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 <h1 align="center"><font color="#00006A">Computing Health  content="text/html; charset=iso-8859-1">
 Expectancies using IMaCh</font></h1>  <meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
   <title></title>
 <h1 align="center"><font color="#00006A" size="5">(a Maximum  </head>
 Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>  
   <body bgcolor="#FFFFFF">
 <p align="center">&nbsp;</p>  
   <hr size="3" color="#EC5E5E">
 <p align="center"><a href="http://www.ined.fr/"><img  
 src="logo-ined.gif" border="0" width="151" height="76"></a><img  <h1 align="center"><font color="#00006A">Computing Health
 src="euroreves2.gif" width="151" height="75"></p>  Expectancies using IMaCh</font></h1>
   
 <h3 align="center"><a href="http://www.ined.fr/"><font  <h1 align="center"><font color="#00006A" size="5">(a Maximum
 color="#00006A">INED</font></a><font color="#00006A"> and </font><a  Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
 href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>  
   <p align="center">&nbsp;</p>
 <p align="center"><font color="#00006A" size="4"><strong>March  
 2000</strong></font></p>  <p align="center"><a href="http://www.ined.fr/"><img
   src="logo-ined.gif" border="0" width="151" height="76"></a><img
 <hr size="3" color="#EC5E5E">  src="euroreves2.gif" width="151" height="75"></p>
   
 <p align="center"><font color="#00006A"><strong>Authors of the  <h3 align="center"><a href="http://www.ined.fr/"><font
 program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font  color="#00006A">INED</font></a><font color="#00006A"> and </font><a
 color="#00006A"><strong>Nicolas Brouard</strong></font></a><font  href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
 color="#00006A"><strong>, senior researcher at the </strong></font><a  
 href="http://www.ined.fr"><font color="#00006A"><strong>Institut  <p align="center"><font color="#00006A" size="4"><strong>Version
 National d'Etudes Démographiques</strong></font></a><font  0.8, March 2002</strong></font></p>
 color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,  
 Health and Epidemiology&quot; Research Unit </strong></font></p>  <hr size="3" color="#EC5E5E">
   
 <p align="center"><font color="#00006A"><strong>and Agnès  <p align="center"><font color="#00006A"><strong>Authors of the
 Lièvre<br clear="left">  program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
 </strong></font></p>  color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
   color="#00006A"><strong>, senior researcher at the </strong></font><a
 <h4><font color="#00006A">Contribution to the mathematics: C. R.  href="http://www.ined.fr"><font color="#00006A"><strong>Institut
 Heathcote </font><font color="#00006A" size="2">(Australian  National d'Etudes Démographiques</strong></font></a><font
 National University, Canberra).</font></h4>  color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,
   Health and Epidemiology&quot; Research Unit </strong></font></p>
 <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  <p align="center"><font color="#00006A"><strong>and Agnès
 color="#00006A">) </font></h4>  Lièvre<br clear="left">
   </strong></font></p>
 <hr>  
   <h4><font color="#00006A">Contribution to the mathematics: C. R.
 <ul>  Heathcote </font><font color="#00006A" size="2">(Australian
     <li><a href="#intro">Introduction</a> </li>  National University, Canberra).</font></h4>
     <li>The detailed statistical model (<a href="docmath.pdf">PDF  
         version</a>),(<a href="docmath.ps">ps version</a>) </li>  <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
     <li><a href="#data">On what kind of data can it be used?</a></li>  href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
     <li><a href="#datafile">The data file</a> </li>  color="#00006A">) </font></h4>
     <li><a href="#biaspar">The parameter file</a> </li>  
     <li><a href="#running">Running Imach</a> </li>  <hr>
     <li><a href="#output">Output files and graphs</a> </li>  
     <li><a href="#example">Exemple</a> </li>  <ul>
 </ul>      <li><a href="#intro">Introduction</a> </li>
       <li><a href="#data">On what kind of data can it be used?</a></li>
 <hr>      <li><a href="#datafile">The data file</a> </li>
       <li><a href="#biaspar">The parameter file</a> </li>
 <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>      <li><a href="#running">Running Imach</a> </li>
       <li><a href="#output">Output files and graphs</a> </li>
 <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal      <li><a href="#example">Exemple</a> </li>
 data</b>. Within the family of Health Expectancies (HE),  </ul>
 Disability-free life expectancy (DFLE) is probably the most  
 important index to monitor. In low mortality countries, there is  <hr>
 a fear that when mortality declines, the increase in DFLE is not  
 proportionate to the increase in total Life expectancy. This case  <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
 is called the <em>Expansion of morbidity</em>. Most of the data  
 collected today, in particular by the international <a  <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
 href="http://euroreves/reves">REVES</a> network on Health  data</b> using the methodology pioneered by Laditka and Wolf (1).
 expectancy, and most HE indices based on these data, are <em>cross-sectional</em>.  Within the family of Health Expectancies (HE), Disability-free
 It means that the information collected comes from a single  life expectancy (DFLE) is probably the most important index to
 cross-sectional survey: people from various ages (but mostly old  monitor. In low mortality countries, there is a fear that when
 people) are surveyed on their health status at a single date.  mortality declines, the increase in DFLE is not proportionate to
 Proportion of people disabled at each age, can then be measured  the increase in total Life expectancy. This case is called the <em>Expansion
 at that date. This age-specific prevalence curve is then used to  of morbidity</em>. Most of the data collected today, in
 distinguish, within the stationary population (which, by  particular by the international <a href="http://www.reves.org">REVES</a>
 definition, is the life table estimated from the vital statistics  network on Health expectancy, and most HE indices based on these
 on mortality at the same date), the disable population from the  data, are <em>cross-sectional</em>. It means that the information
 disability-free population. Life expectancy (LE) (or total  collected comes from a single cross-sectional survey: people from
 population divided by the yearly number of births or deaths of  various ages (but mostly old people) are surveyed on their health
 this stationary population) is then decomposed into DFLE and DLE.  status at a single date. Proportion of people disabled at each
 This method of computing HE is usually called the Sullivan method  age, can then be measured at that date. This age-specific
 (from the name of the author who first described it).</p>  prevalence curve is then used to distinguish, within the
   stationary population (which, by definition, is the life table
 <p>Age-specific proportions of people disable are very difficult  estimated from the vital statistics on mortality at the same
 to forecast because each proportion corresponds to historical  date), the disable population from the disability-free
 conditions of the cohort and it is the result of the historical  population. Life expectancy (LE) (or total population divided by
 flows from entering disability and recovering in the past until  the yearly number of births or deaths of this stationary
 today. The age-specific intensities (or incidence rates) of  population) is then decomposed into DFLE and DLE. This method of
 entering disability or recovering a good health, are reflecting  computing HE is usually called the Sullivan method (from the name
 actual conditions and therefore can be used at each age to  of the author who first described it).</p>
 forecast the future of this cohort. For example if a country is  
 improving its technology of prosthesis, the incidence of  <p>Age-specific proportions of people disable are very difficult
 recovering the ability to walk will be higher at each (old) age,  to forecast because each proportion corresponds to historical
 but the prevalence of disability will only slightly reflect an  conditions of the cohort and it is the result of the historical
 improve because the prevalence is mostly affected by the history  flows from entering disability and recovering in the past until
 of the cohort and not by recent period effects. To measure the  today. The age-specific intensities (or incidence rates) of
 period improvement we have to simulate the future of a cohort of  entering disability or recovering a good health, are reflecting
 new-borns entering or leaving at each age the disability state or  actual conditions and therefore can be used at each age to
 dying according to the incidence rates measured today on  forecast the future of this cohort. For example if a country is
 different cohorts. The proportion of people disabled at each age  improving its technology of prosthesis, the incidence of
 in this simulated cohort will be much lower (using the exemple of  recovering the ability to walk will be higher at each (old) age,
 an improvement) that the proportions observed at each age in a  but the prevalence of disability will only slightly reflect an
 cross-sectional survey. This new prevalence curve introduced in a  improve because the prevalence is mostly affected by the history
 life table will give a much more actual and realistic HE level  of the cohort and not by recent period effects. To measure the
 than the Sullivan method which mostly measured the History of  period improvement we have to simulate the future of a cohort of
 health conditions in this country.</p>  new-borns entering or leaving at each age the disability state or
   dying according to the incidence rates measured today on
 <p>Therefore, the main question is how to measure incidence rates  different cohorts. The proportion of people disabled at each age
 from cross-longitudinal surveys? This is the goal of the IMaCH  in this simulated cohort will be much lower (using the exemple of
 program. From your data and using IMaCH you can estimate period  an improvement) that the proportions observed at each age in a
 HE and not only Sullivan's HE. Also the standard errors of the HE  cross-sectional survey. This new prevalence curve introduced in a
 are computed.</p>  life table will give a much more actual and realistic HE level
   than the Sullivan method which mostly measured the History of
 <p>A cross-longitudinal survey consists in a first survey  health conditions in this country.</p>
 (&quot;cross&quot;) where individuals from different ages are  
 interviewed on their health status or degree of disability. At  <p>Therefore, the main question is how to measure incidence rates
 least a second wave of interviews (&quot;longitudinal&quot;)  from cross-longitudinal surveys? This is the goal of the IMaCH
 should measure each new individual health status. Health  program. From your data and using IMaCH you can estimate period
 expectancies are computed from the transitions observed between  HE and not only Sullivan's HE. Also the standard errors of the HE
 waves and are computed for each degree of severity of disability  are computed.</p>
 (number of life states). More degrees you consider, more time is  
 necessary to reach the Maximum Likelihood of the parameters  <p>A cross-longitudinal survey consists in a first survey
 involved in the model. Considering only two states of disability  (&quot;cross&quot;) where individuals from different ages are
 (disable and healthy) is generally enough but the computer  interviewed on their health status or degree of disability. At
 program works also with more health statuses.<br>  least a second wave of interviews (&quot;longitudinal&quot;)
 <br>  should measure each new individual health status. Health
 The simplest model is the multinomial logistic model where <i>pij</i>  expectancies are computed from the transitions observed between
 is the probability to be observed in state <i>j</i> at the second  waves and are computed for each degree of severity of disability
 wave conditional to be observed in state <em>i</em> at the first  (number of life states). More degrees you consider, more time is
 wave. Therefore a simple model is: log<em>(pij/pii)= aij +  necessary to reach the Maximum Likelihood of the parameters
 bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'  involved in the model. Considering only two states of disability
 is a covariate. The advantage that this computer program claims,  (disable and healthy) is generally enough but the computer
 comes from that if the delay between waves is not identical for  program works also with more health statuses.<br>
 each individual, or if some individual missed an interview, the  <br>
 information is not rounded or lost, but taken into account using  The simplest model is the multinomial logistic model where <i>pij</i>
 an interpolation or extrapolation. <i>hPijx</i> is the  is the probability to be observed in state <i>j</i> at the second
 probability to be observed in state <i>i</i> at age <i>x+h</i>  wave conditional to be observed in state <em>i</em> at the first
 conditional to the observed state <i>i</i> at age <i>x</i>. The  wave. Therefore a simple model is: log<em>(pij/pii)= aij +
 delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)  bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
 of unobserved intermediate states. This elementary transition (by  is a covariate. The advantage that this computer program claims,
 month or quarter trimester, semester or year) is modeled as a  comes from that if the delay between waves is not identical for
 multinomial logistic. The <i>hPx</i> matrix is simply the matrix  each individual, or if some individual missed an interview, the
 product of <i>nh*stepm</i> elementary matrices and the  information is not rounded or lost, but taken into account using
 contribution of each individual to the likelihood is simply <i>hPijx</i>.  an interpolation or extrapolation. <i>hPijx</i> is the
 <br>  probability to be observed in state <i>i</i> at age <i>x+h</i>
 </p>  conditional to the observed state <i>i</i> at age <i>x</i>. The
   delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
 <p>The program presented in this manual is a quite general  of unobserved intermediate states. This elementary transition (by
 program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated  month or quarter trimester, semester or year) is modeled as a
 <strong>MA</strong>rkov <strong>CH</strong>ain), designed to  multinomial logistic. The <i>hPx</i> matrix is simply the matrix
 analyse transition data from longitudinal surveys. The first step  product of <i>nh*stepm</i> elementary matrices and the
 is the parameters estimation of a transition probabilities model  contribution of each individual to the likelihood is simply <i>hPijx</i>.
 between an initial status and a final status. From there, the  <br>
 computer program produces some indicators such as observed and  </p>
 stationary prevalence, life expectancies and their variances and  
 graphs. Our transition model consists in absorbing and  <p>The program presented in this manual is a quite general
 non-absorbing states with the possibility of return across the  program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
 non-absorbing states. The main advantage of this package,  <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
 compared to other programs for the analysis of transition data  analyse transition data from longitudinal surveys. The first step
 (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole  is the parameters estimation of a transition probabilities model
 individual information is used even if an interview is missing, a  between an initial status and a final status. From there, the
 status or a date is unknown or when the delay between waves is  computer program produces some indicators such as observed and
 not identical for each individual. The program can be executed  stationary prevalence, life expectancies and their variances and
 according to parameters: selection of a sub-sample, number of  graphs. Our transition model consists in absorbing and
 absorbing and non-absorbing states, number of waves taken in  non-absorbing states with the possibility of return across the
 account (the user inputs the first and the last interview), a  non-absorbing states. The main advantage of this package,
 tolerance level for the maximization function, the periodicity of  compared to other programs for the analysis of transition data
 the transitions (we can compute annual, quaterly or monthly  (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
 transitions), covariates in the model. It works on Windows or on  individual information is used even if an interview is missing, a
 Unix.<br>  status or a date is unknown or when the delay between waves is
 </p>  not identical for each individual. The program can be executed
   according to parameters: selection of a sub-sample, number of
 <hr>  absorbing and non-absorbing states, number of waves taken in
   account (the user inputs the first and the last interview), a
 <h2><a name="data"><font color="#00006A">On what kind of data can  tolerance level for the maximization function, the periodicity of
 it be used?</font></a></h2>  the transitions (we can compute annual, quarterly or monthly
   transitions), covariates in the model. It works on Windows or on
 <p>The minimum data required for a transition model is the  Unix.<br>
 recording of a set of individuals interviewed at a first date and  </p>
 interviewed again at least one another time. From the  
 observations of an individual, we obtain a follow-up over time of  <hr>
 the occurrence of a specific event. In this documentation, the  
 event is related to health status at older ages, but the program  <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New
 can be applied on a lot of longitudinal studies in different  Methods for Analyzing Active Life Expectancy&quot;. <i>Journal of
 contexts. To build the data file explained into the next section,  Aging and Health</i>. Vol 10, No. 2. </p>
 you must have the month and year of each interview and the  
 corresponding health status. But in order to get age, date of  <hr>
 birth (month and year) is required (missing values is allowed for  
 month). Date of death (month and year) is an important  <h2><a name="data"><font color="#00006A">On what kind of data can
 information also required if the individual is dead. Shorter  it be used?</font></a></h2>
 steps (i.e. a month) will more closely take into account the  
 survival time after the last interview.</p>  <p>The minimum data required for a transition model is the
   recording of a set of individuals interviewed at a first date and
 <hr>  interviewed again at least one another time. From the
   observations of an individual, we obtain a follow-up over time of
 <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>  the occurrence of a specific event. In this documentation, the
   event is related to health status at older ages, but the program
 <p>In this example, 8,000 people have been interviewed in a  can be applied on a lot of longitudinal studies in different
 cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).  contexts. To build the data file explained into the next section,
 Some people missed 1, 2 or 3 interviews. Health statuses are  you must have the month and year of each interview and the
 healthy (1) and disable (2). The survey is not a real one. It is  corresponding health status. But in order to get age, date of
 a simulation of the American Longitudinal Survey on Aging. The  birth (month and year) is required (missing values is allowed for
 disability state is defined if the individual missed one of four  month). Date of death (month and year) is an important
 ADL (Activity of daily living, like bathing, eating, walking).  information also required if the individual is dead. Shorter
 Therefore, even is the individuals interviewed in the sample are  steps (i.e. a month) will more closely take into account the
 virtual, the information brought with this sample is close to the  survival time after the last interview.</p>
 situation of the United States. Sex is not recorded is this  
 sample.</p>  <hr>
   
