>
|
Cross-sectional prevalence in each state: <A
|
| <li><u>Outputs files</u> <br>
|
href="http://euroreves.ined.fr/imach/doc/prmypar.txt">prmypar.txt</A> <BR>-
|
| <br>
|
Period prevalence in each state: <A
|
| - Copy of the parameter file: <a href="ormypar.txt">ormypar.txt</a><br>
|
href="http://euroreves.ined.fr/imach/doc/plrmypar.txt">plrmypar.txt</A> <BR>-
|
| - Gnuplot file name: <a href="mypar.gp.txt">mypar.gp.txt</a><br>
|
Transition probabilities: <A
|
| - Observed prevalence in each state: <a
|
href="http://euroreves.ined.fr/imach/doc/pijrmypar.txt">pijrmypar.txt</A><BR>-
|
| href="prmypar.txt">prmypar.txt</a> <br>
|
Life expectancies by age and initial health status (estepm=24 months): <A
|
| - Stationary prevalence in each state: <a
|
href="http://euroreves.ined.fr/imach/doc/ermypar.txt">ermypar.txt</A> <BR>-
|
| href="plrmypar.txt">plrmypar.txt</a> <br>
|
Parameter file with estimated parameters and the covariance matrix: <A
|
| - Transition probabilities: <a href="pijrmypar.txt">pijrmypar.txt</a><br>
|
href="http://euroreves.ined.fr/imach/doc/rmypar.txt">rmypar.txt</A> <BR>-
|
| - Life expectancies by age and initial health status
|
Variance of one-step probabilities: <A
|
| (estepm=24 months): <a href="ermypar.txt">ermypar.txt</a>
|
href="http://euroreves.ined.fr/imach/doc/probrmypar.txt">probrmypar.txt</A>
|
| <br>
|
<BR>- Variances of life expectancies by age and initial health status
|
| - Parameter file with estimated parameters and the
|
(estepm=24 months): <A
|
| covariance matrix: <a href="rmypar.txt">rmypar.txt</a> <br>
|
href="http://euroreves.ined.fr/imach/doc/vrmypar.txt">vrmypar.txt</A><BR>-
|
| - Variance of one-step probabilities: <a
|
Health expectancies with their variances: <A
|
| href="probrmypar.txt">probrmypar.txt</a> <br>
|
href="http://euroreves.ined.fr/imach/doc/trmypar.txt">trmypar.txt</A> <BR>-
|
| - Variances of life expectancies by age and initial
|
Standard deviation of period prevalences: <A
|
| health status (estepm=24 months): <a href="vrmypar.txt">vrmypar.txt</a><br>
|
href="http://euroreves.ined.fr/imach/doc/vplrmypar.txt">vplrmypar.txt</A>
|
| - Health expectancies with their variances: <a
|
<BR>No population forecast: popforecast = 0 (instead of 1) or stepm = 24
|
| href="trmypar.txt">trmypar.txt</a> <br>
|
(instead of 1) or model=. (instead of .)<BR><BR>
|
| - Standard deviation of stationary prevalences: <a
|
<LI><U>Graphs</U> <BR><BR>-<A
|
| href="vplrmypar.txt">vplrmypar.txt</a> <br>
|
href="http://euroreves.ined.fr/imach/mytry/pemypar1.gif">One-step transition
|
| No population forecast: popforecast = 0 (instead of 1) or
|
probabilities</A><BR>-<A
|
| stepm = 24 (instead of 1) or model=. (instead of .)<br>
|
href="http://euroreves.ined.fr/imach/mytry/pmypar11.gif">Convergence to the
|
| <br>
|
period prevalence</A><BR>-<A
|
| </li>
|
href="http://euroreves.ined.fr/imach/mytry/vmypar11.gif">Cross-sectional and
|
| <li><u>Graphs</u> <br>
|
period prevalence in state (1) with the confident interval</A> <BR>-<A
|
| <br>
|
href="http://euroreves.ined.fr/imach/mytry/vmypar21.gif">Cross-sectional and
|
| -<a href="../mytry/pemypar1.gif">One-step transition
|
period prevalence in state (2) with the confident interval</A> <BR>-<A
|
| probabilities</a><br>
|
href="http://euroreves.ined.fr/imach/mytry/expmypar11.gif">Health life
|
| -<a href="../mytry/pmypar11.gif">Convergence to the
|
expectancies by age and initial health state (1)</A> <BR>-<A
|
| stationary prevalence</a><br>
|
href="http://euroreves.ined.fr/imach/mytry/expmypar21.gif">Health life
|
| -<a href="..\mytry\vmypar11.gif">Observed and stationary
|
expectancies by age and initial health state (2)</A> <BR>-<A
|
| prevalence in state (1) with the confident interval</a> <br>
|
href="http://euroreves.ined.fr/imach/mytry/emypar1.gif">Total life expectancy
|
| -<a href="..\mytry\vmypar21.gif">Observed and stationary
|
by age and health expectancies in states (1) and (2).</A> </LI></UL>
|
| prevalence in state (2) with the confident interval</a> <br>
|
<P>This software have been partly granted by <A
|
| -<a href="..\mytry\expmypar11.gif">Health life
|
href="http://euroreves.ined.fr/">Euro-REVES</A>, a concerted action from the
|
| expectancies by age and initial health state (1)</a> <br>
|
European Union. It will be copyrighted identically to a GNU software product,
|
| -<a href="..\mytry\expmypar21.gif">Health life
|
i.e. program and software can be distributed freely for non commercial use.
|
| expectancies by age and initial health state (2)</a> <br>
|
Sources are not widely distributed today. You can get them by asking us with a
|
| -<a href="..\mytry\emypar1.gif">Total life expectancy by
|
simple justification (name, email, institute) <A
|
| age and health expectancies in states (1) and (2).</a> </li>
|
href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</A> and <A
|
| </ul>
|
href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</A> .</P>
|
|
|
<P>Latest version (0.97b of June 2004) can be accessed at <A
|
| <p>This software have been partly granted by <a
|
href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</A><BR></P></BODY></HTML>
|
| 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 (0.8a of May 2002) can be accessed at <a
|
|
| href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
|
|
| </p>
|
|
| </body>
|
|
| </html>
|
|
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