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   style="tab-interval:35.4pt">
   
 <hr size="3" color="#EC5E5E">  <hr size="3" noshade color="#EC5E5E">
   
 <h1 align="center"><font color="#00006A">Computing Health  <h1 align="center" style="text-align:center"><span lang="EN-GB" style="color:#00006A;
 Expectancies using IMaCh</font></h1>  mso-ansi-language:EN-GB">Computing Health
   Expectancies using IMaCh</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
   
   <h1 align="center" style="text-align:center"><span lang="EN-GB" style="font-size:
   18.0pt;color:#00006A;mso-ansi-language:EN-GB">(a Maximum
   Likelihood Computer Program using Interpolation of Markov Chains)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
   
   <p align="center" style="text-align:center"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">&nbsp;<o:p></o:p></span></p>
   
   <p align="center" style="text-align:center"><a
   href="http://www.ined.fr/"><span style="text-decoration:none;text-underline:none"><img src="logo-ined.gif" border="0"
   width="151" height="76" id="_x0000_i1026"></span></a><img
   src="euroreves2.gif" width="151" height="75" id="_x0000_i1027"></p>
   
   <h3 align="center" style="text-align:center"><a
   href="http://www.ined.fr/"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">INED</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a> and </span><a
   href="http://euroreves.ined.fr"><span lang="EN-GB" style="color:#00006A;
   mso-ansi-language:EN-GB">EUROREVES</span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB"><o:p></o:p></span></a></h3>
   
   <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="font-size:13.5pt;color:#00006A;mso-ansi-language:EN-GB">Version 0.7,
   February 2002</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
   
   <hr size="3" noshade color="#EC5E5E">
   
   <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Authors of
   the program: </span></strong><a href="http://sauvy.ined.fr/brouard"><strong><span lang="EN-GB" style="color:#00006A;
   mso-ansi-language:EN-GB">Nicolas
   Brouard</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></strong></a><strong>, senior researcher at the </span></strong><a
   href="http://www.ined.fr"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Institut National d'Etudes
   Démographiques</span><span lang="EN-GB" style="color:#00006A;
   mso-ansi-language:EN-GB"></strong></a><strong> (INED, Paris) in the
   &quot;Mortality, Health and Epidemiology&quot; Research Unit </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
   
   <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">and Agnès
   Lièvre</span></strong><b><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"><br clear="left"
   style="mso-special-character:line-break">
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></b></p>
   
   <h4><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Contribution to the mathematics: C. R. Heathcote </span><span lang="EN-GB" style="font-size:
   10.0pt;color:#00006A;mso-ansi-language:EN-GB">(Australian
   National University, Canberra).</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
   
 <h1 align="center"><font color="#00006A" size="5">(a Maximum  <h4><span style="color:#00006A">Contact: Agnès Lièvre (</span><a href="mailto:lievre@ined.fr"><i><span style="color:#00006A">lievre@ined.fr</span><span style="color:#00006A"></i></a>)
 Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>  </span></h4>
   
 <p align="center">&nbsp;</p>  
   
 <p align="center"><a href="http://www.ined.fr/"><img  
 src="logo-ined.gif" border="0" width="151" height="76"></a><img  
 src="euroreves2.gif" width="151" height="75"></p>  
   
 <h3 align="center"><a href="http://www.ined.fr/"><font  
 color="#00006A">INED</font></a><font color="#00006A"> and </font><a  
 href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>  
   
 <p align="center"><font color="#00006A" size="4"><strong>Version  
 0.7, February 2002</strong></font></p>  
   
 <hr size="3" color="#EC5E5E">  
   
 <p align="center"><font color="#00006A"><strong>Authors of the  
 program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font  
 color="#00006A"><strong>Nicolas Brouard</strong></font></a><font  
 color="#00006A"><strong>, senior researcher at the </strong></font><a  
 href="http://www.ined.fr"><font color="#00006A"><strong>Institut  
 National d'Etudes Démographiques</strong></font></a><font  
 color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,  
 Health and Epidemiology&quot; Research Unit </strong></font></p>  
   
 <p align="center"><font color="#00006A"><strong>and Agnès  
 Lièvre<br clear="left">  
 </strong></font></p>  
   
 <h4><font color="#00006A">Contribution to the mathematics: C. R.  
 Heathcote </font><font color="#00006A" size="2">(Australian  
 National University, Canberra).</font></h4>  
   
 <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  
 color="#00006A">) </font></h4>  
   
 <hr>  <hr>
   <span style="font-size:12.0pt;font-family:&quot;Times New Roman&quot;;mso-fareast-font-family:
 <ul>  &quot;Times New Roman&quot;;mso-ansi-language:FR;mso-fareast-language:FR;mso-bidi-language:
     <li><a href="#intro">Introduction</a> </li>  AR-SA">
     <li>The detailed statistical model (<a href="docmath.pdf">PDF  <ul type="disc">
         version</a>),(<a href="docmath.ps">ps version</a>) </li>      <li class="MsoNormal"
     <li><a href="#data">On what kind of data can it be used?</a></li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     <li><a href="#datafile">The data file</a> </li>       mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
     <li><a href="#biaspar">The parameter file</a> </li>          href="#intro"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Introduction</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
     <li><a href="#running">Running Imach</a> </li>      <li class="MsoNormal"
     <li><a href="#output">Output files and graphs</a> </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     <li><a href="#example">Exemple</a> </li>       mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#data"><span lang="EN-GB" style="mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#datafile"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The data file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The parameter file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#running"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Running Imach</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#output"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output files and graphs</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
           href="#example">Exemple</a> </li>
 </ul>  </ul>
   </span>
 <hr>  <hr>
   
 <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>  <h2><a name="intro"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Introduction</span><span style="mso-bookmark:intro"></span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB"><o:p></o:p></span></a></h2>
   
 <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This program computes <b>Healthy
 data</b> using the methodology pioneered by Laditka and Wolf (1).  Life Expectancies</b> from <b>cross-longitudinal data</b> using
 Within the family of Health Expectancies (HE), Disability-free  the methodology pioneered by Laditka and Wolf (1). Within the
 life expectancy (DFLE) is probably the most important index to  family of Health Expectancies (HE), Disability-free life
   expectancy (DFLE) is probably the most important index to
 monitor. In low mortality countries, there is a fear that when  monitor. In low mortality countries, there is a fear that when
 mortality declines, the increase in DFLE is not proportionate to  mortality declines, the increase in DFLE is not proportionate to
 the increase in total Life expectancy. This case is called the <em>Expansion  the increase in total Life expectancy. This case is called the <em>Expansion
 of morbidity</em>. Most of the data collected today, in  of morbidity</em>. Most of the data collected today, in
 particular by the international <a href="http://euroreves/reves">REVES</a>  particular by the international </span><a href="http://euroreves/reves"><span lang="EN-GB" style="mso-ansi-language:EN-GB">REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
 network on Health expectancy, and most HE indices based on these  network on Health expectancy, and most HE indices based on these
 data, are <em>cross-sectional</em>. It means that the information  data, are <em>cross-sectional</em>. It means that the information
 collected comes from a single cross-sectional survey: people from  collected comes from a single cross-sectional survey: people from
Line 95  population. Life expectancy (LE) (or tot Line 511  population. Life expectancy (LE) (or tot
 the yearly number of births or deaths of this stationary  the yearly number of births or deaths of this stationary
 population) is then decomposed into DFLE and DLE. This method of  population) is then decomposed into DFLE and DLE. This method of
 computing HE is usually called the Sullivan method (from the name  computing HE is usually called the Sullivan method (from the name
 of the author who first described it).</p>  of the author who first described it).<o:p></o:p></span></p>
   
 <p>Age-specific proportions of people disable are very difficult  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age-specific proportions of people
 to forecast because each proportion corresponds to historical  disable are very difficult to forecast because each proportion
 conditions of the cohort and it is the result of the historical  corresponds to historical conditions of the cohort and it is the
 flows from entering disability and recovering in the past until  result of the historical flows from entering disability and
 today. The age-specific intensities (or incidence rates) of  recovering in the past until today. The age-specific intensities
 entering disability or recovering a good health, are reflecting  (or incidence rates) of entering disability or recovering a good
 actual conditions and therefore can be used at each age to  health, are reflecting actual conditions and therefore can be
 forecast the future of this cohort. For example if a country is  used at each age to forecast the future of this cohort. For
 improving its technology of prosthesis, the incidence of  example if a country is improving its technology of prosthesis,
 recovering the ability to walk will be higher at each (old) age,  the incidence of recovering the ability to walk will be higher at
 but the prevalence of disability will only slightly reflect an  each (old) age, but the prevalence of disability will only
 improve because the prevalence is mostly affected by the history  slightly reflect an improve because the prevalence is mostly
 of the cohort and not by recent period effects. To measure the  affected by the history of the cohort and not by recent period
 period improvement we have to simulate the future of a cohort of  effects. To measure the period improvement we have to simulate
 new-borns entering or leaving at each age the disability state or  the future of a cohort of new-borns entering or leaving at each
 dying according to the incidence rates measured today on  age the disability state or dying according to the incidence
 different cohorts. The proportion of people disabled at each age  rates measured today on different cohorts. The proportion of
 in this simulated cohort will be much lower (using the exemple of  people disabled at each age in this simulated cohort will be much
 an improvement) that the proportions observed at each age in a  lower (using the example of an improvement) that the proportions
 cross-sectional survey. This new prevalence curve introduced in a  observed at each age in a cross-sectional survey. This new
 life table will give a much more actual and realistic HE level  prevalence curve introduced in a life table will give a much more
 than the Sullivan method which mostly measured the History of  actual and realistic HE level than the Sullivan method which
 health conditions in this country.</p>  mostly measured the History of health conditions in this country.<o:p></o:p></span></p>
   
 <p>Therefore, the main question is how to measure incidence rates  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Therefore, the main question is how
 from cross-longitudinal surveys? This is the goal of the IMaCH  to measure incidence rates from cross-longitudinal surveys? This
 program. From your data and using IMaCH you can estimate period  is the goal of the IMaCH program. From your data and using IMaCH
 HE and not only Sullivan's HE. Also the standard errors of the HE  you can estimate period HE and not only Sullivan's HE. Also the
 are computed.</p>  standard errors of the HE are computed.<o:p></o:p></span></p>
   