 <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>  <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
 in this first example) is an individual record which fields are: </p>  
   <p>In this example, 8,000 people have been interviewed in a
 <ul>  cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
     <li><b>Index number</b>: positive number (field 1) </li>  Some people missed 1, 2 or 3 interviews. Health statuses are
     <li><b>First covariate</b> positive number (field 2) </li>  healthy (1) and disable (2). The survey is not a real one. It is
     <li><b>Second covariate</b> positive number (field 3) </li>  a simulation of the American Longitudinal Survey on Aging. The
     <li><a name="Weight"><b>Weight</b></a>: positive number  disability state is defined if the individual missed one of four
         (field 4) . In most surveys individuals are weighted  ADL (Activity of daily living, like bathing, eating, walking).
         according to the stratification of the sample.</li>  Therefore, even is the individuals interviewed in the sample are
     <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are  virtual, the information brought with this sample is close to the
         coded as 99/9999 (field 5) </li>  situation of the United States. Sex is not recorded is this
     <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are  sample.</p>
         coded as 99/9999 (field 6) </li>  
     <li><b>Date of first interview</b>: coded as mm/yyyy. Missing  <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
         dates are coded as 99/9999 (field 7) </li>  in this first example) is an individual record which fields are: </p>
     <li><b>Status at first interview</b>: positive number.  
         Missing values ar coded -1. (field 8) </li>  <ul>
     <li><b>Date of second interview</b>: coded as mm/yyyy.      <li><b>Index number</b>: positive number (field 1) </li>
         Missing dates are coded as 99/9999 (field 9) </li>      <li><b>First covariate</b> positive number (field 2) </li>
     <li><strong>Status at second interview</strong> positive      <li><b>Second covariate</b> positive number (field 3) </li>
         number. Missing values ar coded -1. (field 10) </li>      <li><a name="Weight"><b>Weight</b></a>: positive number
     <li><b>Date of third interview</b>: coded as mm/yyyy. Missing          (field 4) . In most surveys individuals are weighted
         dates are coded as 99/9999 (field 11) </li>          according to the stratification of the sample.</li>
     <li><strong>Status at third interview</strong> positive      <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
         number. Missing values ar coded -1. (field 12) </li>          coded as 99/9999 (field 5) </li>
     <li><b>Date of fourth interview</b>: coded as mm/yyyy.      <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
         Missing dates are coded as 99/9999 (field 13) </li>          coded as 99/9999 (field 6) </li>
     <li><strong>Status at fourth interview</strong> positive      <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
         number. Missing values are coded -1. (field 14) </li>          dates are coded as 99/9999 (field 7) </li>
     <li>etc</li>      <li><b>Status at first interview</b>: positive number.
 </ul>          Missing values ar coded -1. (field 8) </li>
       <li><b>Date of second interview</b>: coded as mm/yyyy.
 <p>&nbsp;</p>          Missing dates are coded as 99/9999 (field 9) </li>
       <li><strong>Status at second interview</strong> positive
 <p>If your longitudinal survey do not include information about          number. Missing values ar coded -1. (field 10) </li>
 weights or covariates, you must fill the column with a number      <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
 (e.g. 1) because a missing field is not allowed.</p>          dates are coded as 99/9999 (field 11) </li>
       <li><strong>Status at third interview</strong> positive
 <hr>          number. Missing values ar coded -1. (field 12) </li>
       <li><b>Date of fourth interview</b>: coded as mm/yyyy.
 <h2><font color="#00006A">Your first example parameter file</font><a          Missing dates are coded as 99/9999 (field 13) </li>
 href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>      <li><strong>Status at fourth interview</strong> positive
           number. Missing values are coded -1. (field 14) </li>
 <h2><a name="biaspar"></a>#Imach version 0.63, February 2000,      <li>etc</li>
 INED-EUROREVES </h2>  </ul>
   
