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 style="tab-interval:35.4pt">  
   
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 <h1 align="center" style="text-align:center"><span lang="EN-GB" style="color:#00006A;  <h1 align="center"><font color="#00006A">Computing Health
 mso-ansi-language:EN-GB">Computing Health  Expectancies using IMaCh</font></h1>
 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>  
   
 <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>)  <h1 align="center"><font color="#00006A" size="5">(a Maximum
 </span></h4>  Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
   
   <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:  
 &quot;Times New Roman&quot;;mso-ansi-language:FR;mso-fareast-language:FR;mso-bidi-language:  <ul>
 AR-SA">      <li><a href="#intro">Introduction</a> </li>
 <ul type="disc">      <li>The detailed statistical model (<a href="docmath.pdf">PDF
     <li class="MsoNormal"          version</a>),(<a href="docmath.ps">ps version</a>) </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><a href="#data">On what kind of data can it be used?</a></li>
      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a      <li><a href="#datafile">The data 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="#biaspar">The parameter file</a> </li>
     <li class="MsoNormal"      <li><a href="#running">Running Imach</a> </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><a href="#output">Output files and graphs</a> </li>
      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a      <li><a href="#example">Exemple</a> </li>
         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"><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:  <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
 EN-GB"><o:p></o:p></span></a></h2>  
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This program computes <b>Healthy  <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
 Life Expectancies</b> from <b>cross-longitudinal data</b> using  data</b> using the methodology pioneered by Laditka and Wolf (1).
 the methodology pioneered by Laditka and Wolf (1). Within the  Within the family of Health Expectancies (HE), Disability-free
 family of Health Expectancies (HE), Disability-free life  life expectancy (DFLE) is probably the most important index to
 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 </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>  particular by the international <a href="http://euroreves/reves">REVES</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 511  population. Life expectancy (LE) (or tot Line 95  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).<o:p></o:p></span></p>  of the author who first described it).</p>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age-specific proportions of people  <p>Age-specific proportions of people disable are very difficult
 disable are very difficult to forecast because each proportion  to forecast because each proportion corresponds to historical
 corresponds to historical conditions of the cohort and it is the  conditions of the cohort and it is the result of the historical
 result of the historical flows from entering disability and  flows from entering disability and recovering in the past until
 recovering in the past until today. The age-specific intensities  today. The age-specific intensities (or incidence rates) of
 (or incidence rates) of entering disability or recovering a good  entering disability or recovering a good health, are reflecting
 health, are reflecting actual conditions and therefore can be  actual conditions and therefore can be used at each age to
 used at each age to forecast the future of this cohort. For  forecast the future of this cohort. For example if a country is
 example if a country is improving its technology of prosthesis,  improving its technology of prosthesis, the incidence of
 the incidence of recovering the ability to walk will be higher at  recovering the ability to walk will be higher at each (old) age,
 each (old) age, but the prevalence of disability will only  but the prevalence of disability will only slightly reflect an
 slightly reflect an improve because the prevalence is mostly  improve because the prevalence is mostly affected by the history
 affected by the history of the cohort and not by recent period  of the cohort and not by recent period effects. To measure the
 effects. To measure the period improvement we have to simulate  period improvement we have to simulate the future of a cohort of
 the future of a cohort of new-borns entering or leaving at each  new-borns entering or leaving at each age the disability state or
 age the disability state or dying according to the incidence  dying according to the incidence rates measured today on
 rates measured today on different cohorts. The proportion of  different cohorts. The proportion of people disabled at each age
 people disabled at each age in this simulated cohort will be much  in this simulated cohort will be much lower (using the exemple of
 lower (using the example of an improvement) that the proportions  an improvement) that the proportions observed at each age in a
 observed at each age in a cross-sectional survey. This new  cross-sectional survey. This new prevalence curve introduced in a
 prevalence curve introduced in a life table will give a much more  life table will give a much more actual and realistic HE level
 actual and realistic HE level than the Sullivan method which  than the Sullivan method which mostly measured the History of
 mostly measured the History of health conditions in this country.<o:p></o:p></span></p>  health conditions in this country.</p>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Therefore, the main question is how  <p>Therefore, the main question is how to measure incidence rates
 to measure incidence rates from cross-longitudinal surveys? This  from cross-longitudinal surveys? This is the goal of the IMaCH
 is the goal of the IMaCH program. From your data and using IMaCH  program. From your data and using IMaCH you can estimate period
 you can estimate period HE and not only Sullivan's HE. Also the  HE and not only Sullivan's HE. Also the standard errors of the HE
 standard errors of the HE are computed.<o:p></o:p></span></p>  are computed.</p>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">A cross-longitudinal survey  <p>A cross-longitudinal survey consists in a first survey
 consists in a first survey (&quot;cross&quot;) where individuals  (&quot;cross&quot;) where individuals from different ages are
 from different ages are interviewed on their health status or  interviewed on their health status or degree of disability. At
 degree of disability. At least a second wave of interviews  least a second wave of interviews (&quot;longitudinal&quot;)
 (&quot;longitudinal&quot;) should measure each new individual  should measure each new individual health status. Health
 health status. Health expectancies are computed from the  expectancies are computed from the transitions observed between
 transitions observed between waves and are computed for each  waves and are computed for each degree of severity of disability
 degree of severity of disability (number of life states). More  (number of life states). More degrees you consider, more time is
 degrees you consider, more time is necessary to reach the Maximum  necessary to reach the Maximum Likelihood of the parameters
 Likelihood of the parameters involved in the model. Considering  involved in the model. Considering only two states of disability
 only two states of disability (disable and healthy) is generally  (disable and healthy) is generally enough but the computer
 enough but the computer program works also with more health  program works also with more health statuses.<br>
 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 576  month or quarter trimester, semester or Line 158  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>.
 <o:p></o:p></span></p>  <br>
   </p>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The program presented in this  <p>The program presented in this manual is a quite general
 manual is a quite general program named <strong>IMaCh</strong>  program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
 (for <strong>I</strong>nterpolated <strong>MA</strong>rkov <strong>CH</strong>ain),  <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
 designed to analyse transition data from longitudinal surveys.  analyse transition data from longitudinal surveys. The first step
 The first step is the parameters estimation of a transition  is the parameters estimation of a transition probabilities model
 probabilities model between an initial status and a final status.  between an initial status and a final status. From there, the
 From there, the computer program produces some indicators such as  computer program produces some indicators such as observed and
 observed and stationary prevalence, life expectancies and their  stationary prevalence, life expectancies and their variances and
 variances and graphs. Our transition model consists in absorbing  graphs. Our transition model consists in absorbing and
 and non-absorbing states with the possibility of return across  non-absorbing states with the possibility of return across the
 the non-absorbing states. The main advantage of this package,  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>(r)</sup>) is that the whole  (For example: Proc Catmod of SAS<sup>®</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 600  account (the user inputs the first and t Line 183  account (the user inputs the first and t
 tolerance level for the maximization function, the periodicity of  tolerance level for the maximization function, the periodicity of
 the transitions (we can compute annual, quarterly 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.<o:p></o:p></span></p>  Unix.<br>
   </p>
   