 <p>A cross-longitudinal survey consists in a first survey  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">A cross-longitudinal survey
 (&quot;cross&quot;) where individuals from different ages are  consists in a first survey (&quot;cross&quot;) where individuals
 interviewed on their health status or degree of disability. At  from different ages are interviewed on their health status or
 least a second wave of interviews (&quot;longitudinal&quot;)  degree of disability. At least a second wave of interviews
 should measure each new individual health status. Health  (&quot;longitudinal&quot;) should measure each new individual
 expectancies are computed from the transitions observed between  health status. Health expectancies are computed from the
 waves and are computed for each degree of severity of disability  transitions observed between waves and are computed for each
 (number of life states). More degrees you consider, more time is  degree of severity of disability (number of life states). More
 necessary to reach the Maximum Likelihood of the parameters  degrees you consider, more time is necessary to reach the Maximum
 involved in the model. Considering only two states of disability  Likelihood of the parameters involved in the model. Considering
 (disable and healthy) is generally enough but the computer  only two states of disability (disable and healthy) is generally
 program works also with more health statuses.<br>  enough but the computer program works also with more health
   statuses.<span style="mso-spacerun:
   yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><br>
 <br>  <br>
 The simplest model is the multinomial logistic model where <i>pij</i>  The simplest model is the multinomial logistic model where <i>pij</i>
 is the probability to be observed in state <i>j</i> at the second  is the probability to be observed in state <i>j</i> at the second
Line 158  month or quarter trimester, semester or Line 576  month or quarter trimester, semester or
 multinomial logistic. The <i>hPx</i> matrix is simply the matrix  multinomial logistic. The <i>hPx</i> matrix is simply the matrix
 product of <i>nh*stepm</i> elementary matrices and the  product of <i>nh*stepm</i> elementary matrices and the
 contribution of each individual to the likelihood is simply <i>hPijx</i>.  contribution of each individual to the likelihood is simply <i>hPijx</i>.
 <br>  <o:p></o:p></span></p>
 </p>  
   
 <p>The program presented in this manual is a quite general  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The program presented in this
 program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated  manual is a quite general program named <strong>IMaCh</strong>
 <strong>MA</strong>rkov <strong>CH</strong>ain), designed to  (for <strong>I</strong>nterpolated <strong>MA</strong>rkov <strong>CH</strong>ain),
 analyse transition data from longitudinal surveys. The first step  designed to analyse transition data from longitudinal surveys.
 is the parameters estimation of a transition probabilities model  The first step is the parameters estimation of a transition
 between an initial status and a final status. From there, the  probabilities model between an initial status and a final status.
 computer program produces some indicators such as observed and  From there, the computer program produces some indicators such as
 stationary prevalence, life expectancies and their variances and  observed and stationary prevalence, life expectancies and their
 graphs. Our transition model consists in absorbing and  variances and graphs. Our transition model consists in absorbing
 non-absorbing states with the possibility of return across the  and non-absorbing states with the possibility of return across
 non-absorbing states. The main advantage of this package,  the non-absorbing states. The main advantage of this package,
 compared to other programs for the analysis of transition data  compared to other programs for the analysis of transition data
 (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole  (For example: Proc Catmod of SAS<sup>(r)</sup>) is that the whole
 individual information is used even if an interview is missing, a  individual information is used even if an interview is missing, a
 status or a date is unknown or when the delay between waves is  status or a date is unknown or when the delay between waves is
 not identical for each individual. The program can be executed  not identical for each individual. The program can be executed
Line 181  according to parameters: selection of a Line 598  according to parameters: selection of a
 absorbing and non-absorbing states, number of waves taken in  absorbing and non-absorbing states, number of waves taken in
 account (the user inputs the first and the last interview), a  account (the user inputs the first and the last interview), a
 tolerance level for the maximization function, the periodicity of  tolerance level for the maximization function, the periodicity of
 the transitions (we can compute annual, quaterly or monthly  the transitions (we can compute annual, quarterly or monthly
 transitions), covariates in the model. It works on Windows or on  transitions), covariates in the model. It works on Windows or on
 Unix.<br>  Unix.<o:p></o:p></span></p>
 </p>  
   
 <hr>  <hr>
   
 <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New  <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New
 Methods for Analyzing Active Life Expectancy&quot;. <i>Journal of  Methods for Analyzing Active Life Expectancy&quot;. <i>Journal of
 Aging and Health</i>. Vol 10, No. 2. </p>  Aging and Health</i>. </span>Vol 10, No. 2. </p>
   
 <hr>  <hr>
   
 <h2><a name="data"><font color="#00006A">On what kind of data can  <h2><a name="data"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span style="mso-bookmark:data"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
 it be used?</font></a></h2>  
   
 <p>The minimum data required for a transition model is the  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The minimum data required for a
 recording of a set of individuals interviewed at a first date and  transition model is the recording of a set of individuals
 interviewed again at least one another time. From the  interviewed at a first date and interviewed again at least one
 observations of an individual, we obtain a follow-up over time of  another time. From the observations of an individual, we obtain a
 the occurrence of a specific event. In this documentation, the  follow-up over time of the occurrence of a specific event. In
 event is related to health status at older ages, but the program  this documentation, the event is related to health status at
 can be applied on a lot of longitudinal studies in different  older ages, but the program can be applied on a lot of
 contexts. To build the data file explained into the next section,  longitudinal studies in different contexts. To build the data
 you must have the month and year of each interview and the  file explained into the next section, you must have the month and
 corresponding health status. But in order to get age, date of  year of each interview and the corresponding health status. But
 birth (month and year) is required (missing values is allowed for  in order to get age, date of birth (month and year) is required
 month). Date of death (month and year) is an important  (missing values is allowed for month). Date of death (month and
 information also required if the individual is dead. Shorter  year) is an important information also required if the individual
 steps (i.e. a month) will more closely take into account the  is dead. Shorter steps (i.e. a month) will more closely take into
 survival time after the last interview.</p>  account the survival time after the last interview.<o:p></o:p></span></p>
   
 <hr>  <hr>
   
 <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>  <h2><a name="datafile"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:
   EN-GB">The data file</span><span style="mso-bookmark:datafile"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
   
 <p>In this example, 8,000 people have been interviewed in a  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, 8,000 people have
 cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).  been interviewed in a cross-longitudinal survey of 4 waves (1984,
 Some people missed 1, 2 or 3 interviews. Health statuses are  1986, 1988, 1990). Some people missed 1, 2 or 3 interviews.
 healthy (1) and disable (2). The survey is not a real one. It is  Health statuses are healthy (1) and disable (2). The survey is
 a simulation of the American Longitudinal Survey on Aging. The  not a real one. It is a simulation of the American Longitudinal
 disability state is defined if the individual missed one of four  Survey on Aging. The disability state is defined if the
 ADL (Activity of daily living, like bathing, eating, walking).  individual missed one of four ADL (Activity of daily living, like
 Therefore, even is the individuals interviewed in the sample are  bathing, eating, walking). Therefore, even is the individuals
 virtual, the information brought with this sample is close to the  interviewed in the sample are virtual, the information brought
 situation of the United States. Sex is not recorded is this  with this sample is close to the situation of the United States.
 sample.</p>  Sex is not recorded is this sample.<o:p></o:p></span></p>
   
 <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>  <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each line of the data set (named </span><a href="data1.txt"><span lang="EN-GB" style="mso-ansi-language:
 in this first example) is an individual record which fields are: </p>  EN-GB">data1.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
   in this first example) is an individual record which fields are: <o:p></o:p></span></p>
 <ul>  
     <li><b>Index number</b>: positive number (field 1) </li>  <ul type="disc">
     <li><b>First covariate</b> positive number (field 2) </li>      <li class="MsoNormal"
     <li><b>Second covariate</b> positive number (field 3) </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     <li><a name="Weight"><b>Weight</b></a>: positive number       mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Index
         (field 4) . In most surveys individuals are weighted          number</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number (field 1) <o:p></o:p></span></li>
         according to the stratification of the sample.</li>      <li class="MsoNormal"
     <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         coded as 99/9999 (field 5) </li>       mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
     <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are          covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 2) <o:p></o:p></span></li>
         coded as 99/9999 (field 6) </li>      <li class="MsoNormal"
     <li><b>Date of first interview</b>: coded as mm/yyyy. Missing      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         dates are coded as 99/9999 (field 7) </li>       mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Second
     <li><b>Status at first interview</b>: positive number.          covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 3) <o:p></o:p></span></li>
         Missing values ar coded -1. (field 8) </li>      <li class="MsoNormal"
     <li><b>Date of second interview</b>: coded as mm/yyyy.      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         Missing dates are coded as 99/9999 (field 9) </li>       mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><a
     <li><strong>Status at second interview</strong> positive          name="Weight"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Weight</span><span style="mso-bookmark:Weight"></span><span lang="EN-GB" style="mso-ansi-language:
         number. Missing values ar coded -1. (field 10) </li>       EN-GB"></b></a>: positive number (field
     <li><b>Date of third interview</b>: coded as mm/yyyy. Missing          4) . In most surveys individuals are weighted according
         dates are coded as 99/9999 (field 11) </li>          to the stratification of the sample.<o:p></o:p></span></li>
     <li><strong>Status at third interview</strong> positive      <li class="MsoNormal"
         number. Missing values ar coded -1. (field 12) </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     <li><b>Date of fourth interview</b>: coded as mm/yyyy.       mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
         Missing dates are coded as 99/9999 (field 13) </li>          of birth</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
     <li><strong>Status at fourth interview</strong> positive          as 99/9999 (field 5) <o:p></o:p></span></li>
         number. Missing values are coded -1. (field 14) </li>      <li class="MsoNormal"
     <li>etc</li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
           of death</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
           as 99/9999 (field 6) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
           of first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
           are coded as 99/9999 (field 7) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
           at first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number. Missing values
           ar coded -1. (field 8) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
           of second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
           are coded as 99/9999 (field 9) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
           at second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
           values ar coded -1. (field 10) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
           of third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
           are coded as 99/9999 (field 11) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
           at third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
           values ar coded -1. (field 12) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
           of fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
           are coded as 99/9999 (field 13) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
           at fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
           values are coded -1. (field 14) <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">etc<o:p></o:p></span></li>
 </ul>  </ul>
   
 <p>&nbsp;</p>  <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></p>
   
 <p>If your longitudinal survey do not include information about  <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If your longitudinal survey do not
 weights or covariates, you must fill the column with a number  include information about weights or covariates, you must fill
 (e.g. 1) because a missing field is not allowed.</p>  the column with a number (e.g. 1) because a missing field is not
   allowed.<o:p></o:p></span></p>
   
 <hr>  <hr>
   
 <h2><font color="#00006A">Your first example parameter file</font><a  <h2><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Your first example parameter file</span><a
 href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>  href="http://euroreves.ined.fr/imach"></a><a name="uio"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
   