 <p>This is a comment. Comments start with a '#'.</p>  <p>&nbsp;</p>
   
 <h4><font color="#FF0000">First uncommented line</font></h4>  <p>If your longitudinal survey do not include information about
   weights or covariates, you must fill the column with a number
 <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>  (e.g. 1) because a missing field is not allowed.</p>
   
 <ul>  <hr>
     <li><b>title=</b> 1st_example is title of the run. </li>  
     <li><b>datafile=</b>data1.txt is the name of the data set.  <h2><font color="#00006A">Your first example parameter file</font><a
         Our example is a six years follow-up survey. It consists  href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
         in a baseline followed by 3 reinterviews. </li>  
     <li><b>lastobs=</b> 8600 the program is able to run on a  <h2><a name="biaspar"></a>#Imach version 0.8, March 2002,
         subsample where the last observation number is lastobs.  INED-EUROREVES </h2>
         It can be set a bigger number than the real number of  
         observations (e.g. 100000). In this example, maximisation  <p>This is a comment. Comments start with a '#'.</p>
         will be done on the 8600 first records. </li>  
     <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more  <h4><font color="#FF0000">First uncommented line</font></h4>
         than two interviews in the survey, the program can be run  
         on selected transitions periods. firstpass=1 means the  <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
         first interview included in the calculation is the  
         baseline survey. lastpass=4 means that the information  <ul>
         brought by the 4th interview is taken into account.</li>      <li><b>title=</b> 1st_example is title of the run. </li>
 </ul>      <li><b>datafile=</b>data1.txt is the name of the data set.
           Our example is a six years follow-up survey. It consists
 <p>&nbsp;</p>          in a baseline followed by 3 reinterviews. </li>
       <li><b>lastobs=</b> 8600 the program is able to run on a
 <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented          subsample where the last observation number is lastobs.
 line</font></a></h4>          It can be set a bigger number than the real number of
           observations (e.g. 100000). In this example, maximisation
 <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>          will be done on the 8600 first records. </li>
       <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
 <ul>          than two interviews in the survey, the program can be run
     <li><b>ftol=1e-8</b> Convergence tolerance on the function          on selected transitions periods. firstpass=1 means the
         value in the maximisation of the likelihood. Choosing a          first interview included in the calculation is the
         correct value for ftol is difficult. 1e-8 is a correct          baseline survey. lastpass=4 means that the information
         value for a 32 bits computer.</li>          brought by the 4th interview is taken into account.</li>
     <li><b>stepm=1</b> Time unit in months for interpolation.  </ul>
         Examples:<ul>  
             <li>If stepm=1, the unit is a month </li>  <p>&nbsp;</p>
             <li>If stepm=4, the unit is a trimester</li>  
             <li>If stepm=12, the unit is a year </li>  <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
             <li>If stepm=24, the unit is two years</li>  line</font></a></h4>
             <li>... </li>  
         </ul>  <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
     </li>  
     <li><b>ncov=2</b> Number of covariates to be add to the  <ul>
         model. The intercept and the age parameter are counting      <li><b>ftol=1e-8</b> Convergence tolerance on the function
         for 2 covariates. For example, if you want to add gender          value in the maximisation of the likelihood. Choosing a
         in the covariate vector you must write ncov=3 else          correct value for ftol is difficult. 1e-8 is a correct
         ncov=2. </li>          value for a 32 bits computer.</li>
     <li><b>nlstate=2</b> Number of non-absorbing (live) states.      <li><b>stepm=1</b> Time unit in months for interpolation.
         Here we have two alive states: disability-free is coded 1          Examples:<ul>
         and disability is coded 2. </li>              <li>If stepm=1, the unit is a month </li>
     <li><b>ndeath=1</b> Number of absorbing states. The absorbing              <li>If stepm=4, the unit is a trimester</li>
         state death is coded 3. </li>              <li>If stepm=12, the unit is a year </li>
     <li><b>maxwav=4</b> Maximum number of waves. The program can              <li>If stepm=24, the unit is two years</li>
         not include more than 4 interviews. </li>              <li>... </li>
     <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the          </ul>
         Maximisation Likelihood Estimation. <ul>      </li>
             <li>If mle=1 the program does the maximisation and      <li><b>ncovcol=2</b> Number of covariate columns in the datafile
                 the calculation of heath expectancies </li>      which precede the date of birth. Here you can put variables that
             <li>If mle=0 the program only does the calculation of      won't necessary be used during the run. It is not the number of
                 the health expectancies. </li>      covariates that will be specified by the model. The 'model'
         </ul>      syntax describe the covariates to take into account. </li>
     </li>      <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
     <li><b>weight=0</b> Possibility to add weights. <ul>          Here we have two alive states: disability-free is coded 1
             <li>If weight=0 no weights are included </li>          and disability is coded 2. </li>
             <li>If weight=1 the maximisation integrates the      <li><b>ndeath=1</b> Number of absorbing states. The absorbing
                 weights which are in field <a href="#Weight">4</a></li>          state death is coded 3. </li>
         </ul>      <li><b>maxwav=4</b> Number of waves in the datafile.</li>
     </li>      <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
 </ul>          Maximisation Likelihood Estimation. <ul>
               <li>If mle=1 the program does the maximisation and
 <h4><font color="#FF0000">Guess values for optimization</font><font                  the calculation of health expectancies </li>
 color="#00006A"> </font></h4>              <li>If mle=0 the program only does the calculation of
                   the health expectancies. </li>
 <p>You must write the initial guess values of the parameters for          </ul>
 optimization. The number of parameters, <em>N</em> depends on the      </li>
 number of absorbing states and non-absorbing states and on the      <li><b>weight=0</b> Possibility to add weights. <ul>
 number of covariates. <br>              <li>If weight=0 no weights are included </li>
 <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +              <li>If weight=1 the maximisation integrates the
 <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>                  weights which are in field <a href="#Weight">4</a></li>
 <br>          </ul>
 Thus in the simple case with 2 covariates (the model is log      </li>
 (pij/pii) = aij + bij * age where intercept and age are the two  </ul>
 covariates), and 2 health degrees (1 for disability-free and 2  
 for disability) and 1 absorbing state (3), you must enter 8  <h4><font color="#FF0000">Covariates</font></h4>
 initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can  
 start with zeros as in this example, but if you have a more  <p>Intercept and age are systematically included in the model.
 precise set (for example from an earlier run) you can enter it  Additional covariates can be included with the command: </p>
 and it will speed up them<br>  
 Each of the four lines starts with indices &quot;ij&quot;: <br>  <pre>model=<em>list of covariates</em></pre>
 <br>  
 <b>ij aij bij</b> </p>  <ul>
       <li>if<strong> model=. </strong>then no covariates are
 <blockquote>          included</li>
     <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age      <li>if <strong>model=V1</strong> the model includes the first
 12 -14.155633  0.110794           covariate (field 2)</li>
 13  -7.925360  0.032091       <li>if <strong>model=V2 </strong>the model includes the
 21  -1.890135 -0.029473           second covariate (field 3)</li>
 23  -6.234642  0.022315 </pre>      <li>if <strong>model=V1+V2 </strong>the model includes the
 </blockquote>          first and the second covariate (fields 2 and 3)</li>
       <li>if <strong>model=V1*V2 </strong>the model includes the
 <p>or, to simplify: </p>          product of the first and the second covariate (fields 2
           and 3)</li>
 <blockquote>      <li>if <strong>model=V1+V1*age</strong> the model includes
     <pre>12 0.0 0.0          the product covariate*age</li>
 13 0.0 0.0  </ul>
 21 0.0 0.0  
 23 0.0 0.0</pre>  <p>In this example, we have two covariates in the data file
 </blockquote>  (fields 2 and 3). The number of covariates included in the data file
   between the id and the date of birth is ncovcol=2 (it was named ncov
 <h4><font color="#FF0000">Guess values for computing variances</font></h4>  in version prior to 0.8). If you have 3 covariates in the datafile
   (fields 2, 3 and 4), you will set ncovcol=3. Then you can run the
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  programme with a new parametrisation taking into account the
 used as an input to get the vairous output data files (Health  third covariate. For example, <strong>model=V1+V3 </strong>estimates
 expectancies, stationary prevalence etc.) and figures without  a model with the first and third covariates. More complicated
 rerunning the rather long maximisation phase (mle=0). </p>  models can be used, but it will takes more time to converge. With
   a simple model (no covariates), the programme estimates 8
 <p>The scales are small values for the evaluation of numerical  parameters. Adding covariates increases the number of parameters
 derivatives. These derivatives are used to compute the hessian  : 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
 matrix of the parameters, that is the inverse of the covariance  </strong>and 20 for <strong>model=V1+V2+V3.</strong></p>
 matrix, and the variances of health expectancies. Each line  
 consists in indices &quot;ij&quot; followed by the initial scales  <h4><font color="#FF0000">Guess values for optimization</font><font
 (zero to simplify) associated with aij and bij. </p>  color="#00006A"> </font></h4>
   