 <hr>  <hr>
   
 <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New  <p>(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>. </span>Vol 10, No. 2. </p>  Aging and Health</i>. Vol 10, No. 2. </p>
   
 <hr>  <hr>
   
 <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>  <h2><a name="data"><font color="#00006A">On what kind of data can
   it be used?</font></a></h2>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The minimum data required for a  <p>The minimum data required for a transition model is the
 transition model is the recording of a set of individuals  recording of a set of individuals interviewed at a first date and
 interviewed at a first date and interviewed again at least one  interviewed again at least one another time. From the
 another time. From the observations of an individual, we obtain a  observations of an individual, we obtain a follow-up over time of
 follow-up over time of the occurrence of a specific event. In  the occurrence of a specific event. In this documentation, the
 this documentation, the event is related to health status at  event is related to health status at older ages, but the program
 older ages, but the program can be applied on a lot of  can be applied on a lot of longitudinal studies in different
 longitudinal studies in different contexts. To build the data  contexts. To build the data file explained into the next section,
 file explained into the next section, you must have the month and  you must have the month and year of each interview and the
 year of each interview and the corresponding health status. But  corresponding health status. But in order to get age, date of
 in order to get age, date of birth (month and year) is required  birth (month and year) is required (missing values is allowed for
 (missing values is allowed for month). Date of death (month and  month). Date of death (month and year) is an important
 year) is an important information also required if the individual  information also required if the individual is dead. Shorter
 is dead. Shorter steps (i.e. a month) will more closely take into  steps (i.e. a month) will more closely take into account the
 account the survival time after the last interview.<o:p></o:p></span></p>  survival time after the last interview.</p>
   