 <h2><a name="biaspar"></a>#Imach version 0.7, February 2002,  <h2><a name="biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>#Imach version 0.7, February 2002,
 INED-EUROREVES </h2>  INED-EUROREVES <o:p></o:p></span></h2>
   
 <p>This is a comment. Comments start with a '#'.</p>  <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">This is a comment. Comments start with a '#'.<o:p></o:p></span></p>
   
 <h4><font color="#FF0000">First uncommented line</font></h4>  <h4><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">First uncommented line</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
   
 <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4<o:p></o:p></span></pre>
   
 <ul>  <ul type="disc">
     <li><b>title=</b> 1st_example is title of the run. </li>      <li class="MsoNormal"
     <li><b>datafile=</b>data1.txt is the name of the data set.      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         Our example is a six years follow-up survey. It consists       text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
         in a baseline followed by 3 reinterviews. </li>          1st_example is title of the run. <o:p></o:p></span></li>
     <li><b>lastobs=</b> 8600 the program is able to run on a      <li class="MsoNormal"
         subsample where the last observation number is lastobs.      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         It can be set a bigger number than the real number of       text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">datafile=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>data1.txt
         observations (e.g. 100000). In this example, maximisation          is the name of the data set. Our example is a six years
         will be done on the 8600 first records. </li>          follow-up survey. It consists in a baseline followed by 3
     <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more          reinterviews. <o:p></o:p></span></li>
         than two interviews in the survey, the program can be run      <li class="MsoNormal"
         on selected transitions periods. firstpass=1 means the      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         first interview included in the calculation is the       text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">lastobs=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
         baseline survey. lastpass=4 means that the information          8600 the program is able to run on a subsample where the
         brought by the 4th interview is taken into account.</li>          last observation number is lastobs. It can be set a
           bigger number than the real number of observations (e.g.
           100000). In this example, maximisation will be done on
           the 8600 first records. <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">firstpass=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           , <b>lastpass=4 </b>In case of more than two interviews
           in the survey, the program can be run on selected
           transitions periods. firstpass=1 means the first
           interview included in the calculation is the baseline
           survey. lastpass=4 means that the information brought by
           the 4th interview is taken into account.<o:p></o:p></span></li>
 </ul>  </ul>
   
 <p>&nbsp;</p>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></p>
 <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented  
 line</font></a></h4>  
   
 <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>  <h4
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Second
 <ul>  uncommented line</span><a name="biaspar-2"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h4>
     <li><b>ftol=1e-8</b> Convergence tolerance on the function  
         value in the maximisation of the likelihood. Choosing a  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
         correct value for ftol is difficult. 1e-8 is a correct  
         value for a 32 bits computer.</li>  <ul type="disc">
     <li><b>stepm=1</b> Time unit in months for interpolation.      <li class="MsoNormal"
         Examples:<ul>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
             <li>If stepm=1, the unit is a month </li>       text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1e-8</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
             <li>If stepm=4, the unit is a trimester</li>          Convergence tolerance on the function value in the
             <li>If stepm=12, the unit is a year </li>          maximisation of the likelihood. Choosing a correct value
             <li>If stepm=24, the unit is two years</li>          for ftol is difficult. 1e-8 is a correct value for a 32
             <li>... </li>          bits computer.<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">stepm=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Time unit in months for interpolation. Examples:<o:p></o:p></span></li>
       <li><ul type="circle">
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   stepm=1, the unit is a month <o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   stepm=4, the unit is a trimester<o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   stepm=12, the unit is a year <o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   stepm=24, the unit is two years<o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">...
   <o:p></o:p></span>            </li>
         </ul>          </ul>
     </li>      </li>
     <li><b>ncov=2</b> Number of covariates in the datafile. The      <li class="MsoNormal"
         intercept and the age parameter are counting for 2      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         covariates.</li>       text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ncov=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
     <li><b>nlstate=2</b> Number of non-absorbing (alive) states.          Number of covariates in the datafile. The intercept and
         Here we have two alive states: disability-free is coded 1          the age parameter are counting for 2 covariates.<o:p></o:p></span></li>
         and disability is coded 2. </li>      <li class="MsoNormal"
     <li><b>ndeath=1</b> Number of absorbing states. The absorbing      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         state death is coded 3. </li>       text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">nlstate=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
     <li><b>maxwav=4</b> Number of waves in the datafile.</li>          Number of non-absorbing (alive) states. Here we have two
     <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the          alive states: disability-free is coded 1 and disability
         Maximisation Likelihood Estimation. <ul>          is coded 2. <o:p></o:p></span></li>
             <li>If mle=1 the program does the maximisation and      <li class="MsoNormal"
                 the calculation of health expectancies </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
             <li>If mle=0 the program only does the calculation of       text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ndeath=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
                 the health expectancies. </li>          Number of absorbing states. The absorbing state death is
           coded 3. <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">maxwav=4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Number of waves in the datafile.<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><a
           name="mle"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b></a><b>=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for the
           Maximisation Likelihood Estimation. <o:p></o:p></span></li>
       <li><ul type="circle">
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   mle=1 the program does the maximisation and the
                   calculation of health expectancies <o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   mle=0 the program only does the calculation of
                   the health expectancies. <o:p></o:p></span></li>
         </ul>          </ul>
     </li>      </li>
     <li><b>weight=0</b> Possibility to add weights. <ul>      <li class="MsoNormal"
             <li>If weight=0 no weights are included </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
             <li>If weight=1 the maximisation integrates the       text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">weight=0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
                 weights which are in field <a href="#Weight">4</a></li>          Possibility to add weights. <o:p></o:p></span></li>
       <li><ul type="circle">
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   weight=0 no weights are included <o:p></o:p></span></li>
               <li class="MsoNormal"
               style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
         auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
                   weight=1 the maximisation integrates the weights
                   which are in field </span><a href="#Weight"><span lang="EN-GB" style="mso-ansi-language:EN-GB">4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
         </ul>          </ul>
     </li>      </li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Covariates</font></h4>  <h4
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariates</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
 <p>Intercept and age are systematically included in the model.  
 Additional covariates can be included with the command </p>  
   
 <pre>model=<em>list of covariates</em></pre>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Intercept
 <ul>  and age are systematically included in the model. Additional
     <li>if<strong> model=. </strong>then no covariates are  covariates can be included with the command <o:p></o:p></span></p>
         included</li>  
     <li>if <strong>model=V1</strong> the model includes the first  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">model=<em>list of covariates<o:p></o:p></span></em></pre>
         covariate (field 2)</li>  
     <li>if <strong>model=V2 </strong>the model includes the  <ul type="disc">
         second covariate (field 3)</li>      <li class="MsoNormal"
     <li>if <strong>model=V1+V2 </strong>the model includes the      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         first and the second covariate (fields 2 and 3)</li>       text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if<strong>
     <li>if <strong>model=V1*V2 </strong>the model includes the          model=. </strong>then no covariates are included<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
           <strong>model=V1</strong> the model includes the first
           covariate (field 2)<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
           <strong>model=V2 </strong>the model includes the second
           covariate (field 3)<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
           <strong>model=V1+V2 </strong>the model includes the first
           and the second covariate (fields 2 and 3)<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
           <strong>model=V1*V2 </strong>the model includes the
         product of the first and the second covariate (fields 2          product of the first and the second covariate (fields 2
         and 3)</li>          and 3)<o:p></o:p></span></li>
     <li>if <strong>model=V1+V1*age</strong> the model includes      <li class="MsoNormal"
         the product covariate*age</li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
           <strong>model=V1+V1*age</strong> the model includes the
           product covariate*age<o:p></o:p></span></li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Guess values for optimization</font><font  <h4
 color="#00006A"> </font></h4>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
   values for optimisation</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
 <p>You must write the initial guess values of the parameters for  
 optimization. The number of parameters, <em>N</em> depends on the  <p
   style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">You
   must write the initial guess values of the parameters for
   optimisation. The number of parameters, <em>N</em> depends on the
 number of absorbing states and non-absorbing states and on the  number of absorbing states and non-absorbing states and on the
 number of covariates. <br>  number of covariates. <br>
 <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +  <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
Line 388  start with zeros as in this example, but Line 940  start with zeros as in this example, but
 precise set (for example from an earlier run) you can enter it  precise set (for example from an earlier run) you can enter it
 and it will speed up them<br>  and it will speed up them<br>
 Each of the four lines starts with indices &quot;ij&quot;: <b>ij  Each of the four lines starts with indices &quot;ij&quot;: <b>ij
 aij bij</b> </p>  aij bij</b> <o:p></o:p></span></p>
   
 <blockquote>  
     <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age  
 12 -14.155633  0.110794  
 13  -7.925360  0.032091  
 21  -1.890135 -0.029473  
 23  -6.234642  0.022315 </pre>  
 </blockquote>  
   
 <p>or, to simplify: </p>  
   
 <blockquote>  
     <pre>12 0.0 0.0  
 13 0.0 0.0  
 21 0.0 0.0  
 23 0.0 0.0</pre>  
 </blockquote>  
   
 <h4><font color="#FF0000">Guess values for computing variances</font></h4>  
   
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  <pre
 used as an input to get the various output data files (Health  style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
   36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Guess values of aij and bij in log (pij/pii) = aij + bij * age<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">12 -14.155633<span style="mso-spacerun: yes">&nbsp; </span>0.110794 <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">13<span style="mso-spacerun: yes">&nbsp; </span>-7.925360<span style="mso-spacerun: yes">&nbsp; </span>0.032091 <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">21<span style="mso-spacerun: yes">&nbsp; </span>-1.890135 -0.029473 <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">23<span style="mso-spacerun: yes">&nbsp; </span>-6.234642<span style="mso-spacerun: yes">&nbsp; </span>0.022315 <o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">or,
   to simplify: <o:p></o:p></span></p>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
   36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12 0.0 0.0<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">13 0.0 0.0<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:
   36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
   justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">21 0.0 0.0<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">23 0.0 0.0<o:p></o:p></span></pre>
   
   <h4
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
   values for computing variances</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
   an input to get the various output data files (Health
 expectancies, stationary prevalence etc.) and figures without  expectancies, stationary prevalence etc.) and figures without
 rerunning the rather long maximisation phase (mle=0). </p>  rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
   