 <ul>  <p>You must write the initial guess values of the parameters for
     <li>If mle=1 you can enter zeros:</li>  optimization. The number of parameters, <em>N</em> depends on the
 </ul>  number of absorbing states and non-absorbing states and on the
   number of covariates. <br>
 <blockquote>  <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
     <pre># Scales (for hessian or gradient estimation)  <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncovmodel</em>&nbsp;. <br>
 12 0. 0.   <br>
 13 0. 0.   Thus in the simple case with 2 covariates (the model is log
 21 0. 0.   (pij/pii) = aij + bij * age where intercept and age are the two
 23 0. 0. </pre>  covariates), and 2 health degrees (1 for disability-free and 2
 </blockquote>  for disability) and 1 absorbing state (3), you must enter 8
   initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
 <ul>  start with zeros as in this example, but if you have a more
     <li>If mle=0 you must enter a covariance matrix (usually  precise set (for example from an earlier run) you can enter it
         obtained from an earlier run).</li>  and it will speed up them<br>
 </ul>  Each of the four lines starts with indices &quot;ij&quot;: <b>ij
   aij bij</b> </p>
 <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>  
   <blockquote>
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be      <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
 used as an input to get the vairous output data files (Health  12 -14.155633  0.110794
 expectancies, stationary prevalence etc.) and figures without  13  -7.925360  0.032091
 rerunning the rather long maximisation phase (mle=0). </p>  21  -1.890135 -0.029473
   23  -6.234642  0.022315 </pre>
 <p>Each line starts with indices &quot;ijk&quot; followed by the  </blockquote>
 covariances between aij and bij: </p>  
   <p>or, to simplify (in most of cases it converges but there is no
 <pre>  warranty!): </p>
    121 Var(a12)   
    122 Cov(b12,a12)  Var(b12)   <blockquote>
           ...      <pre>12 0.0 0.0
    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>  13 0.0 0.0
   21 0.0 0.0
 <ul>  23 0.0 0.0</pre>
     <li>If mle=1 you can enter zeros. </li>  </blockquote>
 </ul>  
   <p> In order to speed up the convergence you can make a first run with
 <blockquote>  a large stepm i.e stepm=12 or 24 and then decrease the stepm until
     <pre># Covariance matrix  stepm=1 month. If newstepm is the new shorter stepm and stepm can be
 121 0.  expressed as a multiple of newstepm, like newstepm=n stepm, then the
 122 0. 0.  following approximation holds:
 131 0. 0. 0.   <pre>aij(stepm) = aij(n . stepm) - ln(n)
 132 0. 0. 0. 0.   </pre> and
 211 0. 0. 0. 0. 0.   <pre>bij(stepm) = bij(n . stepm) .</pre>
 212 0. 0. 0. 0. 0. 0.   
 231 0. 0. 0. 0. 0. 0. 0.   <p> For example if you already ran for a 6 months interval and
 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>  got:<br>
 </blockquote>   <pre># Parameters
   12 -13.390179  0.126133
 <ul>  13  -7.493460  0.048069
     <li>If mle=0 you must enter a covariance matrix (usually  21   0.575975 -0.041322
         obtained from an earlier run).<br>  23  -4.748678  0.030626
         </li>  </pre>
 </ul>  If you now want to get the monthly estimates, you can guess the aij by
   substracting ln(6)= 1,7917<br> and running<br>
 <h4><a name="biaspar-l"></a><font color="#FF0000">last  <pre>12 -15.18193847  0.126133
 uncommented line</font></h4>  13 -9.285219469  0.048069
   21 -1.215784469 -0.041322
 <pre>agemin=70 agemax=100 bage=50 fage=100</pre>  23 -6.540437469  0.030626
   </pre>
 <p>Once we obtained the estimated parameters, the program is able  and get<br>
 to calculated stationary prevalence, transitions probabilities  <pre>12 -15.029768 0.124347
 and life expectancies at any age. Choice of age ranges is useful  13 -8.472981 0.036599
 for extrapolation. In our data file, ages varies from age 70 to  21 -1.472527 -0.038394
 102. Setting bage=50 and fage=100, makes the program computing  23 -6.553602 0.029856
 life expectancy from age bage to age fage. As we use a model, we  </br>
 can compute life expectancy on a wider age range than the age  which is closer to the results. The approximation is probably useful
 range from the data. But the model can be rather wrong on big  only for very small intervals and we don't have enough experience to
 intervals.</p>  know if you will speed up the convergence or not.
   <pre>         -ln(12)= -2.484
 <p>Similarly, it is possible to get extrapolated stationary   -ln(6/1)=-ln(6)= -1.791
 prevalence by age raning from agemin to agemax. </p>   -ln(3/1)=-ln(3)= -1.0986
   -ln(12/6)=-ln(2)= -0.693
 <ul>  </pre>
     <li><b>agemin=</b> Minimum age for calculation of the  
         stationary prevalence </li>  <h4><font color="#FF0000">Guess values for computing variances</font></h4>
     <li><b>agemax=</b> Maximum age for calculation of the  
         stationary prevalence </li>  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
     <li><b>bage=</b> Minimum age for calculation of the health  used as an input to get the various output data files (Health
         expectancies </li>  expectancies, stationary prevalence etc.) and figures without
     <li><b>fage=</b> Maximum ages for calculation of the health  rerunning the rather long maximisation phase (mle=0). </p>
         expectancies </li>  
 </ul>  <p>The scales are small values for the evaluation of numerical
   derivatives. These derivatives are used to compute the hessian
 <hr>  matrix of the parameters, that is the inverse of the covariance
   matrix, and the variances of health expectancies. Each line
 <h2><a name="running"></a><font color="#00006A">Running Imach  consists in indices &quot;ij&quot; followed by the initial scales
 with this example</font></h2>  (zero to simplify) associated with aij and bij. </p>
   <ul> <li>If mle=1 you can enter zeros:</li>
 <p>We assume that you entered your <a href="biaspar.txt">1st_example  <blockquote><pre># Scales (for hessian or gradient estimation)
 parameter file</a> as explained <a href="#biaspar">above</a>. To  12 0. 0.
 run the program you should click on the imach.exe icon and enter  13 0. 0.
 the name of the parameter file which is for example <a  21 0. 0.
 href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>  23 0. 0. </pre>
 (you also can click on the biaspar.txt icon located in <br>  </blockquote>
 <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with      <li>If mle=0 you must enter a covariance matrix (usually
 the mouse on the imach window).<br>          obtained from an earlier run).</li>
 </p>  </ul>
   
 <p>The time to converge depends on the step unit that you used (1  <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
 month is cpu consuming), on the number of cases, and on the  
 number of variables.</p>  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
   used as an input to get the various output data files (Health
 <p>The program outputs many files. Most of them are files which  expectancies, stationary prevalence etc.) and figures without
 will be plotted for better understanding.</p>  rerunning the rather long maximisation phase (mle=0). <br>
   Each line starts with indices &quot;ijk&quot; followed by the
 <hr>  covariances between aij and bij:<br>
   <pre>
 <h2><a name="output"><font color="#00006A">Output of the program     121 Var(a12)
 and graphs</font> </a></h2>     122 Cov(b12,a12)  Var(b12)
             ...
 <p>Once the optimization is finished, some graphics can be made     232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>
 with a grapher. We use Gnuplot which is an interactive plotting  <ul>
 program copyrighted but freely distributed. Imach outputs the      <li>If mle=1 you can enter zeros. </li>
 source of a gnuplot file, named 'graph.gp', which can be directly      <pre># Covariance matrix
 input into gnuplot.<br>  121 0.
 When the running is finished, the user should enter a caracter  122 0. 0.
 for plotting and output editing. </p>  131 0. 0. 0.
   132 0. 0. 0. 0.
 <p>These caracters are:</p>  211 0. 0. 0. 0. 0.
   212 0. 0. 0. 0. 0. 0.
 <ul>  231 0. 0. 0. 0. 0. 0. 0.
     <li>'c' to start again the program from the beginning.</li>  232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
     <li>'g' to made graphics. The output graphs are in GIF format      <li>If mle=0 you must enter a covariance matrix (usually
         and you have no control over which is produced. If you          obtained from an earlier run). </li>
         want to modify the graphics or make another one, you  </ul>
         should modify the parameters in the file <b>graph.gp</b>  
         located in imach\bin. A gnuplot reference manual is  <h4><font color="#FF0000">Age range for calculation of stationary
         available <a  prevalences and health expectancies</font></h4>
         href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.  
     </li>  <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
     <li>'e' opens the <strong>index.htm</strong> file to edit the  
         output files and graphs. </li>  <br>Once we obtained the estimated parameters, the program is able
     <li>'q' for exiting.</li>  to calculated stationary prevalence, transitions probabilities
 </ul>  and life expectancies at any age. Choice of age range is useful
   for extrapolation. In our data file, ages varies from age 70 to
 <h5><font size="4"><strong>Results files </strong></font><br>  102. It is possible to get extrapolated stationary prevalence by
 <br>  age ranging from agemin to agemax.
 <font color="#EC5E5E" size="3"><strong>- </strong></font><a  
 name="Observed prevalence in each state"><font color="#EC5E5E"  <br>Setting bage=50 (begin age) and fage=100 (final age), makes
 size="3"><strong>Observed prevalence in each state</strong></font></a><font  the program computing life expectancy from age 'bage' to age
 color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:  'fage'. As we use a model, we can interessingly compute life
 </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>  expectancy on a wider age range than the age range from the data.
 </h5>  But the model can be rather wrong on much larger intervals.
   Program is limited to around 120 for upper age!
 <p>The first line is the title and displays each field of the  <ul>
 file. The first column is age. The fields 2 and 6 are the      <li><b>agemin=</b> Minimum age for calculation of the
 proportion of individuals in states 1 and 2 respectively as          stationary prevalence </li>
 observed during the first exam. Others fields are the numbers of      <li><b>agemax=</b> Maximum age for calculation of the
 people in states 1, 2 or more. The number of columns increases if          stationary prevalence </li>
 the number of states is higher than 2.<br>      <li><b>bage=</b> Minimum age for calculation of the health
 The header of the file is </p>          expectancies </li>
       <li><b>fage=</b> Maximum age for calculation of the health
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N          expectancies </li>
 70 1.00000 631 631 70 0.00000 0 631  </ul>
 71 0.99681 625 627 71 0.00319 2 627   
 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>  <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
   color="#FF0000"> the observed prevalence</font></h4>
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  
     70 0.95721 604 631 70 0.04279 27 631</pre>  <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
   