 <hr>  <hr>
   
 <h2><a name="datafile"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:  <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
 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 style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, 8,000 people have  <p>In this example, 8,000 people have been interviewed in a
 been interviewed in a cross-longitudinal survey of 4 waves (1984,  cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
 1986, 1988, 1990). Some people missed 1, 2 or 3 interviews.  Some people missed 1, 2 or 3 interviews. Health statuses are
 Health statuses are healthy (1) and disable (2). The survey is  healthy (1) and disable (2). The survey is not a real one. It is
 not a real one. It is a simulation of the American Longitudinal  a simulation of the American Longitudinal Survey on Aging. The
 Survey on Aging. The disability state is defined if the  disability state is defined if the individual missed one of four
 individual missed one of four ADL (Activity of daily living, like  ADL (Activity of daily living, like bathing, eating, walking).
 bathing, eating, walking). Therefore, even is the individuals  Therefore, even is the individuals interviewed in the sample are
 interviewed in the sample are virtual, the information brought  virtual, the information brought with this sample is close to the
 with this sample is close to the situation of the United States.  situation of the United States. Sex is not recorded is this
 Sex is not recorded is this sample.<o:p></o:p></span></p>  sample.</p>
   
 <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:  <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
 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: </p>
 in this first example) is an individual record which fields are: <o:p></o:p></span></p>  
   <ul>
 <ul type="disc">      <li><b>Index number</b>: positive number (field 1) </li>
     <li class="MsoNormal"      <li><b>First covariate</b> positive number (field 2) </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>Second covariate</b> positive number (field 3) </li>
      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Index      <li><a name="Weight"><b>Weight</b></a>: positive number
         number</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number (field 1) <o:p></o:p></span></li>          (field 4) . In most surveys individuals are weighted
     <li class="MsoNormal"          according to the stratification of the sample.</li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">First          coded as 99/9999 (field 5) </li>
         covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 2) <o:p></o:p></span></li>      <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
     <li class="MsoNormal"          coded as 99/9999 (field 6) </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Second          dates are coded as 99/9999 (field 7) </li>
         covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 3) <o:p></o:p></span></li>      <li><b>Status at first interview</b>: positive number.
     <li class="MsoNormal"          Missing values ar coded -1. (field 8) </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>Date of second interview</b>: coded as mm/yyyy.
      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><a          Missing dates are coded as 99/9999 (field 9) </li>
         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:      <li><strong>Status at second interview</strong> positive
      EN-GB"></b></a>: positive number (field          number. Missing values ar coded -1. (field 10) </li>
         4) . In most surveys individuals are weighted according      <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
         to the stratification of the sample.<o:p></o:p></span></li>          dates are coded as 99/9999 (field 11) </li>
     <li class="MsoNormal"      <li><strong>Status at third interview</strong> positive
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          number. Missing values ar coded -1. (field 12) </li>
      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date      <li><b>Date of fourth interview</b>: coded as mm/yyyy.
         of birth</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded          Missing dates are coded as 99/9999 (field 13) </li>
         as 99/9999 (field 5) <o:p></o:p></span></li>      <li><strong>Status at fourth interview</strong> positive
     <li class="MsoNormal"          number. Missing values are coded -1. (field 14) </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li>etc</li>
      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><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></p>  <p>&nbsp;</p>
   
 <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If your longitudinal survey do not  <p>If your longitudinal survey do not include information about
 include information about weights or covariates, you must fill  weights or covariates, you must fill the column with a number
 the column with a number (e.g. 1) because a missing field is not  (e.g. 1) because a missing field is not allowed.</p>
 allowed.<o:p></o:p></span></p>  
   
 <hr>  <hr>
   
 <h2><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Your first example parameter file</span><a  <h2><font color="#00006A">Your first example parameter file</font><a
 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>  href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
   
 <h2><a name="biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>#Imach version 0.7, February 2002,  <h2><a name="biaspar"></a>#Imach version 0.7, February 2002,
 INED-EUROREVES <o:p></o:p></span></h2>  INED-EUROREVES </h2>
   
 <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>  <p>This is a comment. Comments start with a '#'.</p>
   
 <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>  <h4><font color="#FF0000">First uncommented line</font></h4>
   