 <p>The scales are small values for the evaluation of numerical  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   scales are small values for the evaluation of numerical
 derivatives. These derivatives are used to compute the hessian  derivatives. These derivatives are used to compute the hessian
 matrix of the parameters, that is the inverse of the covariance  matrix of the parameters, that is the inverse of the covariance
 matrix, and the variances of health expectancies. Each line  matrix, and the variances of health expectancies. Each line
 consists in indices &quot;ij&quot; followed by the initial scales  consists in indices &quot;ij&quot; followed by the initial scales
 (zero to simplify) associated with aij and bij. </p>  (zero to simplify) associated with aij and bij. <o:p></o:p></span></p>
   
 <ul>  <ul type="disc">
     <li>If mle=1 you can enter zeros:</li>      <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l16 level1 lfo18;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
           mle=1 you can enter zeros:<o:p></o:p></span></li>
 </ul>  </ul>
   
 <blockquote>  <pre
     <pre># Scales (for hessian or gradient estimation)  style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
 12 0. 0.  36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Scales (for hessian or gradient estimation)<o:p></o:p></span></pre>
 13 0. 0.  
 21 0. 0.  <pre
 23 0. 0. </pre>  style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
 </blockquote>  margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">12 0. 0. <o:p></o:p></span></pre>
 <ul>  
     <li>If mle=0 you must enter a covariance matrix (usually  <pre
         obtained from an earlier run).</li>  style="margin-top:0cm;margin-right:
   36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
   justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">13 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">21 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:
   36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
   justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">23 0. 0. <o:p></o:p></span></pre>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l11 level1 lfo21;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
           mle=0 you must enter a covariance matrix (usually
           obtained from an earlier run).<o:p></o:p></span></li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>  <h4
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariance
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  matrix of parameters</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
 used as an input to get the various output data files (Health  
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
   an input to get the various output data files (Health
 expectancies, stationary prevalence etc.) and figures without  expectancies, stationary prevalence etc.) and figures without
 rerunning the rather long maximisation phase (mle=0). </p>  rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each
   line starts with indices &quot;ijk&quot; followed by the
   covariances between aij and bij: <o:p></o:p></span></p>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span>121 Var(a12) <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;</span>122 Cov(b12,a12)<span style="mso-spacerun: yes">&nbsp; </span>Var(b12) <o:p></o:p></span></pre>
   
 <p>Each line starts with indices &quot;ijk&quot; followed by the  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>...<o:p></o:p></span></pre>
 covariances between aij and bij: </p>  
   
 <pre>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span>232 Cov(b23,a12)<span style="mso-spacerun: yes">&nbsp; </span>Cov(b23,b12) ... Var (b23) <o:p></o:p></span></pre>
    121 Var(a12)  
    122 Cov(b12,a12)  Var(b12)  <ul type="disc">
           ...      <li class="MsoNormal"
    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l18 level1 lfo24;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
           mle=1 you can enter zeros. <o:p></o:p></span></li>
   </ul>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
   36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Covariance matrix<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">121 0.<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:
   36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
   justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">122 0. 0.<o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">131 0. 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;
   margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
   text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">132 0. 0. 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">211 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;
   margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
   text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">212 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
   margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">231 0. 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
   
   <pre
   style="margin-top:
   0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:
   .0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">232 0. 0. 0. 0. 0. 0. 0. 0.<o:p></o:p></span></pre>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l7 level1 lfo27;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
           mle=0 you must enter a covariance matrix (usually
           obtained from an earlier run).<o:p></o:p></span></li>
   </ul>
   
 <ul>  <h4
     <li>If mle=1 you can enter zeros. </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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Age
   range for calculation of stationary prevalences and health
   expectancies</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
   we obtained the estimated parameters, the program is able to
   calculated stationary prevalence, transitions probabilities and
   life expectancies at any age. Choice of age range is useful for
   extrapolation. In our data file, ages varies from age 70 to 102.
   Setting bage=50 and fage=100, makes the program computing life
   expectancy from age bage to age fage. As we use a model, we can
   compute life expectancy on a wider age range than the age range
   from the data. But the model can be rather wrong on big
   intervals.<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Similarly,
   it is possible to get extrapolated stationary prevalence by age
   ranging from agemin to agemax. <o:p></o:p></span></p>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Minimum age for calculation of the stationary prevalence <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemax=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Maximum age for calculation of the stationary prevalence <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">bage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Minimum age for calculation of the health expectancies <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">fage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           Maximum age for calculation of the health expectancies <o:p></o:p></span></li>
 </ul>  </ul>
   
 <blockquote>  <h4
     <pre># Covariance matrix  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
 121 0.  name="Computing"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Computing</span><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB"></a> the observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
 122 0. 0.  
 131 0. 0. 0.  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=1/1/1984 end-prev-date=1/6/1988 <o:p></o:p></span></pre>
 132 0. 0. 0. 0.  
 211 0. 0. 0. 0. 0.  <p
 212 0. 0. 0. 0. 0. 0.  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Statements
 231 0. 0. 0. 0. 0. 0. 0.  'begin-prev-date' and 'end-prev-date' allow to select the period
 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>  in which we calculate the observed prevalences in each state. In
 </blockquote>  this example, the prevalences are calculated on data survey
   collected between 1 January 1984 and 1 June 1988. <o:p></o:p></span></p>
 <ul>  
     <li>If mle=0 you must enter a covariance matrix (usually  <ul type="disc">
         obtained from an earlier run).<br>      <li class="MsoNormal"
         </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>Starting date (day/month/year)<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">end-prev-date=
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>Final date (day/month/year)<o:p></o:p></span></li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Age range for calculation of stationary  <h4
 prevalences and health expectancies</font></h4>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Population-
   or status-based health expectancies</span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB"><o:p></o:p></span></h4>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pop_based=0<o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   user has the possibility to choose between population-based or
   status-based health expectancies. If pop_based=0 then
   status-based health expectancies are computed and if pop_based=1,
   the programme computes population-based health expectancies.
   Health expectancies are weighted averages of health expectancies
   respective of the initial state. For a status-based index, the
   weights are the cross-sectional prevalences observed between two
   dates, as </span><a href="#Computing"><span lang="EN-GB" style="mso-ansi-language:EN-GB">previously explained</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, whereas
   for a population-based index, the weights are the stationary
   prevalences.<o:p></o:p></span></p>
   
   <h4
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Prevalence
   forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 <o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Prevalence
   and population projections are available only if the
   interpolation unit is a month, i.e. stepm=1. The programme
   estimates the prevalence in each state at a precise date
   expressed in day/month/year. The programme computes one
   forecasted prevalence a year from a starting date (1 January of
   1989 in this example) to a final date (1 January 1992). The
   statement mov_average allows to compute smoothed forecasted
   prevalences with a five-age moving average centred at the mid-age
   of the five-age period. <o:p></o:p></span></p>
   
 <pre>agemin=70 agemax=100 bage=50 fage=100</pre>  <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
           starting date (day/month/year) of forecasting<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">final-proj-date=
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>final date (day/month/year) of forecasting<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">mov_average</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
           smoothing with a five-age moving average centred at the
           mid-age of the five-age period. The command<strong>
           mov_average</strong> takes value 1 if the prevalences are
           smoothed and 0 otherwise.<o:p></o:p></span></li>
   </ul>
   
 <p>Once we obtained the estimated parameters, the program is able  <h4
 to calculated stationary prevalence, transitions probabilities  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Last
 and life expectancies at any age. Choice of age range is useful  uncommented line : Population forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
 for extrapolation. In our data file, ages varies from age 70 to  
 102. Setting bage=50 and fage=100, makes the program computing  <pre><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992<o:p></o:p></span></pre>
 life expectancy from age bage to age fage. As we use a model, we  
 can compute life expectancy on a wider age range than the age  <p
 range from the data. But the model can be rather wrong on big  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
 intervals.</p>  command is available if the interpolation unit is a month, i.e.
   stepm=1 and if popforecast=1. From a data file including age and
 <p>Similarly, it is possible to get extrapolated stationary  number of persons alive at the precise date &#145;</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:&quot;Courier New&quot;;
 prevalence by age ranging from agemin to agemax. </p>  mso-ansi-language:EN-GB">popfiledate&#146;,
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">you can forecast the number of persons in each state until date</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:
 <ul>  12.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">
     <li><b>agemin=</b> Minimum age for calculation of the  &#145;last-popfiledate&#146;. </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, the popfile </span><a
         stationary prevalence </li>  href="pyram.txt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">pyram.txt</span><span style="mso-ansi-language:EN-GB"></b></a><b> </span><span lang="EN-GB" style="mso-ansi-language:
     <li><b>agemax=</b> Maximum age for calculation of the  EN-GB"><span style="mso-spacerun: yes"></b>&nbsp;</span>includes real
         stationary prevalence </li>  data which are the Japanese population in 1989.<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></p>
     <li><b>bage=</b> Minimum age for calculation of the health  
         expectancies </li>  <ul type="disc">
     <li><b>fage=</b> Maximum age for calculation of the health      <li class="MsoNormal"
         expectancies </li>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=
           0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for population forecasting. If
           popforecast=1, the programme does the forecasting<b>.<o:p></o:p></span></b></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfile=
   </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </b>name of the population file<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfiledate=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
           date of the population population<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">last-popfiledate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>=
           date of the last population projection&nbsp;<o:p></o:p></span></li>
 </ul>  </ul>
   
 <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font  <hr>
 color="#FF0000"> the observed prevalence</font></h4>  
   
 <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>  <h2
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
   name="running"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Running Imach with this example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">We
   assume that you entered your </span><a href="biaspar.imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">1st_example
   parameter file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> as explained </span><a href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">above</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. To
   run the program you should click on the imach.exe icon and enter
   the name of the parameter file which is for example </span><a
   href="..\mle\biaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle\biaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> (you
   also can click on the biaspar.txt icon located in </span><a
   href="..\mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and put it with the mouse on
   the imach window).<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   time to converge depends on the step unit that you used (1 month
   is cpu consuming), on the number of cases, and on the number of
   variables.<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   program outputs many files. Most of them are files which will be
   plotted for better understanding.<o:p></o:p></span></p>
   