 <p>It means that at age 70, the prevalence in state 1 is 1.000  <br>Statements 'begin-prev-date' and 'end-prev-date' allow to
 and in state 2 is 0.00 . At age 71 the number of individuals in  select the period in which we calculate the observed prevalences
 state 1 is 625 and in state 2 is 2, hence the total number of  in each state. In this example, the prevalences are calculated on
 people aged 71 is 625+2=627. <br>  data survey collected between 1 january 1984 and 1 june 1988.
 </p>  <ul>
       <li><strong>begin-prev-date= </strong>Starting date
 <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and          (day/month/year)</li>
 covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>      <li><strong>end-prev-date= </strong>Final date
           (day/month/year)</li>
 <p>This file contains all the maximisation results: </p>  </ul>
   
 <pre> Number of iterations=47  <h4><font color="#FF0000">Population- or status-based health
  -2 log likelihood=46553.005854373667    expectancies</font></h4>
  Estimated parameters: a12 = -12.691743 b12 = 0.095819   
                        a13 = -7.815392   b13 = 0.031851   <pre>pop_based=0</pre>
                        a21 = -1.809895 b21 = -0.030470   
                        a23 = -7.838248  b23 = 0.039490    <p>The program computes status-based health expectancies, i.e
  Covariance matrix: Var(a12) = 1.03611e-001  health expectancies which depends on your initial health state.
                     Var(b12) = 1.51173e-005  If you are healthy your healthy life expectancy (e11) is higher
                     Var(a13) = 1.08952e-001  than if you were disabled (e21, with e11 &gt; e21).<br>
                     Var(b13) = 1.68520e-005    To compute a healthy life expectancy independant of the initial
                     Var(a21) = 4.82801e-001  status we have to weight e11 and e21 according to the probability
                     Var(b21) = 6.86392e-005  to be in each state at initial age or, with other word, according
                     Var(a23) = 2.27587e-001  to the proportion of people in each state.<br>
                     Var(b23) = 3.04465e-005   We prefer computing a 'pure' period healthy life expectancy based
  </pre>  only on the transtion forces. Then the weights are simply the
   stationnary prevalences or 'implied' prevalences at the initial
 <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:  age.<br>
 </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>  Some other people would like to use the cross-sectional
   prevalences (the &quot;Sullivan prevalences&quot;) observed at
 <p>Here are the transitions probabilities Pij(x, x+nh) where nh  the initial age during a period of time <a href="#Computing">defined
 is a multiple of 2 years. The first column is the starting age x  just above</a>. <br>
 (from age 50 to 100), the second is age (x+nh) and the others are  
 the transition probabilities p11, p12, p13, p21, p22, p23. For  <ul>
 example, line 5 of the file is: </p>      <li><strong>popbased= 0 </strong>Health expectancies are
           computed at each age from stationary prevalences
 <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>          'expected' at this initial age.</li>
       <li><strong>popbased= 1 </strong>Health expectancies are
 <p>and this means: </p>          computed at each age from cross-sectional 'observed'
           prevalence at this initial age. As all the population is
 <pre>p11(100,106)=0.03286          not observed at the same exact date we define a short
 p12(100,106)=0.23512          period were the observed prevalence is computed.</li>
 p13(100,106)=0.73202  </ul>
 p21(100,106)=0.02330  
 p22(100,106)=0.19210   <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
 p22(100,106)=0.78460 </pre>  
   <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  
 name="Stationary prevalence in each state"><font color="#EC5E5E"  <p>Prevalence and population projections are only available if
 size="3"><b>Stationary prevalence in each state</b></font></a><b>:  the interpolation unit is a month, i.e. stepm=1 and if there are
 </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>  no covariate. The programme estimates the prevalence in each
   state at a precise date expressed in day/month/year. The
 <pre>#Age 1-1 2-2   programme computes one forecasted prevalence a year from a
 70 0.92274 0.07726   starting date (1 january of 1989 in this example) to a final date
 71 0.91420 0.08580   (1 january 1992). The statement mov_average allows to compute
 72 0.90481 0.09519   smoothed forecasted prevalences with a five-age moving average
 73 0.89453 0.10547</pre>  centered at the mid-age of the five-age period. <br>
   
 <p>At age 70 the stationary prevalence is 0.92274 in state 1 and  <ul>
 0.07726 in state 2. This stationary prevalence differs from      <li><strong>starting-proj-date</strong>= starting date
 observed prevalence. Here is the point. The observed prevalence          (day/month/year) of forecasting</li>
 at age 70 results from the incidence of disability, incidence of      <li><strong>final-proj-date= </strong>final date
 recovery and mortality which occurred in the past of the cohort.          (day/month/year) of forecasting</li>
 Stationary prevalence results from a simulation with actual      <li><strong>mov_average</strong>= smoothing with a five-age
 incidences and mortality (estimated from this cross-longitudinal          moving average centered at the mid-age of the five-age
 survey). It is the best predictive value of the prevalence in the          period. The command<strong> mov_average</strong> takes
 future if &quot;nothing changes in the future&quot;. This is          value 1 if the prevalences are smoothed and 0 otherwise.</li>
 exactly what demographers do with a Life table. Life expectancy  </ul>
 is the expected mean time to survive if observed mortality rates  
 (incidence of mortality) &quot;remains constant&quot; in the  <h4><font color="#FF0000">Last uncommented line : Population
 future. </p>  forecasting </font></h4>
   
 <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of  <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
 stationary prevalence</b></font><b>: </b><a  
 href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>  <p>This command is available if the interpolation unit is a
   month, i.e. stepm=1 and if popforecast=1. From a data file
 <p>The stationary prevalence has to be compared with the observed  including age and number of persons alive at the precise date
 prevalence by age. But both are statistical estimates and  &#145;popfiledate&#146;, you can forecast the number of persons
 subjected to stochastic errors due to the size of the sample, the  in each state until date &#145;last-popfiledate&#146;. In this
 design of the survey, and, for the stationary prevalence to the  example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
 model used and fitted. It is possible to compute the standard  includes real data which are the Japanese population in 1989.<br>
 deviation of the stationary prevalence at each age.</p>  
   <ul type="disc">
 <h6><font color="#EC5E5E" size="3">Observed and stationary      <li class="MsoNormal"
 prevalence in state (2=disable) with the confident interval</font>:<b>      style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
 vbiaspar2.gif</b></h6>          0 </b>Option for population forecasting. If
           popforecast=1, the programme does the forecasting<b>.</b></li>
 <p><br>      <li class="MsoNormal"
 This graph exhibits the stationary prevalence in state (2) with      style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
 the confidence interval in red. The green curve is the observed          </b>name of the population file</li>
 prevalence (or proportion of individuals in state (2)). Without      <li class="MsoNormal"
 discussing the results (it is not the purpose here), we observe      style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
 that the green curve is rather below the stationary prevalence.          date of the population population</li>
 It suggests an increase of the disability prevalence in the      <li class="MsoNormal"
 future.</p>      style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
           date of the last population projection&nbsp;</li>
 <p><img src="vbiaspar2.gif" width="400" height="300"></p>  </ul>
   
 <h6><font color="#EC5E5E" size="3"><b>Convergence to the  <hr>
 stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>  
 <img src="pbiaspar1.gif" width="400" height="300"> </h6>  <h2><a name="running"></a><font color="#00006A">Running Imach
   with this example</font></h2>
 <p>This graph plots the conditional transition probabilities from  
 an initial state (1=healthy in red at the bottom, or 2=disable in  We assume that you typed in your <a href="biaspar.imach">1st_example
 green on top) at age <em>x </em>to the final state 2=disable<em> </em>at  parameter file</a> as explained <a href="#biaspar">above</a>.
 age <em>x+h. </em>Conditional means at the condition to be alive  <br>To run the program you should either:
 at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The  <ul> <li> click on the imach.exe icon and enter
 curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>  the name of the parameter file which is for example <a
 + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary  href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
 prevalence of disability</em>. In order to get the stationary  <li> You also can locate the biaspar.imach icon in
 prevalence at age 70 we should start the process at an earlier  <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with
 age, i.e.50. If the disability state is defined by severe  the mouse on the imach window).
 disability criteria with only a few chance to recover, then the  <li> With latest version (0.7 and higher) if you setup windows in order to
 incidence of recovery is low and the time to convergence is  understand ".imach" extension you can right click the
 probably longer. But we don't have experience yet.</p>  biaspar.imach icon and either edit with notepad the parameter file or
   execute it with imach or whatever.
 <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age  </ul>  
 and initial health status</b></font><b>: </b><a  
 href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>  The time to converge depends on the step unit that you used (1
   month is cpu consuming), on the number of cases, and on the
 <pre># Health expectancies   number of variables.
 # Age 1-1 1-2 2-1 2-2   
 70 10.7297 2.7809 6.3440 5.9813   <br>The program outputs many files. Most of them are files which
 71 10.3078 2.8233 5.9295 5.9959   will be plotted for better understanding.
 72 9.8927 2.8643 5.5305 6.0033   
 73 9.4848 2.9036 5.1474 6.0035 </pre>  <hr>
   
 <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:  <h2><a name="output"><font color="#00006A">Output of the program
 e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>  and graphs</font> </a></h2>
   