 <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>  <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
   
 <ul type="disc">  <ul>
     <li class="MsoNormal"      <li><b>title=</b> 1st_example is title of the run. </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>datafile=</b>data1.txt is the name of the data set.
      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>          Our example is a six years follow-up survey. It consists
         1st_example is title of the run. <o:p></o:p></span></li>          in a baseline followed by 3 reinterviews. </li>
     <li class="MsoNormal"      <li><b>lastobs=</b> 8600 the program is able to run on a
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          subsample where the last observation number is lastobs.
      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          It can be set a bigger number than the real number of
         is the name of the data set. Our example is a six years          observations (e.g. 100000). In this example, maximisation
         follow-up survey. It consists in a baseline followed by 3          will be done on the 8600 first records. </li>
         reinterviews. <o:p></o:p></span></li>      <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
     <li class="MsoNormal"          than two interviews in the survey, the program can be run
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          on selected transitions periods. firstpass=1 means 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>          first interview included in the calculation is the
         8600 the program is able to run on a subsample where the          baseline survey. lastpass=4 means that the information
         last observation number is lastobs. It can be set a          brought by the 4th interview is taken into account.</li>
         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  <p>&nbsp;</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>
   
 <h4  <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</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="color:red;mso-ansi-language:EN-GB">Second  
 uncommented line</span><a name="biaspar-2"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h4>  <ul>
       <li><b>ftol=1e-8</b> Convergence tolerance on the function
 <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>          value in the maximisation of the likelihood. Choosing a
           correct value for ftol is difficult. 1e-8 is a correct
 <ul type="disc">          value for a 32 bits computer.</li>
     <li class="MsoNormal"      <li><b>stepm=1</b> Time unit in months for interpolation.
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          Examples:<ul>
      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=1, the unit is a month </li>
         Convergence tolerance on the function value in the              <li>If stepm=4, the unit is a trimester</li>
         maximisation of the likelihood. Choosing a correct value              <li>If stepm=12, the unit is a year </li>
         for ftol is difficult. 1e-8 is a correct value for a 32              <li>If stepm=24, the unit is two years</li>
         bits computer.<o:p></o:p></span></li>              <li>... </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 class="MsoNormal"      <li><b>ncov=2</b> Number of covariates in the datafile. The
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          intercept and the age parameter are counting for 2
      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>          covariates.</li>
         Number of covariates in the datafile. The intercept and      <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
         the age parameter are counting for 2 covariates.<o:p></o:p></span></li>          Here we have two alive states: disability-free is coded 1
     <li class="MsoNormal"          and disability is coded 2. </li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li><b>ndeath=1</b> Number of absorbing states. The absorbing
      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>          state death is coded 3. </li>
         Number of non-absorbing (alive) states. Here we have two      <li><b>maxwav=4</b> Number of waves in the datafile.</li>
         alive states: disability-free is coded 1 and disability      <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
         is coded 2. <o:p></o:p></span></li>          Maximisation Likelihood Estimation. <ul>
     <li class="MsoNormal"              <li>If mle=1 the program does the maximisation and
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;                  the calculation of health expectancies </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">ndeath=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>              <li>If mle=0 the program only does the calculation of
         Number of absorbing states. The absorbing state death is                  the health expectancies. </li>
         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 class="MsoNormal"      <li><b>weight=0</b> Possibility to add weights. <ul>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;              <li>If weight=0 no weights are included </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">weight=0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>              <li>If weight=1 the maximisation integrates the
         Possibility to add weights. <o:p></o:p></span></li>                  weights which are in field <a href="#Weight">4</a></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  <h4><font color="#FF0000">Covariates</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">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>
   
 <p  <pre>model=<em>list of covariates</em></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="mso-ansi-language:EN-GB">Intercept  
 and age are systematically included in the model. Additional  <ul>
 covariates can be included with the command <o:p></o:p></span></p>      <li>if<strong> model=. </strong>then no covariates are
           included</li>
 <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>      <li>if <strong>model=V1</strong> the model includes the first
           covariate (field 2)</li>
 <ul type="disc">      <li>if <strong>model=V2 </strong>the model includes the
     <li class="MsoNormal"          second covariate (field 3)</li>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;      <li>if <strong>model=V1+V2 </strong>the model includes the
      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>          first and the second covariate (fields 2 and 3)</li>
         model=. </strong>then no covariates are included<o:p></o:p></span></li>      <li>if <strong>model=V1*V2 </strong>the model includes the
     <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)<o:p></o:p></span></li>          and 3)</li>
     <li class="MsoNormal"      <li>if <strong>model=V1+V1*age</strong> the model includes
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          the product covariate*age</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>model=V1+V1*age</strong> the model includes the  
         product covariate*age<o:p></o:p></span></li>  
 </ul>  </ul>
   