   <hr>
   
 <p>Statements 'begin-prev-date' and 'end-prev-date' allow to  <h2
 select the period in which we calculate the observed prevalences  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
 in each state. In this example, the prevalences are calculated on  name="output"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Output of the program and graphs</span><span style="mso-bookmark:output"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
 data survey collected between 1 january 1984 and 1 june 1988. </p>  
   <p
 <ul>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
     <li><strong>begin-prev-date= </strong>Starting date  the optimization is finished, some graphics can be made with a
         (day/month/year)</li>  grapher. We use Gnuplot which is an interactive plotting program
     <li><strong>end-prev-date= </strong>Final date  copyrighted but freely distributed. A gnuplot reference manual is
         (day/month/year)</li>  available </span><a href="http://www.gnuplot.info/"><span lang="EN-GB" style="mso-ansi-language:EN-GB">here</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. <br>
   When the running is finished, the user should enter a character
   for plotting and output editing. <o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">These
   characters are:<o:p></o:p></span></p>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'c'
           to start again the program from the beginning.<o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'e'
           opens the </span><a href="biaspar.htm"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">biaspar.htm</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong></a>
           file to edit the output files and graphs. <o:p></o:p></span></li>
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'q'
           for exiting.<o:p></o:p></span></li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Population- or status-based health  <h5
 expectancies</font></h4>  style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:18.0pt;mso-bidi-font-size:10.0pt;color:#00006A;
   mso-ansi-language:EN-GB">Results
   files</span><strong><span lang="EN-GB" style="font-size:13.5pt;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong><br>
   <br>
   </span><strong><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;
   mso-ansi-language:EN-GB">- </strong><a name="Observed_prevalence_in_each_state"><strong>Observed
   prevalence in each state</strong></a><strong> (and at first pass)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>:
   </span><a href="prbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">prbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   first line is the title and displays each field of the file. The
   first column is age. The fields 2 and 6 are the proportion of
   individuals in states 1 and 2 respectively as observed during the
   first exam. Others fields are the numbers of people in states 1,
   2 or more. The number of columns increases if the number of
   states is higher than 2.<br>
   The header of the file is <o:p></o:p></span></p>
   
 <pre>pop_based=0</pre>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age Prev(1) N(1) N Age Prev(2) N(2) N<o:p></o:p></span></pre>
   
 <p>The user has the possibility to choose between  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 1.00000 631 631 70 0.00000 0 631<o:p></o:p></span></pre>
 population-based or status-based health expectancies. If  
 pop_based=0 then status-based health expectancies are computed  
 and if pop_based=1, the programme computes population-based  
 health expectancies. Health expectancies are weighted averages of  
 health expectancies respective of the initial state. For a  
 status-based index, the weights are the cross-sectional  
 prevalences observed between two dates, as <a href="#Computing">previously  
 explained</a>, whereas for a population-based index, the weights  
 are the stationary prevalences.</p>  
   
 <h4><font color="#FF0000">Prevalence forecasting </font></h4>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.99681 625 627 71 0.00319 2 627 <o:p></o:p></span></pre>
   
 <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.97125 1115 1148 72 0.02875 33 1148 <o:p></o:p></span></pre>
   
 <p>Prevalence and population projections are only available if  <p
 the interpolation unit is a month, i.e. stepm=1. The programme  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">It
 estimates the prevalence in each state at a precise date  means that at age 70, the prevalence in state 1 is 1.000 and in
 expressed in day/month/year. The programme computes one  state 2 is 0.00 . At age 71 the number of individuals in state 1
 forecasted prevalence a year from a starting date (1 january of  is 625 and in state 2 is 2, hence the total number of people aged
 1989 in this example) to a final date (1 january 1992). The  71 is 625+2=627. <o:p></o:p></span></p>
 statement mov_average allows to compute smoothed forecasted  
 prevalences with a five-age moving average centered at the  
 mid-age of the five-age period. </p>  
   
 <ul>  <h5
     <li><strong>starting-proj-date</strong>= starting date  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
         (day/month/year) of forecasting</li>  Estimated parameters and covariance matrix</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
     <li><strong>final-proj-date= </strong>final date  href="rbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
         (day/month/year) of forecasting</li>  
     <li><strong>mov_average</strong>= smoothing with a five-age  
         moving average centered at the mid-age of the five-age  
         period. The command<strong> mov_average</strong> takes  
         value 1 if the prevalences are smoothed and 0 otherwise.</li>  
 </ul>  
   
 <h4><font color="#FF0000">Last uncommented line : Population  <p
 forecasting </font></h4>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   file contains all the maximisation results: <o:p></o:p></span></p>
   
 <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>-2 log likelihood= 21660.918613445392<o:p></o:p></span></pre>
   
 <p>This command is available if the interpolation unit is a  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> Estimated parameters: a12 = -12.290174 b12 = 0.092161 <o:p></o:p></span></pre>
 month, i.e. stepm=1 and if popforecast=1. From a data file </p>  
   
 <p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span style="mso-spacerun: yes">&nbsp;</span>a13 = -9.155590<span style="mso-spacerun: yes">&nbsp; </span>b13 = 0.046627 <o:p></o:p></span></pre>
 : </b>age numbers</p>  
   
 <p>&nbsp;</p>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>a21 = -2.629849<span style="mso-spacerun: yes">&nbsp; </span>b21 = -0.022030 <o:p></o:p></span></pre>
   
 <hr>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>a23 = -7.958519<span style="mso-spacerun: yes">&nbsp; </span>b23 = 0.042614<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></pre>
   
 <h2><a name="running"></a><font color="#00006A">Running Imach  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>Covariance matrix: Var(a12) = 1.47453e-001<o:p></o:p></span></pre>
 with this example</font></h2>  
   
 <p>We assume that you entered your <a href="biaspar.imach">1st_example  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b12) = 2.18676e-005<o:p></o:p></span></pre>
 parameter file</a> as explained <a href="#biaspar">above</a>. To  
 run the program you should click on the imach.exe icon and enter  
 the name of the parameter file which is for example <a  
 href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>  
 (you also can click on the biaspar.txt icon located in <br>  
 <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with  
 the mouse on the imach window).<br>  
 </p>  
   
 <p>The time to converge depends on the step unit that you used (1  
 month is cpu consuming), on the number of cases, and on the  
 number of variables.</p>  
   
 <p>The program outputs many files. Most of them are files which  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(a13) = 2.09715e-001<o:p></o:p></span></pre>
 will be plotted for better understanding.</p>  
   
 <hr>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b13) = 3.28937e-005<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></pre>
   
 <h2><a name="output"><font color="#00006A">Output of the program  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>Var(a21) = 9.19832e-001<o:p></o:p></span></pre>
 and graphs</font> </a></h2>  
   
 <p>Once the optimization is finished, some graphics can be made  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b21) = 1.29229e-004<o:p></o:p></span></pre>
 with a grapher. We use Gnuplot which is an interactive plotting  
 program copyrighted but freely distributed. A gnuplot reference  
 manual is available <a href="http://www.gnuplot.info/">here</a>. <br>  
 When the running is finished, the user should enter a caracter  
 for plotting and output editing. </p>  
   
 <p>These caracters are:</p>  
   
 <ul>  
     <li>'c' to start again the program from the beginning.</li>  
     <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>  
         file to edit the output files and graphs. </li>  
     <li>'q' for exiting.</li>  
 </ul>  
   
 <h5><font size="4"><strong>Results files </strong></font><br>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="DE" style="mso-ansi-language:DE">Var(a23) = 4.48405e-001<o:p></o:p></span></pre>
 <br>  
 <font color="#EC5E5E" size="3"><strong>- </strong></font><a  <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b23) = 5.85631e-005 <o:p></o:p></span></pre>
 name="Observed prevalence in each state"><font color="#EC5E5E"  
 size="3"><strong>Observed prevalence in each state</strong></font></a><font  <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes">&nbsp;</span><o:p></o:p></span></pre>
 color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:  
 </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>  <p
 </h5>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">By
   substitution of these parameters in the regression model, we
 <p>The first line is the title and displays each field of the  obtain the elementary transition probabilities:<o:p></o:p></span></p>
 file. The first column is age. The fields 2 and 6 are the  
 proportion of individuals in states 1 and 2 respectively as  <p
 observed during the first exam. Others fields are the numbers of  style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><img
 people in states 1, 2 or more. The number of columns increases if  src="pebiaspar1.gif" width="400" height="300" id="_x0000_i1037"></p>
 the number of states is higher than 2.<br>  
 The header of the file is </p>  <h5
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  Transition probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="pijrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
 70 1.00000 631 631 70 0.00000 0 631  EN-GB">pijrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
 71 0.99681 625 627 71 0.00319 2 627  EN-GB"><o:p></o:p></span></a></h5>
 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>  
   <p
 <p>It means that at age 70, the prevalence in state 1 is 1.000  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Here
 and in state 2 is 0.00 . At age 71 the number of individuals in  are the transitions probabilities Pij(x, x+nh) where nh is a
 state 1 is 625 and in state 2 is 2, hence the total number of  multiple of 2 years. The first column is the starting age x (from
 people aged 71 is 625+2=627. <br>  age 50 to 100), the second is age (x+nh) and the others are the
 </p>  transition probabilities p11, p12, p13, p21, p22, p23. For
   example, line 5 of the file is: <o:p></o:p></span></p>
 <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and  
 covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 <o:p></o:p></span></pre>
   
 <p>This file contains all the maximisation results: </p>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">and
 <pre> -2 log likelihood= 21660.918613445392  this means: <o:p></o:p></span></p>
  Estimated parameters: a12 = -12.290174 b12 = 0.092161  
                        a13 = -9.155590  b13 = 0.046627  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p11(100,106)=0.02655<o:p></o:p></span></pre>
                        a21 = -2.629849  b21 = -0.022030  
                        a23 = -7.958519  b23 = 0.042614    
  Covariance matrix: Var(a12) = 1.47453e-001  
                     Var(b12) = 2.18676e-005  
                     Var(a13) = 2.09715e-001  
                     Var(b13) = 3.28937e-005    
                     Var(a21) = 9.19832e-001  
                     Var(b21) = 1.29229e-004  
                     Var(a23) = 4.48405e-001  
                     Var(b23) = 5.85631e-005  
  </pre>  
   
 <p>By substitution of these parameters in the regression model,  
 we obtain the elementary transition probabilities:</p>  
   
 <p><img src="pebiaspar1.gif" width="400" height="300"></p>  
   
 <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:  
 </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>  
   
 <p>Here are the transitions probabilities Pij(x, x+nh) where nh  
 is a multiple of 2 years. The first column is the starting age x  
 (from age 50 to 100), the second is age (x+nh) and the others are  
 the transition probabilities p11, p12, p13, p21, p22, p23. For  
 example, line 5 of the file is: </p>  
   
 <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>  
   
 <p>and this means: </p>  
   
 <pre>p11(100,106)=0.02655  
 p12(100,106)=0.17622  
 p13(100,106)=0.79722  
 p21(100,106)=0.01809  
 p22(100,106)=0.13678  
 p22(100,106)=0.84513 </pre>  
   
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  
 name="Stationary prevalence in each state"><font color="#EC5E5E"  
 size="3"><b>Stationary prevalence in each state</b></font></a><b>:  
 </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>  
   