 <pre><img src="exbiaspar1.gif" width="400" height="300"><img  <p>Once the optimization is finished, some graphics can be made
 src="exbiaspar2.gif" width="400" height="300"></pre>  with a grapher. We use Gnuplot which is an interactive plotting
   program copyrighted but freely distributed. A gnuplot reference
 <p>For example, life expectancy of a healthy individual at age 70  manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
 is 10.73 in the healthy state and 2.78 in the disability state  When the running is finished, the user should enter a caracter
 (=13.51 years). If he was disable at age 70, his life expectancy  for plotting and output editing.
 will be shorter, 6.34 in the healthy state and 5.98 in the  
 disability state (=12.32 years). The total life expectancy is a  <br>These caracters are:<br>
 weighted mean of both, 13.51 and 12.32; weight is the proportion  
 of people disabled at age 70. In order to get a pure period index  <ul>
 (i.e. based only on incidences) we use the <a      <li>'c' to start again the program from the beginning.</li>
 href="#Stationary prevalence in each state">computed or      <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
 stationary prevalence</a> at age 70 (i.e. computed from          file to edit the output files and graphs. </li>
 incidences at earlier ages) instead of the <a      <li>'q' for exiting.</li>
 href="#Observed prevalence in each state">observed prevalence</a>  </ul>
 (for example at first exam) (<a href="#Health expectancies">see  
 below</a>).</p>  <h5><font size="4"><strong>Results files </strong></font><br>
   <br>
 <h5><font color="#EC5E5E" size="3"><b>- Variances of life  <font color="#EC5E5E" size="3"><strong>- </strong></font><a
 expectancies by age and initial health status</b></font><b>: </b><a  name="Observed prevalence in each state"><font color="#EC5E5E"
 href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>  size="3"><strong>Observed prevalence in each state</strong></font></a><font
   color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
 <p>For example, the covariances of life expectancies Cov(ei,ej)  </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
 at age 50 are (line 3) </p>  </h5>
   
 <pre>   Cov(e1,e1)=0.4667  Cov(e1,e2)=0.0605=Cov(e2,e1)  Cov(e2,e2)=0.0183</pre>  <p>The first line is the title and displays each field of the
   file. The first column is age. The fields 2 and 6 are the
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  proportion of individuals in states 1 and 2 respectively as
 name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health  observed during the first exam. Others fields are the numbers of
 expectancies</b></font></a><font color="#EC5E5E" size="3"><b>  people in states 1, 2 or more. The number of columns increases if
 with standard errors in parentheses</b></font><b>: </b><a  the number of states is higher than 2.<br>
 href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>  The header of the file is </p>
   
 <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>  <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
   70 1.00000 631 631 70 0.00000 0 631
 <pre>70 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09) </pre>  71 0.99681 625 627 71 0.00319 2 627
   72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
 <p>Thus, at age 70 the total life expectancy, e..=13.42 years is  
 the weighted mean of e1.=13.51 and e2.=12.32 by the stationary  <p>It means that at age 70, the prevalence in state 1 is 1.000
 prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in  and in state 2 is 0.00 . At age 71 the number of individuals in
 state 2, respectively (the sum is equal to one). e.1=10.39 is the  state 1 is 625 and in state 2 is 2, hence the total number of
 Disability-free life expectancy at age 70 (it is again a weighted  people aged 71 is 625+2=627. <br>
 mean of e11 and e21). e.2=3.03 is also the life expectancy at age  </p>
 70 to be spent in the disability state.</p>  
   <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
 <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by  covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>
 age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:  
 ebiaspar.gif</b></h6>  <p>This file contains all the maximisation results: </p>
   
 <p>This figure represents the health expectancies and the total  <pre> -2 log likelihood= 21660.918613445392
 life expectancy with the confident interval in dashed curve. </p>   Estimated parameters: a12 = -12.290174 b12 = 0.092161
                          a13 = -9.155590  b13 = 0.046627
 <pre>        <img src="ebiaspar.gif" width="400" height="300"></pre>                         a21 = -2.629849  b21 = -0.022030
                          a23 = -7.958519  b23 = 0.042614  
 <p>Standard deviations (obtained from the information matrix of   Covariance matrix: Var(a12) = 1.47453e-001
 the model) of these quantities are very useful.                      Var(b12) = 2.18676e-005
 Cross-longitudinal surveys are costly and do not involve huge                      Var(a13) = 2.09715e-001
 samples, generally a few thousands; therefore it is very                      Var(b13) = 3.28937e-005  
 important to have an idea of the standard deviation of our                      Var(a21) = 9.19832e-001
 estimates. It has been a big challenge to compute the Health                      Var(b21) = 1.29229e-004
 Expectancy standard deviations. Don't be confuse: life expectancy                      Var(a23) = 4.48405e-001
 is, as any expected value, the mean of a distribution; but here                      Var(b23) = 5.85631e-005
 we are not computing the standard deviation of the distribution,   </pre>
 but the standard deviation of the estimate of the mean.</p>  
   <p>By substitution of these parameters in the regression model,
 <p>Our health expectancies estimates vary according to the sample  we obtain the elementary transition probabilities:</p>
 size (and the standard deviations give confidence intervals of  
 the estimate) but also according to the model fitted. Let us  <p><img src="pebiaspar1.gif" width="400" height="300"></p>
 explain it in more details.</p>  
   <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
 <p>Choosing a model means ar least two kind of choices. First we  </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
 have to decide the number of disability states. Second we have to  
 design, within the logit model family, the model: variables,  <p>Here are the transitions probabilities Pij(x, x+nh) where nh
 covariables, confonding factors etc. to be included.</p>  is a multiple of 2 years. The first column is the starting age x
   (from age 50 to 100), the second is age (x+nh) and the others are
 <p>More disability states we have, better is our demographical  the transition probabilities p11, p12, p13, p21, p22, p23. For
 approach of the disability process, but smaller are the number of  example, line 5 of the file is: </p>
 transitions between each state and higher is the noise in the  
 measurement. We do not have enough experiments of the various  <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
 models to summarize the advantages and disadvantages, but it is  
 important to say that even if we had huge and unbiased samples,  <p>and this means: </p>
 the total life expectancy computed from a cross-longitudinal  
 survey, varies with the number of states. If we define only two  <pre>p11(100,106)=0.02655
 states, alive or dead, we find the usual life expectancy where it  p12(100,106)=0.17622
 is assumed that at each age, people are at the same risk to die.  p13(100,106)=0.79722
 If we are differentiating the alive state into healthy and  p21(100,106)=0.01809
 disable, and as the mortality from the disability state is higher  p22(100,106)=0.13678
 than the mortality from the healthy state, we are introducing  p22(100,106)=0.84513 </pre>
 heterogeneity in the risk of dying. The total mortality at each  
 age is the weighted mean of the mortality in each state by the  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 prevalence in each state. Therefore if the proportion of people  name="Stationary prevalence in each state"><font color="#EC5E5E"
 at each age and in each state is different from the stationary  size="3"><b>Stationary prevalence in each state</b></font></a><b>:
 equilibrium, there is no reason to find the same total mortality  </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
 at a particular age. Life expectancy, even if it is a very useful  
 tool, has a very strong hypothesis of homogeneity of the  <pre>#Prevalence
 population. Our main purpose is not to measure differential  #Age 1-1 2-2
 mortality but to measure the expected time in a healthy or  
 disability state in order to maximise the former and minimize the  #************
 latter. But the differential in mortality complexifies the  70 0.90134 0.09866
 measurement.</p>  71 0.89177 0.10823
   72 0.88139 0.11861
 <p>Incidences of disability or recovery are not affected by the  73 0.87015 0.12985 </pre>
 number of states if these states are independant. But incidences  
 estimates are dependant on the specification of the model. More  <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
 covariates we added in the logit model better is the model, but  0.09866 in state 2. This stationary prevalence differs from
 some covariates are not well measured, some are confounding  observed prevalence. Here is the point. The observed prevalence
 factors like in any statistical model. The procedure to &quot;fit  at age 70 results from the incidence of disability, incidence of
 the best model' is similar to logistic regression which itself is  recovery and mortality which occurred in the past of the cohort.
 similar to regression analysis. We haven't yet been sofar because  Stationary prevalence results from a simulation with actual
 we also have a severe limitation which is the speed of the  incidences and mortality (estimated from this cross-longitudinal
 convergence. On a Pentium III, 500 MHz, even the simplest model,  survey). It is the best predictive value of the prevalence in the
 estimated by month on 8,000 people may take 4 hours to converge.  future if &quot;nothing changes in the future&quot;. This is
 Also, the program is not yet a statistical package, which permits  exactly what demographers do with a Life table. Life expectancy
 a simple writing of the variables and the model to take into  is the expected mean time to survive if observed mortality rates
 account in the maximisation. The actual program allows only to  (incidence of mortality) &quot;remains constant&quot; in the
 add simple variables without covariations, like age+sex but  future. </p>
 without age+sex+ age*sex . This can be done from the source code  
 (you have to change three lines in the source code) but will  <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
 never be general enough. But what is to remember, is that  stationary prevalence</b></font><b>: </b><a
 incidences or probability of change from one state to another is  href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
 affected by the variables specified into the model.</p>  
   <p>The stationary prevalence has to be compared with the observed
 <p>Also, the age range of the people interviewed has a link with  prevalence by age. But both are statistical estimates and
 the age range of the life expectancy which can be estimated by  subjected to stochastic errors due to the size of the sample, the
 extrapolation. If your sample ranges from age 70 to 95, you can  design of the survey, and, for the stationary prevalence to the
 clearly estimate a life expectancy at age 70 and trust your  model used and fitted. It is possible to compute the standard
 confidence interval which is mostly based on your sample size,  deviation of the stationary prevalence at each age.</p>
 but if you want to estimate the life expectancy at age 50, you  
 should rely in your model, but fitting a logistic model on a age  <h5><font color="#EC5E5E" size="3">-Observed and stationary
 range of 70-95 and estimating probabilties of transition out of  prevalence in state (2=disable) with the confident interval</font>:<b>
 this age range, say at age 50 is very dangerous. At least you  </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
 should remember that the confidence interval given by the  
 standard deviation of the health expectancies, are under the  <p>This graph exhibits the stationary prevalence in state (2)
 strong assumption that your model is the 'true model', which is  with the confidence interval in red. The green curve is the
 probably not the case.</p>  observed prevalence (or proportion of individuals in state (2)).
   Without discussing the results (it is not the purpose here), we
 <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter  observe that the green curve is rather below the stationary
 file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>  prevalence. It suggests an increase of the disability prevalence
   in the future.</p>
 <p>This copy of the parameter file can be useful to re-run the  
 program while saving the old output files. </p>  <p><img src="vbiaspar21.gif" width="400" height="300"></p>
   