 <h4  <h4><font color="#FF0000">Guess values for optimization</font><font
 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  color="#00006A"> </font></h4>
 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
 <p  optimization. The number of parameters, <em>N</em> depends on the
 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 940  start with zeros as in this example, but Line 388  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> <o:p></o:p></span></p>  aij bij</b> </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>
   
 <pre  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
 style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:  used as an input to get the various output data files (Health
 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). <o:p></o:p></span></p>  rerunning the rather long maximisation phase (mle=0). </p>
   
 <p  <p>The scales are small values for the evaluation of numerical
 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. <o:p></o:p></span></p>  (zero to simplify) associated with aij and bij. </p>
   
 <ul type="disc">  <ul>
     <li class="MsoNormal"      <li>If mle=1 you can enter zeros:</li>
     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>
   
 <pre  <blockquote>
 style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:      <pre># Scales (for hessian or gradient estimation)
 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>  12 0. 0.
   13 0. 0.
 <pre  21 0. 0.
 style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;  23 0. 0. </pre>
 margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:  </blockquote>
 EN-GB">12 0. 0. <o:p></o:p></span></pre>  
   <ul>
 <pre      <li>If mle=0 you must enter a covariance matrix (usually
 style="margin-top:0cm;margin-right:          obtained from an earlier run).</li>
 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  <h4><font color="#FF0000">Covariance matrix of parameters</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">Covariance  
 matrix of parameters</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  
 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>  
   
 <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>  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
   used as an input to get the various output data files (Health
 <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>  expectancies, stationary prevalence etc.) and figures without
   rerunning the rather long maximisation phase (mle=0). </p>
   
 <ul type="disc">  <p>Each line starts with indices &quot;ijk&quot; followed by the
     <li class="MsoNormal"  covariances between aij and bij: </p>
     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  <pre>
 style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:     121 Var(a12)
 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>     122 Cov(b12,a12)  Var(b12)
             ...
 <pre     232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </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>  
   
 <h4  <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="color:red;mso-ansi-language:EN-GB">Age      <li>If mle=1 you can enter zeros. </li>
 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>
   
 <h4  <blockquote>
 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      <pre># Covariance matrix
 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>  121 0.
   122 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>  131 0. 0. 0.
   132 0. 0. 0. 0.
 <p  211 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  212 0. 0. 0. 0. 0. 0.
 'begin-prev-date' and 'end-prev-date' allow to select the period  231 0. 0. 0. 0. 0. 0. 0.
 in which we calculate the observed prevalences in each state. In  232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
 this example, the prevalences are calculated on data survey  </blockquote>
 collected between 1 January 1984 and 1 June 1988. <o:p></o:p></span></p>  
   <ul>
 <ul type="disc">      <li>If mle=0 you must enter a covariance matrix (usually
     <li class="MsoNormal"          obtained from an earlier run).<br>
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          </li>
      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  <h4><font color="#FF0000">Age range for calculation of stationary
 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-  prevalences and health expectancies</font></h4>
 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>  
   
 <ul type="disc">  <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
     <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>  
   
 <h4  <p>Once we obtained the estimated parameters, the program is able
 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  to calculated stationary prevalence, transitions probabilities
 uncommented line : Population forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>  and life expectancies at any age. Choice of age range is useful
   for extrapolation. In our data file, ages varies from age 70 to
 <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>  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
 <p  can compute life expectancy on a wider age range than the age
 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  range from the data. But the model can be rather wrong on big
 command is available if the interpolation unit is a month, i.e.  intervals.</p>
 stepm=1 and if popforecast=1. From a data file including age and  
 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;;  <p>Similarly, it is possible to get extrapolated stationary
 mso-ansi-language:EN-GB">popfiledate&#146;,  prevalence by age ranging from agemin to agemax. </p>
 </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:  
 12.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">  <ul>
 &#145;last-popfiledate&#146;. </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, the popfile </span><a      <li><b>agemin=</b> Minimum age for calculation of the
 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:          stationary prevalence </li>
 EN-GB"><span style="mso-spacerun: yes"></b>&nbsp;</span>includes real      <li><b>agemax=</b> Maximum age for calculation of the
 data which are the Japanese population in 1989.<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></p>          stationary prevalence </li>
       <li><b>bage=</b> Minimum age for calculation of the health
 <ul type="disc">          expectancies </li>
     <li class="MsoNormal"      <li><b>fage=</b> Maximum age for calculation of the health
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          expectancies </li>
      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>
   