 <pre>#Prevalence  
 #Age 1-1 2-2  
   
 #************  
 70 0.90134 0.09866  
 71 0.89177 0.10823  
 72 0.88139 0.11861  
 73 0.87015 0.12985 </pre>  
   
 <p>At age 70 the stationary prevalence is 0.90134 in state 1 and  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p12(100,106)=0.17622<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p13(100,106)=0.79722<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p21(100,106)=0.01809<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.13678<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.84513 <o:p></o:p></span></pre>
   
   <h5
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
   <a name="Stationary_prevalence_in_each_state">Stationary
   prevalence in each state</span><span style="mso-bookmark:Stationary_prevalence_in_each_state"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>: </span><a href="plrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">plrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Prevalence<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Age 1-1 2-2<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#************ <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 0.90134 0.09866<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.89177 0.10823 <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.88139 0.11861 <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.87015 0.12985 <o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">At
   age 70 the stationary prevalence is 0.90134 in state 1 and
 0.09866 in state 2. This stationary prevalence differs from  0.09866 in state 2. This stationary prevalence differs from
 observed prevalence. Here is the point. The observed prevalence  observed prevalence. Here is the point. The observed prevalence
 at age 70 results from the incidence of disability, incidence of  at age 70 results from the incidence of disability, incidence of
Line 718  future if &quot;nothing changes in the f Line 1507  future if &quot;nothing changes in the f
 exactly what demographers do with a Life table. Life expectancy  exactly what demographers do with a Life table. Life expectancy
 is the expected mean time to survive if observed mortality rates  is the expected mean time to survive if observed mortality rates
 (incidence of mortality) &quot;remains constant&quot; in the  (incidence of mortality) &quot;remains constant&quot; in the
 future. </p>  future. <o:p></o:p></span></p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of  <h5
 stationary prevalence</b></font><b>: </b><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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
 href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>  Standard deviation of stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
   href="vplrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vplrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
 <p>The stationary prevalence has to be compared with the observed  
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
   stationary prevalence has to be compared with the observed
 prevalence by age. But both are statistical estimates and  prevalence by age. But both are statistical estimates and
 subjected to stochastic errors due to the size of the sample, the  subjected to stochastic errors due to the size of the sample, the
 design of the survey, and, for the stationary prevalence to the  design of the survey, and, for the stationary prevalence to the
 model used and fitted. It is possible to compute the standard  model used and fitted. It is possible to compute the standard
 deviation of the stationary prevalence at each age.</p>  deviation of the stationary prevalence at each age.<o:p></o:p></span></p>
   
 <h5><font color="#EC5E5E" size="3">-Observed and stationary  
 prevalence in state (2=disable) with the confident interval</font>:<b>  
 </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>  
   
 <p>This graph exhibits the stationary prevalence in state (2)  
 with the confidence interval in red. The green curve is the  
 observed prevalence (or proportion of individuals in state (2)).  
 Without discussing the results (it is not the purpose here), we  
 observe that the green curve is rather below the stationary  
 prevalence. It suggests an increase of the disability prevalence  
 in the future.</p>  
   
 <p><img src="vbiaspar21.gif" width="400" height="300"></p>  
   
 <h5><font color="#EC5E5E" size="3"><b>-Convergence to the  
 stationary prevalence of disability</b></font><b>: </b><a  
 href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>  
 <img src="pbiaspar11.gif" width="400" height="300"> </h5>  
   
 <p>This graph plots the conditional transition probabilities from  <h5
 an initial state (1=healthy in red at the bottom, or 2=disable in  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Observed
   and stationary prevalence in state (2=disable) with the confident
   interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="vbiaspar21.htm"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vbiaspar21.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   graph exhibits the stationary prevalence in state (2) with the
   confidence interval in red. The green curve is the observed
   prevalence (or proportion of individuals in state (2)). Without
   discussing the results (it is not the purpose here), we observe
   that the green curve is rather below the stationary prevalence.
   It suggests an increase of the disability prevalence in the
   future.<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><img
   src="vbiaspar21.gif" width="400" height="300" id="_x0000_i1038"></p>
   
   <h5
   style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Convergence
   to the stationary prevalence of disability</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
   href="pbiaspar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pbiaspar11.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
   </span><img src="pbiaspar11.gif" width="400" height="300"
   id="_x0000_i1039"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h5>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   graph plots the conditional transition probabilities from an
   initial state (1=healthy in red at the bottom, or 2=disable in
 green on top) at age <em>x </em>to the final state 2=disable<em> </em>at  green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
 age <em>x+h. </em>Conditional means at the condition to be alive  age <em>x+h. </em>Conditional means at the condition to be alive
 at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The  at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
Line 762  prevalence at age 70 we should start the Line 1563  prevalence at age 70 we should start the
 age, i.e.50. If the disability state is defined by severe  age, i.e.50. If the disability state is defined by severe
 disability criteria with only a few chance to recover, then the  disability criteria with only a few chance to recover, then the
 incidence of recovery is low and the time to convergence is  incidence of recovery is low and the time to convergence is
 probably longer. But we don't have experience yet.</p>  probably longer. But we don't have experience yet.<o:p></o:p></span></p>
   
   <h5
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
   Life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
   href="erbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">erbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Health expectancies <o:p></o:p></span></pre>
   
 <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age 1-1 1-2 2-1 2-2 <o:p></o:p></span></pre>
 and initial health status</b></font><b>: </b><a  
 href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>  
   
 <pre># Health expectancies  
 # Age 1-1 1-2 2-1 2-2  
 70 10.9226 3.0401 5.6488 6.2122  
 71 10.4384 3.0461 5.2477 6.1599  
 72 9.9667 3.0502 4.8663 6.1025  
 73 9.5077 3.0524 4.5044 6.0401 </pre>  
   
 <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 10.9226 3.0401 5.6488 6.2122 <o:p></o:p></span></pre>
 e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>  
   
 <pre><img src="expbiaspar21.gif" width="400" height="300"><img  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 10.4384 3.0461 5.2477 6.1599 <o:p></o:p></span></pre>
 src="expbiaspar11.gif" width="400" height="300"></pre>  
   
 <p>For example, life expectancy of a healthy individual at age 70  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 9.9667 3.0502 4.8663 6.1025 <o:p></o:p></span></pre>
 is 10.92 in the healthy state and 3.04 in the disability state  
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 9.5077 3.0524 4.5044 6.0401 <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For example 70 10.9226 3.0401 5.6488 6.2122 means:<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE">e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122<o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><img src="expbiaspar21.gif"
   width="400" height="300" id="_x0000_i1040"><img
   src="expbiaspar11.gif" width="400" height="300" id="_x0000_i1041"></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
   example, life expectancy of a healthy individual at age 70 is
   10.92 in the healthy state and 3.04 in the disability state
 (=13.96 years). If he was disable at age 70, his life expectancy  (=13.96 years). If he was disable at age 70, his life expectancy
 will be shorter, 5.64 in the healthy state and 6.21 in the  will be shorter, 5.64 in the healthy state and 6.21 in the
 disability state (=11.85 years). The total life expectancy is a  disability state (=11.85 years). The total life expectancy is a
 weighted mean of both, 13.96 and 11.85; weight is the proportion  weighted mean of both, 13.96 and 11.85; weight is the proportion
 of people disabled at age 70. In order to get a pure period index  of people disabled at age 70. In order to get a pure period index
 (i.e. based only on incidences) we use the <a  (i.e. based only on incidences) we use the </span><a
 href="#Stationary prevalence in each state">computed or  href="#Stationary prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:EN-GB">computed or
 stationary prevalence</a> at age 70 (i.e. computed from  stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> at age 70 (i.e. computed from
 incidences at earlier ages) instead of the <a  incidences at earlier ages) instead of the </span><a
 href="#Observed prevalence in each state">observed prevalence</a>  href="#Observed prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:
 (for example at first exam) (<a href="#Health expectancies">see  EN-GB">observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:
 below</a>).</p>  EN-GB"></a>
   (for example at first exam) (</span><a href="#Health expectancies"><span lang="EN-GB" style="mso-ansi-language:EN-GB">see
 <h5><font color="#EC5E5E" size="3"><b>- Variances of life  below</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>).<o:p></o:p></span></p>
 expectancies by age and initial health status</b></font><b>: </b><a  
 href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>  <h5
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
 <p>For example, the covariances of life expectancies Cov(ei,ej)  Variances of life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
 at age 50 are (line 3) </p>  href="vrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
 <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</pre>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  example, the covariances of life expectancies Cov(ei,ej) at age
 name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health  50 are (line 3) <o:p></o:p></span></p>
 expectancies</b></font></a><font color="#EC5E5E" size="3"><b>  
 with standard errors in parentheses</b></font><b>: </b><a  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span></span><span lang="DE" style="mso-ansi-language:DE">Cov(e1,e1)=0.4776<span style="mso-spacerun: yes">&nbsp; </span>Cov(e1,e2)=0.0488=Cov(e2,e1)<span style="mso-spacerun: yes">&nbsp; </span>Cov(e2,e2)=0.0424<o:p></o:p></span></pre>
 href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>  
   <h5
 <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
   <a name="Health_expectancies">Health expectancies</a> with
 <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>  standard errors in parentheses</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="trbiaspar.txt"><span lang="EN-GB" style="font-family:&quot;Courier New&quot;;
   mso-ansi-language:EN-GB">trbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
 <p>Thus, at age 70 the total life expectancy, e..=13.76years is  
 the weighted mean of e1.=13.96 and e2.=11.85 by the stationary  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) <o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Thus,
   at age 70 the total life expectancy, e..=13.76years is the
   weighted mean of e1.=13.96 and e2.=11.85 by the stationary
 prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in  prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
 state 2, respectively (the sum is equal to one). e.1=10.40 is the  state 2, respectively (the sum is equal to one). e.1=10.40 is the
 Disability-free life expectancy at age 70 (it is again a weighted  Disability-free life expectancy at age 70 (it is again a weighted
 mean of e11 and e21). e.2=3.35 is also the life expectancy at age  mean of e11 and e21). e.2=3.35 is also the life expectancy at age
 70 to be spent in the disability state.</p>  70 to be spent in the disability state.<o:p></o:p></span></p>
   