 <hr>  <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
   stationary prevalence of disability</b></font><b>: </b><a
 <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>  href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
   <img src="pbiaspar11.gif" width="400" height="300"> </h5>
 <p>Since you know how to run the program, it is time to test it  
 on your own computer. Try for example on a parameter file named <a  <p>This graph plots the conditional transition probabilities from
 href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a  an initial state (1=healthy in red at the bottom, or 2=disable in
 copy of <font size="2" face="Courier New">mypar.txt</font>  green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
 included in the subdirectory of imach, <font size="2"  age <em>x+h. </em>Conditional means at the condition to be alive
 face="Courier New">mytry</font>. Edit it to change the name of  at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
 the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>  curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
 if you don't want to copy it on the same directory. The file <font  + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
 face="Courier New">mydata.txt</font> is a smaller file of 3,000  prevalence of disability</em>. In order to get the stationary
 people but still with 4 waves. </p>  prevalence at age 70 we should start the process at an earlier
   age, i.e.50. If the disability state is defined by severe
 <p>Click on the imach.exe icon to open a window. Answer to the  disability criteria with only a few chance to recover, then the
 question:'<strong>Enter the parameter file name:'</strong></p>  incidence of recovery is low and the time to convergence is
   probably longer. But we don't have experience yet.</p>
 <table border="1">  
     <tr>  <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
         <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter  and initial health status</b></font><b>: </b><a
         the parameter file name: ..\mytry\imachpar.txt</strong></p>  href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
         </td>  
     </tr>  <pre># Health expectancies
 </table>  # Age 1-1 1-2 2-1 2-2
   70 10.9226 3.0401 5.6488 6.2122
 <p>Most of the data files or image files generated, will use the  71 10.4384 3.0461 5.2477 6.1599
 'imachpar' string into their name. The running time is about 2-3  72 9.9667 3.0502 4.8663 6.1025
 minutes on a Pentium III. If the execution worked correctly, the  73 9.5077 3.0524 4.5044 6.0401 </pre>
 outputs files are created in the current directory, and should be  
 the same as the mypar files initially included in the directory <font  <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
 size="2" face="Courier New">mytry</font>.</p>  e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
   
 <ul>  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
     <li><pre><u>Output on the screen</u> The output screen looks like <a  src="expbiaspar11.gif" width="400" height="300"></pre>
 href="imachrun.LOG">this Log file</a>  
 #  <p>For example, life expectancy of a healthy individual at age 70
   is 10.42 in the healthy state and 3.04 in the disability state
 title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3  (=13.46 years). If he was disable at age 70, his life expectancy
 ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>  will be shorter, 5.64 in the healthy state and 5.71 in the
     </li>  disability state (=11.35 years). The total life expectancy is a
     <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92  weighted mean of both, 13.46 and 11.35; weight is the proportion
   of people disabled at age 70. In order to get a pure period index
 Warning, no any valid information for:126 line=126  (i.e. based only on incidences) we use the <a
 Warning, no any valid information for:2307 line=2307  href="#Stationary prevalence in each state">computed or
 Delay (in months) between two waves Min=21 Max=51 Mean=24.495826  stationary prevalence</a> at age 70 (i.e. computed from
 <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>  incidences at earlier ages) instead of the <a
 Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14  href="#Observed prevalence in each state">observed prevalence</a>
  prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1  (for example at first exam) (<a href="#Health expectancies">see
 Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>  below</a>).</p>
     </li>  
 </ul>  <h5><font color="#EC5E5E" size="3"><b>- Variances of life
   expectancies by age and initial health status</b></font><b>: </b><a
 <p>&nbsp;</p>  href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
   
 <ul>  <p>For example, the covariances of life expectancies Cov(ei,ej)
     <li>Maximisation with the Powell algorithm. 8 directions are  at age 50 are (line 3) </p>
         given corresponding to the 8 parameters. this can be  
         rather long to get convergence.<br>  <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</pre>
         <font size="1" face="Courier New"><br>  
         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
         0.000000000000 3<br>  name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
         0.000000000000 4 0.000000000000 5 0.000000000000 6  expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
         0.000000000000 7 <br>  with standard errors in parentheses</b></font><b>: </b><a
         0.000000000000 8 0.000000000000<br>  href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
         1..........2.................3..........4.................5.........<br>  
         6................7........8...............<br>  <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
         Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283  
         <br>  <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
         2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>  
         5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>  <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
         8 0.051272038506<br>  the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
         1..............2...........3..............4...........<br>  prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
         5..........6................7...........8.........<br>  state 2, respectively (the sum is equal to one). e.1=9.95 is the
         #Number of iterations = 23, -2 Log likelihood =  Disability-free life expectancy at age 70 (it is again a weighted
         6744.954042573691<br>  mean of e11 and e21). e.2=3.30 is also the life expectancy at age
         # Parameters<br>  70 to be spent in the disability state.</p>
         12 -12.966061 0.135117 <br>  
         13 -7.401109 0.067831 <br>  <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
         21 -0.672648 -0.006627 <br>  age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
         23 -5.051297 0.051271 </font><br>  </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
         </li>  
     <li><pre><font size="2">Calculation of the hessian matrix. Wait...  <p>This figure represents the health expectancies and the total
 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78  life expectancy with the confident interval in dashed curve. </p>
   
 Inverting the hessian to get the covariance matrix. Wait...  <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>
   
 #Hessian matrix#  <p>Standard deviations (obtained from the information matrix of
 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001   the model) of these quantities are very useful.
 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003   Cross-longitudinal surveys are costly and do not involve huge
 -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001   samples, generally a few thousands; therefore it is very
 -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003   important to have an idea of the standard deviation of our
 -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003   estimates. It has been a big challenge to compute the Health
 -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005   Expectancy standard deviations. Don't be confuse: life expectancy
 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004   is, as any expected value, the mean of a distribution; but here
 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006   we are not computing the standard deviation of the distribution,
 # Scales  but the standard deviation of the estimate of the mean.</p>
 12 1.00000e-004 1.00000e-006  
 13 1.00000e-004 1.00000e-006  <p>Our health expectancies estimates vary according to the sample
 21 1.00000e-003 1.00000e-005  size (and the standard deviations give confidence intervals of
 23 1.00000e-004 1.00000e-005  the estimate) but also according to the model fitted. Let us
 # Covariance  explain it in more details.</p>
   1 5.90661e-001  
   2 -7.26732e-003 8.98810e-005  <p>Choosing a model means ar least two kind of choices. First we
   3 8.80177e-002 -1.12706e-003 5.15824e-001  have to decide the number of disability states. Second we have to
   4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005  design, within the logit model family, the model: variables,
   5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000  covariables, confonding factors etc. to be included.</p>
   6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004  
   7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000  <p>More disability states we have, better is our demographical
   8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004  approach of the disability process, but smaller are the number of
 # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).  transitions between each state and higher is the noise in the
   measurement. We do not have enough experiments of the various
   models to summarize the advantages and disadvantages, but it is
 agemin=70 agemax=100 bage=50 fage=100  important to say that even if we had huge and unbiased samples,
 Computing prevalence limit: result on file 'plrmypar.txt'   the total life expectancy computed from a cross-longitudinal
 Computing pij: result on file 'pijrmypar.txt'   survey, varies with the number of states. If we define only two
 Computing Health Expectancies: result on file 'ermypar.txt'   states, alive or dead, we find the usual life expectancy where it
 Computing Variance-covariance of DFLEs: file 'vrmypar.txt'   is assumed that at each age, people are at the same risk to die.
 Computing Total LEs with variances: file 'trmypar.txt'   If we are differentiating the alive state into healthy and
 Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'   disable, and as the mortality from the disability state is higher
 End of Imach  than the mortality from the healthy state, we are introducing
 </font></pre>  heterogeneity in the risk of dying. The total mortality at each
     </li>  age is the weighted mean of the mortality in each state by the
 </ul>  prevalence in each state. Therefore if the proportion of people
   at each age and in each state is different from the stationary
 <p><font size="3">Once the running is finished, the program  equilibrium, there is no reason to find the same total mortality
 requires a caracter:</font></p>  at a particular age. Life expectancy, even if it is a very useful
   tool, has a very strong hypothesis of homogeneity of the
 <table border="1">  population. Our main purpose is not to measure differential
     <tr>  mortality but to measure the expected time in a healthy or
         <td width="100%"><strong>Type g for plotting (available  disability state in order to maximise the former and minimize the
         if mle=1), e to edit output files, c to start again,</strong><p><strong>and  latter. But the differential in mortality complexifies the
         q for exiting:</strong></p>  measurement.</p>
         </td>  
     </tr>  <p>Incidences of disability or recovery are not affected by the
 </table>  number of states if these states are independant. But incidences
   estimates are dependant on the specification of the model. More
 <p><font size="3">First you should enter <strong>g</strong> to  covariates we added in the logit model better is the model, but
 make the figures and then you can edit all the results by typing <strong>e</strong>.  some covariates are not well measured, some are confounding
 </font></p>  factors like in any statistical model. The procedure to &quot;fit
   the best model' is similar to logistic regression which itself is
 <ul>  similar to regression analysis. We haven't yet been sofar because
     <li><u>Outputs files</u> <br>  we also have a severe limitation which is the speed of the
         - index.htm, this file is the master file on which you  convergence. On a Pentium III, 500 MHz, even the simplest model,
         should click first.<br>  estimated by month on 8,000 people may take 4 hours to converge.
         - Observed prevalence in each state: <a  Also, the program is not yet a statistical package, which permits
         href="..\mytry\prmypar.txt">mypar.txt</a> <br>  a simple writing of the variables and the model to take into
         - Estimated parameters and the covariance matrix: <a  account in the maximisation. The actual program allows only to
         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>  add simple variables like age+sex or age+sex+ age*sex but will
         - Stationary prevalence in each state: <a  never be general enough. But what is to remember, is that
         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>  incidences or probability of change from one state to another is
         - Transition probabilities: <a  affected by the variables specified into the model.</p>
         href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>  
         - Copy of the parameter file: <a  <p>Also, the age range of the people interviewed has a link with
         href="..\mytry\ormypar.txt">ormypar.txt</a> <br>  the age range of the life expectancy which can be estimated by
         - Life expectancies by age and initial health status: <a  extrapolation. If your sample ranges from age 70 to 95, you can
         href="..\mytry\ermypar.txt">ermypar.txt</a> <br>  clearly estimate a life expectancy at age 70 and trust your
         - Variances of life expectancies by age and initial  confidence interval which is mostly based on your sample size,
         health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>  but if you want to estimate the life expectancy at age 50, you
         <br>  should rely in your model, but fitting a logistic model on a age
         - Health expectancies with their variances: <a  range of 70-95 and estimating probabilties of transition out of
         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>  this age range, say at age 50 is very dangerous. At least you
         - Standard deviation of stationary prevalence: <a  should remember that the confidence interval given by the
         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>  standard deviation of the health expectancies, are under the
         <br>  strong assumption that your model is the 'true model', which is
         </li>  probably not the case.</p>
     <li><u>Graphs</u> <br>  
         <br>  <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
         -<a href="..\mytry\vmypar1.gif">Observed and stationary  file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
         prevalence in state (1) with the confident interval</a> <br>  
         -<a href="..\mytry\vmypar2.gif">Observed and stationary  <p>This copy of the parameter file can be useful to re-run the
         prevalence in state (2) with the confident interval</a> <br>  program while saving the old output files. </p>
         -<a href="..\mytry\exmypar1.gif">Health life expectancies  
         by age and initial health state (1)</a> <br>  <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
         -<a href="..\mytry\exmypar2.gif">Health life expectancies  </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
         by age and initial health state (2)</a> <br>  
         -<a href="..\mytry\emypar.gif">Total life expectancy by  <p
         age and health expectancies in states (1) and (2).</a> </li>  style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,
 </ul>  we have estimated the observed prevalence between 1/1/1984 and
   1/6/1988. The mean date of interview (weighed average of the
 <p>This software have been partly granted by <a  interviews performed between1/1/1984 and 1/6/1988) is estimated
 href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted  to be 13/9/1985, as written on the top on the file. Then we
 action from the European Union. It will be copyrighted  forecast the probability to be in each state. </p>
 identically to a GNU software product, i.e. program and software  
 can be distributed freely for non commercial use. Sources are not  <p
 widely distributed today. You can get them by asking us with a  style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,
 simple justification (name, email, institute) <a  at date 1/1/1989 : </p>
 href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a  
 href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>  <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
   # Forecasting at date 1/1/1989
 <p>Latest version (0.63 of 16 march 2000) can be accessed at <a    73 0.807 0.078 0.115</pre>
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>  
 </p>  <p
 </body>  style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Since
 </html>  the minimum age is 70 on the 13/9/1985, the youngest forecasted
   age is 73. This means that at age a person aged 70 at 13/9/1989
   has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
   Similarly, the probability to be in state 2 is 0.078 and the
   probability to die is 0.115. Then, on the 1/1/1989, the
   prevalence of disability at age 73 is estimated to be 0.088.</p>
   