 <hr>  <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
   color="#FF0000"> the observed prevalence</font></h4>
   
 <h2  <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </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"><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>  
   
 <h2  <p>Statements 'begin-prev-date' and 'end-prev-date' allow to
 style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><a  select the period in which we calculate the observed prevalences
 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>  in each state. In this example, the prevalences are calculated on
   data survey collected between 1 january 1984 and 1 june 1988. </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">Once  <ul>
 the optimization is finished, some graphics can be made with a      <li><strong>begin-prev-date= </strong>Starting date
 grapher. We use Gnuplot which is an interactive plotting program          (day/month/year)</li>
 copyrighted but freely distributed. A gnuplot reference manual is      <li><strong>end-prev-date= </strong>Final date
 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>          (day/month/year)</li>
 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>
   
 <h5  <h4><font color="#FF0000">Population- or status-based health
 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;  expectancies</font></h4>
 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 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>  
   
 <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>  
   
 <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 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  
 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  
 means that at age 70, the prevalence in state 1 is 1.000 and in  
 state 2 is 0.00 . At age 71 the number of individuals in state 1  
 is 625 and in state 2 is 2, hence the total number of people aged  
 71 is 625+2=627. <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">-  
 Estimated parameters and covariance matrix</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a  
 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>  
   
 <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  
 file contains all the maximisation results: <o:p></o:p></span></p>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <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>  <pre>pop_based=0</pre>
   
 <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>  <p>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 <a href="#Computing">previously
   explained</a>, whereas for a population-based index, the weights
   are the stationary prevalences.</p>
   
 <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>  <h4><font color="#FF0000">Prevalence forecasting </font></h4>
   
 <p  <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </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="mso-ansi-language:EN-GB">By  
 substitution of these parameters in the regression model, we  
 obtain the elementary transition probabilities:<o:p></o:p></span></p>  
   
 <p  <p>Prevalence and population projections are only available if
 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  the interpolation unit is a month, i.e. stepm=1. The programme
 src="pebiaspar1.gif" width="400" height="300" id="_x0000_i1037"></p>  estimates the prevalence in each state at a precise date
   expressed in day/month/year. The programme computes one
 <h5  forecasted prevalence a year from a starting date (1 january of
 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">-  1989 in this example) to a final date (1 january 1992). The
 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:  statement mov_average allows to compute smoothed forecasted
 EN-GB">pijrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:  prevalences with a five-age moving average centered at the
 EN-GB"><o:p></o:p></span></a></h5>  mid-age of the five-age period. </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">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: <o:p></o:p></span></p>  
   
 <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  
 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  
 this means: <o:p></o:p></span></p>  
   
 <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>  
   
 <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>  <ul>
       <li><strong>starting-proj-date</strong>= starting date
           (day/month/year) of forecasting</li>
       <li><strong>final-proj-date= </strong>final date
           (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>
   
 <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>  <h4><font color="#FF0000">Last uncommented line : Population
   forecasting </font></h4>
   
 <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>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">p22(100,106)=0.13678<o:p></o:p></span></pre>  <p>This command is available if the interpolation unit is a
   month, i.e. stepm=1 and if popforecast=1. From a data file </p>
   
 <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>  <p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>
   : </b>age numbers</p>
   
 <h5  <p>&nbsp;</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="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>  <hr>
   
 <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>  <h2><a name="running"></a><font color="#00006A">Running Imach
   with this example</font></h2>
   
 <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>  <p>We assume that you entered your <a href="biaspar.imach">1st_example
   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>
   
 <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#************ <o:p></o:p></span></pre>  <p>The program outputs many files. Most of them are files which
   will be plotted for better understanding.</p>
   
 <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>  <hr>
   
 <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>  <h2><a name="output"><font color="#00006A">Output of the program
   and graphs</font> </a></h2>
   