 <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by  <h5
 age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Total
 </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>  life expectancy by age and health expectancies in states
   (1=healthy) and (2=disable)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="ebiaspar1.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ebiaspar1.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
 <p>This figure represents the health expectancies and the total  
 life expectancy with the confident interval in dashed curve. </p>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
 <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>  figure represents the health expectancies and the total life
   expectancy with the confident interval in dashed curve. <o:p></o:p></span></p>
 <p>Standard deviations (obtained from the information matrix of  
 the model) of these quantities are very useful.  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><img
 Cross-longitudinal surveys are costly and do not involve huge  src="ebiaspar1.gif" width="400" height="300" id="_x0000_i1042"></pre>
 samples, generally a few thousands; therefore it is very  
 important to have an idea of the standard deviation of our  <p
 estimates. It has been a big challenge to compute the Health  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Standard
 Expectancy standard deviations. Don't be confuse: life expectancy  deviations (obtained from the information matrix of the model) of
 is, as any expected value, the mean of a distribution; but here  these quantities are very useful. Cross-longitudinal surveys are
 we are not computing the standard deviation of the distribution,  costly and do not involve huge samples, generally a few
 but the standard deviation of the estimate of the mean.</p>  thousands; therefore it is very important to have an idea of the
   standard deviation of our estimates. It has been a big challenge
 <p>Our health expectancies estimates vary according to the sample  to compute the Health Expectancy standard deviations. Don't be
 size (and the standard deviations give confidence intervals of  confuse: life expectancy is, as any expected value, the mean of a
 the estimate) but also according to the model fitted. Let us  distribution; but here we are not computing the standard
 explain it in more details.</p>  deviation of the distribution, but the standard deviation of the
   estimate of the mean.<o:p></o:p></span></p>
 <p>Choosing a model means ar least two kind of choices. First we  
 have to decide the number of disability states. Second we have to  <p
 design, within the logit model family, the model: variables,  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Our
 covariables, confonding factors etc. to be included.</p>  health expectancies estimates vary according to the sample size
   (and the standard deviations give confidence intervals of the
 <p>More disability states we have, better is our demographical  estimate) but also according to the model fitted. Let us explain
 approach of the disability process, but smaller are the number of  it in more details.<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Choosing
   a model means at least two kind of choices. First we have to
   decide the number of disability states. Second we have to design,
   within the logit model family, the model: variables, covariables,
   confounding factors etc. to be included.<o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">More
   disability states we have, better is our demographical approach
   of the disability process, but smaller are the number of
 transitions between each state and higher is the noise in the  transitions between each state and higher is the noise in the
 measurement. We do not have enough experiments of the various  measurement. We do not have enough experiments of the various
 models to summarize the advantages and disadvantages, but it is  models to summarize the advantages and disadvantages, but it is
Line 877  population. Our main purpose is not to m Line 1707  population. Our main purpose is not to m
 mortality but to measure the expected time in a healthy or  mortality but to measure the expected time in a healthy or
 disability state in order to maximise the former and minimize the  disability state in order to maximise the former and minimize the
 latter. But the differential in mortality complexifies the  latter. But the differential in mortality complexifies the
 measurement.</p>  measurement.<o:p></o:p></span></p>
   
 <p>Incidences of disability or recovery are not affected by the  <p
 number of states if these states are independant. But incidences  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Incidences
 estimates are dependant on the specification of the model. More  of disability or recovery are not affected by the number of
 covariates we added in the logit model better is the model, but  states if these states are independant. But incidences estimates
 some covariates are not well measured, some are confounding  are dependant on the specification of the model. More covariates
 factors like in any statistical model. The procedure to &quot;fit  we added in the logit model better is the model, but some
 the best model' is similar to logistic regression which itself is  covariates are not well measured, some are confounding factors
 similar to regression analysis. We haven't yet been sofar because  like in any statistical model. The procedure to &quot;fit the
 we also have a severe limitation which is the speed of the  best model' is similar to logistic regression which itself is
 convergence. On a Pentium III, 500 MHz, even the simplest model,  similar to regression analysis. We haven't yet been so far
 estimated by month on 8,000 people may take 4 hours to converge.  because we also have a severe limitation which is the speed of
 Also, the program is not yet a statistical package, which permits  the convergence. On a Pentium III, 500 MHz, even the simplest
 a simple writing of the variables and the model to take into  model, estimated by month on 8,000 people may take 4 hours to
 account in the maximisation. The actual program allows only to  converge. Also, the program is not yet a statistical package,
 add simple variables like age+sex or age+sex+ age*sex but will  which permits a simple writing of the variables and the model to
 never be general enough. But what is to remember, is that  take into account in the maximisation. The actual program allows
   only to add simple variables like age+sex or age+sex+ age*sex but
   will never be general enough. But what is to remember, is that
 incidences or probability of change from one state to another is  incidences or probability of change from one state to another is
 affected by the variables specified into the model.</p>  affected by the variables specified into the model.<o:p></o:p></span></p>
   
 <p>Also, the age range of the people interviewed has a link with  <p
 the age range of the life expectancy which can be estimated by  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Also,
   the age range of the people interviewed has a link with the age
   range of the life expectancy which can be estimated by
 extrapolation. If your sample ranges from age 70 to 95, you can  extrapolation. If your sample ranges from age 70 to 95, you can
 clearly estimate a life expectancy at age 70 and trust your  clearly estimate a life expectancy at age 70 and trust your
 confidence interval which is mostly based on your sample size,  confidence interval which is mostly based on your sample size,
 but if you want to estimate the life expectancy at age 50, you  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  should rely in your model, but fitting a logistic model on a age
 range of 70-95 and estimating probabilties of transition out of  range of 70-95 and estimating probabilities of transition out of
 this age range, say at age 50 is very dangerous. At least you  this age range, say at age 50 is very dangerous. At least you
 should remember that the confidence interval given by the  should remember that the confidence interval given by the
 standard deviation of the health expectancies, are under the  standard deviation of the health expectancies, are under the
 strong assumption that your model is the 'true model', which is  strong assumption that your model is the 'true model', which is
 probably not the case.</p>  probably not the case.<o:p></o:p></span></p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter  <h5
 file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
   Copy of the parameter file</span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">: </span><a href="orbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">orbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
 <p>This copy of the parameter file can be useful to re-run the  <p
 program while saving the old output files. </p>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   copy of the parameter file can be useful to re-run the program
   while saving the old output files. <o:p></o:p></span></p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:  <h5
 </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
   Prevalence forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="frbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
   
 <p>On a d'abord estimé la date moyenne des interviaew. ie  <p
 13/9/1995. This file contains </p>  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First,
   we have estimated the observed prevalence between 1/1/1984 and
   1/6/1988. <span style="mso-spacerun:
   yes">&nbsp;</span>The mean date of interview (weighed average of
   the interviews performed between1/1/1984 and 1/6/1988) is
   estimated to be 13/9/1985, as written on the top on the file.
   Then we forecast the probability to be in each state. <o:p></o:p></span></p>
   
 <p>Example, at date 1/1/1989 : </p>  <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Example,
   at date 1/1/1989 : <o:p></o:p></span></p>
   
 <p>73 0.807 0.078 0.115 </p>  <p class="MsoNormal"><span lang="DE" style="mso-ansi-language:DE"># StartingAge FinalAge P.1 P.2 P.3<o:p></o:p></span></p>
   
 <p>This means that at age 73, the probability for a person age 70  <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></p>
 at 13/9/1989 to be in state 1 is 0.807, in state 2 is 0.078 and  
 to die is 0.115 at 1/1/1989.</p>  
   
 <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:  <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.807 0.078 0.115 <o:p></o:p></span></p>
 </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>  
   
 <pre># Age P.1 P.2 P.3 [Population]  <p
 # Forecasting at date 1/1/1989  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
 75 572685.22 83798.08  the minimum age is 70 on the 13/9/1985, the youngest forecasted
 74 621296.51 79767.99  age is 73. This means that at age a person aged 70 at 13/9/1989
 73 645857.70 69320.60 </pre>  has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
   Similarly, the probability to be in state 2 is 0.078 and the
   probability to die is 0.115. Then, on the 1/1/1989, the
   prevalence of disability at age 73 is estimated to be 0.088.<o:p></o:p></span></p>
   
 <pre># Forecasting at date 1/1/19909  <h5
 76 442986.68 92721.14 120775.48  style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
 75 487781.02 91367.97 121915.51  Population forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="poprbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
 74 512892.07 85003.47 117282.76 </pre>  EN-GB">poprbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB"><o:p></o:p></span></a></h5>
   
 <hr>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age P.1 P.2 P.3 [Population]<o:p></o:p></span></pre>
   
 <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></pre>
   
 <p>Since you know how to run the program, it is time to test it  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">75 572685.22 83798.08 <o:p></o:p></span></pre>
 on your own computer. Try for example on a parameter file named <a  
 href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font  
 size="2" face="Courier New">mypar.txt</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  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">74 621296.51 79767.99 <o:p></o:p></span></pre>
 question:'<strong>Enter the parameter file name:'</strong></p>  
   
 <table border="1">  <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 645857.70 69320.60 <o:p></o:p></span></pre>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1990<o:p></o:p></span></pre>
   
   <pre style="text-align:justify">76 442986.68 92721.14 120775.48</pre>
   
   <pre style="text-align:justify">75 487781.02 91367.97 121915.51</pre>
   
   <pre style="text-align:justify">74 512892.07 85003.47 117282.76 </pre>
   
   <pre style="text-align:justify">&nbsp;<o:p></o:p></pre>
   
   <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">From the population file, we estimate the
   number of people in each state. At age 73, 645857 persons are in
   state 1 and 69320 are in state 2. One year latter, 512892 are
   still in state 1, 85003 are in state 2 and 117282 died before
   1/1/1990.<o:p></o:p></span></p>
   
   <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <hr>
   
   <h2
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a
   name="example"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Trying an example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
   you know how to run the program, it is time to test it on your
   own computer. Try for example on a parameter file named </span><a
   href="..\mytry\imachpar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> which is a copy of </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">
   included in the subdirectory of imach, </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;
   mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:
   EN-GB">. Edit it to change
   the name of the data file to </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:
   EN-GB">..\data\mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> if you don't want
   to copy it on the same directory. The file </span><span lang="EN-GB" style="font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> is a
   smaller file of 3,000 people but still with 4 waves. <o:p></o:p></span></p>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Click
   on the imach.exe icon to open a window. Answer to the question: '<strong>Enter
   the parameter file name:'<o:p></o:p></span></strong></p>
   
   <table border="1" cellpadding="0"
   style="mso-cellspacing:1.5pt;mso-padding-alt:
    0cm 0cm 0cm 0cm">
     <tr>      <tr>
         <td width="100%"><strong>IMACH, Version 0.7</strong><p><strong>Enter          <td width="100%"
         the parameter file name: ..\mytry\imachpar.txt</strong></p>          style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">IMACH,
           Version 0.7</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong><p style="text-align:justify"><strong><span lang="EN-GB" style="mso-ansi-language:
     EN-GB">Enter
           the parameter file name: ..\mytry\imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
         </td>          </td>
     </tr>      </tr>
 </table>  </table>
   