   <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
   </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
   
   <pre># Age P.1 P.2 P.3 [Population]
   # Forecasting at date 1/1/1989
   75 572685.22 83798.08
   74 621296.51 79767.99
   73 645857.70 69320.60 </pre>
   
   <pre># Forecasting at date 1/1/19909
   76 442986.68 92721.14 120775.48
   75 487781.02 91367.97 121915.51
   74 512892.07 85003.47 117282.76 </pre>
   
   <p>From the population file, we estimate the number of people in
   each state. At age 73, 645857 persons are in state 1 and 69320
   are in state 2. One year latter, 512892 are still in state 1,
   85003 are in state 2 and 117282 died before 1/1/1990.</p>
   
   <hr>
   
   <h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>
   
   <p>Since you know how to run the program, it is time to test it
   on your own computer. Try for example on a parameter file named <a
   href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of <font
   size="2" face="Courier New">mypar.imach</font> included in the
   subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
   Edit it to change the name of the data file to <font size="2"
   face="Courier New">..\data\mydata.txt</font> if you don't want to
   copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
   is a smaller file of 3,000 people but still with 4 waves. </p>
   
   <p>Click on the imach.exe icon to open a window. Answer to the
   question:'<strong>Enter the parameter file name:'</strong></p>
   
   <table border="1">
       <tr>
           <td width="100%"><strong>IMACH, Version 0.8</strong><p><strong>Enter
           the parameter file name: ..\mytry\imachpar.imach</strong></p>
           </td>
       </tr>
   </table>
   
   <p>Most of the data files or image files generated, will use the
   'imachpar' string into their name. The running time is about 2-3
   minutes on a Pentium III. If the execution worked correctly, the
   outputs files are created in the current directory, and should be
   the same as the mypar files initially included in the directory <font
   size="2" face="Courier New">mytry</font>.</p>
   
   <ul>
       <li><pre><u>Output on the screen</u> The output screen looks like <a
   href="imachrun.LOG">this Log file</a>
   #
   
   title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
   ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
       </li>
       <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
   
   Warning, no any valid information for:126 line=126
   Warning, no any valid information for:2307 line=2307
   Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
   <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
   Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
    prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
   Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
       </li>
   </ul>
   
   <p>&nbsp;</p>
   
   <ul>
       <li>Maximisation with the Powell algorithm. 8 directions are
           given corresponding to the 8 parameters. this can be
           rather long to get convergence.<br>
           <font size="1" face="Courier New"><br>
           Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
           0.000000000000 3<br>
           0.000000000000 4 0.000000000000 5 0.000000000000 6
           0.000000000000 7 <br>
           0.000000000000 8 0.000000000000<br>
           1..........2.................3..........4.................5.........<br>
           6................7........8...............<br>
           Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
           <br>
           2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
           5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
           8 0.051272038506<br>
           1..............2...........3..............4...........<br>
           5..........6................7...........8.........<br>
           #Number of iterations = 23, -2 Log likelihood =
           6744.954042573691<br>
           # Parameters<br>
           12 -12.966061 0.135117 <br>
           13 -7.401109 0.067831 <br>
           21 -0.672648 -0.006627 <br>
           23 -5.051297 0.051271 </font><br>
           </li>
       <li><pre><font size="2">Calculation of the hessian matrix. Wait...
   12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78
   
   Inverting the hessian to get the covariance matrix. Wait...
   
   #Hessian matrix#
   3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
   2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
   -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
   -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
   -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
   -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
   3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
   3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
   # Scales
   12 1.00000e-004 1.00000e-006
   13 1.00000e-004 1.00000e-006
   21 1.00000e-003 1.00000e-005
   23 1.00000e-004 1.00000e-005
   # Covariance
     1 5.90661e-001
     2 -7.26732e-003 8.98810e-005
     3 8.80177e-002 -1.12706e-003 5.15824e-001
     4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
     5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
     6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
     7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
     8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004
   # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
   
   
   agemin=70 agemax=100 bage=50 fage=100
   Computing prevalence limit: result on file 'plrmypar.txt'
   Computing pij: result on file 'pijrmypar.txt'
   Computing Health Expectancies: result on file 'ermypar.txt'
   Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
   Computing Total LEs with variances: file 'trmypar.txt'
   Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
   End of Imach
   </font></pre>
       </li>
   </ul>
   
   <p><font size="3">Once the running is finished, the program
   requires a caracter:</font></p>
   
   <table border="1">
       <tr>
           <td width="100%"><strong>Type e to edit output files, c
           to start again, and q for exiting:</strong></td>
       </tr>
   </table>
   
   <p><font size="3">First you should enter <strong>e </strong>to
   edit the master file mypar.htm. </font></p>
   
   <ul>
       <li><u>Outputs files</u> <br>
           <br>
           - Observed prevalence in each state: <a
           href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
           - Estimated parameters and the covariance matrix: <a
           href="..\mytry\rmypar.txt">rmypar.imach</a> <br>
           - Stationary prevalence in each state: <a
           href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
           - Transition probabilities: <a
           href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
           - Copy of the parameter file: <a
           href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
           - Life expectancies by age and initial health status: <a
           href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
           - Variances of life expectancies by age and initial
           health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
           <br>
           - Health expectancies with their variances: <a
           href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
           - Standard deviation of stationary prevalence: <a
           href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
           - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
           <br>
           - Population forecasting (if popforecast=1): <a
           href="poprmypar.txt">poprmypar.txt</a> <br>
           </li>
       <li><u>Graphs</u> <br>
           <br>
           -<a href="../mytry/pemypar1.gif">One-step transition probabilities</a><br>
           -<a href="../mytry/pmypar11.gif">Convergence to the stationary prevalence</a><br>
           -<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> <br>
           -<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> <br>
           -<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> <br>
           -<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> <br>
           -<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li>
   </ul>
   
   <p>This software have been partly granted by <a
   href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
   action from the European Union. It will be copyrighted
   identically to a GNU software product, i.e. program and software
   can be distributed freely for non commercial use. Sources are not
   widely distributed today. You can get them by asking us with a
   simple justification (name, email, institute) <a
   href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
   href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
   
   <p>Latest version (0.8 of March 2002) can be accessed at <a
   href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
   </p>
   </body>
   </html>

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