 <p>Most of the data files or image files generated, will use the  <p
   style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Most
   of the data files or image files generated, will use the
 'imachpar' string into their name. The running time is about 2-3  'imachpar' string into their name. The running time is about 2-3
 minutes on a Pentium III. If the execution worked correctly, the  minutes on a Pentium III. If the execution worked correctly, the
 outputs files are created in the current directory, and should be  outputs files are created in the current directory, and should be
 the same as the mypar files initially included in the directory <font  the same as the mypar files initially included in the directory </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">.<o:p></o:p></span></p>
 size="2" face="Courier New">mytry</font>.</p>  
   
 <ul>  <pre
     <li><pre><u>Output on the screen</u> The output screen looks like <a  style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l5 level1 lfo43"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output on the screen</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> The output screen looks like </span><a
 href="imachrun.LOG">this Log file</a>  href="imachrun.LOG"><span lang="EN-GB" style="mso-ansi-language:EN-GB">this Log file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></pre>
 #  
   
 title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
 ftol=1.000000e-008 stepm=24 ncov=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  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3<o:p></o:p></span></pre>
 Warning, no any valid information for:2307 line=2307  
 Delay (in months) between two waves Min=21 Max=51 Mean=24.495826  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
 <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  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92<o:p></o:p></span></pre>
  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>  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
     </li>  
 </ul>  <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:126 line=126<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:2307 line=2307<o:p></o:p></span></pre>
   
 <p>&nbsp;</p>  <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Delay (in months) between two waves Min=21 Max=51 Mean=24.495826<o:p></o:p></span></pre>
   
 <ul>  <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-GB">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></pre>
     <li>Maximisation with the Powell algorithm. 8 directions are  
         given corresponding to the 8 parameters. this can be  <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14<o:p></o:p></span></pre>
         rather long to get convergence.<br>  
         <font size="1" face="Courier New"><br>  <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 <o:p></o:p></span></pre>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l6 level1 lfo46;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Maximisation
           with the Powell algorithm. 8 directions are given
           corresponding to the 8 parameters. This can be rather
           long to get convergence.<br>
   </span><span lang="EN-GB" style="font-size:7.5pt;font-family:&quot;Courier New&quot;;
        mso-ansi-language:EN-GB">        <br>
         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2          Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
         0.000000000000 3<br>          0.000000000000 3<br>
         0.000000000000 4 0.000000000000 5 0.000000000000 6          0.000000000000 4 0.000000000000 5 0.000000000000 6
Line 1025  Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]= Line 1925  Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=
         12 -12.966061 0.135117 <br>          12 -12.966061 0.135117 <br>
         13 -7.401109 0.067831 <br>          13 -7.401109 0.067831 <br>
         21 -0.672648 -0.006627 <br>          21 -0.672648 -0.006627 <br>
         23 -5.051297 0.051271 </font><br>          23 -5.051297 0.051271 </span><span lang="EN-GB" style="mso-ansi-language:
         </li>       EN-GB"><o:p></o:p></span></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>  </ul>
   
 <p><font size="3">Once the running is finished, the program  <pre
 requires a caracter:</font></p>  style="margin-left:36.0pt;text-align:justify;text-indent:-18.0pt;
   mso-list:l6 level1 lfo46"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB">Calculation of the hessian matrix. Wait...<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Inverting the hessian to get the covariance matrix. </span>Wait...</pre>
   
   <pre style="margin-left:18.0pt;text-align:justify">&nbsp;<o:p></o:p></pre>
   
 <table border="1">  <pre style="margin-left:18.0pt;text-align:justify">#Hessian matrix#</pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"># Scales<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:
   justify"><span lang="DE" style="mso-ansi-language:DE">12 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE">13 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
   
   <pre style="margin-left:
   18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE">21 1.00000e-003 1.00000e-005<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE">23 1.00000e-004 1.00000e-005<o:p></o:p></span></pre>
   
   <pre style="margin-left:
   18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE"># Covariance<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>1 5.90661e-001<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>2 -7.26732e-003 8.98810e-005<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>3 8.80177e-002 -1.12706e-003 5.15824e-001<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
   DE"><span style="mso-spacerun: yes">&nbsp; </span>8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing prevalence limit: result on file 'plrmypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing pij: result on file 'pijrmypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Health Expectancies: result on file 'ermypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of DFLEs: file 'vrmypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Total LEs with variances: file 'trmypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' <o:p></o:p></span></pre>
   
   <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">End of Imach<o:p></o:p></span></pre>
   
   <p
   style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
   the running is finished, the program requires a caracter:<o:p></o:p></span></p>
   
   <table border="1" cellpadding="0"
   style="mso-cellspacing:1.5pt;mso-padding-alt:
    0cm 0cm 0cm 0cm">
     <tr>      <tr>
         <td width="100%"><strong>Type e to edit output files, c          <td width="100%"
         to start again, and q for exiting:</strong></td>          style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Type
           e to edit output files, c to start again, and q for
           exiting:</span><span lang="EN-GB" style="mso-ansi-language:
     EN-GB"><o:p></o:p></span></strong></td>
     </tr>      </tr>
 </table>  </table>
   
 <p><font size="3">First you should enter <strong>e </strong>to  <p
 edit the master file mypar.htm. </font></p>  style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
   you should enter <strong>e </strong>to edit the master file
 <ul>  mypar.htm. <o:p></o:p></span></p>
     <li><u>Outputs files</u> <br>  
   <ul type="disc">
       <li class="MsoNormal"
       style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Outputs
           files</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> <br>
         <br>          <br>
         - Observed prevalence in each state: <a          - Observed prevalence in each state: </span><a
         href="..\mytry\prmypar.txt">pmypar.txt</a> <br>          href="..\mytry\prmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
         - Estimated parameters and the covariance matrix: <a          - Estimated parameters and the covariance matrix: </span><a
         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>          href="..\mytry\rmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
         - Stationary prevalence in each state: <a          - Stationary prevalence in each state: </span><a
         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>          href="..\mytry\plrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
         - Transition probabilities: <a       EN-GB">plrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
         href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>       EN-GB"></a> <br>
         - Copy of the parameter file: <a          - Transition probabilities: </span><a
         href="..\mytry\ormypar.txt">ormypar.txt</a> <br>          href="..\mytry\pijrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pijrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
         - Life expectancies by age and initial health status: <a          - Copy of the parameter file: </span><a
         href="..\mytry\ermypar.txt">ermypar.txt</a> <br>          href="..\mytry\ormypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ormypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
           - Life expectancies by age and initial health status: </span><a
           href="..\mytry\ermypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        EN-GB">ermypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a> <br>
         - Variances of life expectancies by age and initial          - Variances of life expectancies by age and initial
         health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>          health status: </span><a href="..\mytry\vrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        EN-GB">vrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a>
           <br>
           - Health expectancies with their variances: </span><a
           href="..\mytry\trmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        EN-GB">trmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a> <br>
           - Standard deviation of stationary prevalence: </span><a
           href="..\mytry\vplrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        EN-GB">vplrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a><br>
           - Prevalences forecasting: </span><a href="frmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
         <br>          <br>
         - Health expectancies with their variances: <a          - Population forecasting (if popforecast=1): </span><a
         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>          href="poprmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">poprmypar.txt</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
         - Standard deviation of stationary prevalence: <a      <li class="MsoNormal"
         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>      style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
         - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>       mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Graphs</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u>
         <br>          <br>
         - Population forecasting (if popforecast=1): <a  
         href="poprmypar.txt">poprmypar.txt</a> <br>  
         </li>  
     <li><u>Graphs</u> <br>  
         <br>          <br>
         -<a href="../mytry/pemypar1.gif">One-step transition          -</span><a href="..\mytry\pemypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
         probabilities</a><br>       EN-GB">One-step transition
         -<a href="../mytry/pmypar11.gif">Convergence to the          probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
         stationary prevalence</a><br>          -</span><a href="..\mytry\pmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
         -<a href="..\mytry\vmypar11.gif">Observed and stationary       EN-GB">Convergence to the
         prevalence in state (1) with the confident interval</a> <br>          stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
         -<a href="..\mytry\vmypar21.gif">Observed and stationary          -</span><a href="..\mytry\vmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
         prevalence in state (2) with the confident interval</a> <br>       EN-GB">Observed and stationary
         -<a href="..\mytry\expmypar11.gif">Health life          prevalence in state (1) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
         expectancies by age and initial health state (1)</a> <br>          -</span><a href="..\mytry\vmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:
         -<a href="..\mytry\expmypar21.gif">Health life       EN-GB">Observed and stationary
         expectancies by age and initial health state (2)</a> <br>          prevalence in state (2) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
         -<a href="..\mytry\emypar1.gif">Total life expectancy by          -</span><a href="..\mytry\expmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
         age and health expectancies in states (1) and (2).</a> </li>          expectancies by age and initial health state (1)</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a> <br>
           -</span><a href="..\mytry\expmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
           expectancies by age and initial health state (2)</span><span lang="EN-GB" style="mso-ansi-language:
        EN-GB"></a> <br>
           -</span><a href="..\mytry\emypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
        EN-GB">Total life expectancy by
           age and health expectancies in states (1) and (2).</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
 </ul>  </ul>
   
 <p>This software have been partly granted by <a  <p
 href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted  style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
   software have been partly granted by </span><a
   href="http://euroreves.ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Euro-REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, a concerted
 action from the European Union. It will be copyrighted  action from the European Union. It will be copyrighted
 identically to a GNU software product, i.e. program and software  identically to a GNU software product, i.e. program and software
 can be distributed freely for non commercial use. Sources are not  can be distributed freely for non commercial use. Sources are not
 widely distributed today. You can get them by asking us with a  widely distributed today. You can get them by asking us with a
 simple justification (name, email, institute) <a  simple justification (name, email, institute) </span><a
 href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a  href="mailto:brouard@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:brouard@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and </span><a
 href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>  href="mailto:lievre@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:lievre@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> .<o:p></o:p></span></p>
   
 <p>Latest version (0.7 of February 2002) can be accessed at <a  <p
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>  style="tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Latest
 </p>  version (0.7 of February 2002) can be accessed at </span><a
   href="http://euroreves.ined.fr/imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">http://euroreves.ined.fr/imach</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></p>
 </body>  </body>
 </html>  </html>
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