 <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>  <p>Once the optimization is finished, some graphics can be made
   with a grapher. We use Gnuplot which is an interactive plotting
   program copyrighted but freely distributed. A gnuplot reference
   manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
   When the running is finished, the user should enter a caracter
   for plotting and output editing. </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>
   
 <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>  <h5><font size="4"><strong>Results files </strong></font><br>
   <br>
   <font color="#EC5E5E" size="3"><strong>- </strong></font><a
   name="Observed prevalence in each state"><font color="#EC5E5E"
   size="3"><strong>Observed prevalence in each state</strong></font></a><font
   color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
   </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
   </h5>
   
   <p>The first line is the title and displays each field of the
   file. The first column is age. The fields 2 and 6 are the
   proportion of individuals in states 1 and 2 respectively as
   observed during the first exam. Others fields are the numbers of
   people in states 1, 2 or more. The number of columns increases if
   the number of states is higher than 2.<br>
   The header of the file is </p>
   
   <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
   70 1.00000 631 631 70 0.00000 0 631
   71 0.99681 625 627 71 0.00319 2 627
   72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
   
   <p>It means that at age 70, the prevalence in state 1 is 1.000
   and in state 2 is 0.00 . At age 71 the number of individuals in
   state 1 is 625 and in state 2 is 2, hence the total number of
   people aged 71 is 625+2=627. <br>
   </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>
   
   <p>This file contains all the maximisation results: </p>
   
   <pre> -2 log likelihood= 21660.918613445392
    Estimated parameters: a12 = -12.290174 b12 = 0.092161
                          a13 = -9.155590  b13 = 0.046627
                          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  <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
 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 1507  future if &quot;nothing changes in the f Line 718  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. <o:p></o:p></span></p>  future. </p>
   
 <h5  <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
 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">-  stationary prevalence</b></font><b>: </b><a
 Standard deviation of stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a  href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
 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.<o:p></o:p></span></p>  deviation of the stationary prevalence at each age.</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>
   
 <h5  <p>This graph plots the conditional transition probabilities from
 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  an initial state (1=healthy in red at the bottom, or 2=disable in
 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 1563  prevalence at age 70 we should start the Line 762  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.<o:p></o:p></span></p>  probably longer. But we don't have experience yet.</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>  
   
 <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>  <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
   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 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>  <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:
   e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>
   
 <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>  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
   src="expbiaspar11.gif" width="400" height="300"></pre>
   
 <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>  <p>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
 <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 </span><a  (i.e. based only on incidences) we use the <a
 href="#Stationary prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:EN-GB">computed or  href="#Stationary prevalence in each state">computed or
 stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> at age 70 (i.e. computed from  stationary prevalence</a> at age 70 (i.e. computed from
 incidences at earlier ages) instead of the </span><a  incidences at earlier ages) instead of the <a
 href="#Observed prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:  href="#Observed prevalence in each state">observed prevalence</a>
 EN-GB">observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:  (for example at first exam) (<a href="#Health expectancies">see
 EN-GB"></a>  below</a>).</p>
 (for example at first exam) (</span><a href="#Health expectancies"><span lang="EN-GB" style="mso-ansi-language:EN-GB">see  
 below</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>).<o:p></o:p></span></p>  <h5><font color="#EC5E5E" size="3"><b>- Variances of life
   expectancies by age and initial health status</b></font><b>: </b><a
 <h5  href="vrbiaspar.txt"><b>vrbiaspar.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">-  
 Variances of life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a  <p>For example, the covariances of life expectancies Cov(ei,ej)
 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>  at age 50 are (line 3) </p>
   
 <p  <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</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="mso-ansi-language:EN-GB">For  
 example, the covariances of life expectancies Cov(ei,ej) at age  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 50 are (line 3) <o:p></o:p></span></p>  name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
   expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
 <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>  with standard errors in parentheses</b></font><b>: </b><a
   href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></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">-  <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
 <a name="Health_expectancies">Health expectancies</a> with  
 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;;  <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>
 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
 <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>  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">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.<o:p></o:p></span></p>  70 to be spent in the disability state.</p>
   
 <h5  <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy 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="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Total  age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
 life expectancy by age and health expectancies in states  </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
 (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
 <p  life expectancy with the confident interval in dashed curve. </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  
 figure represents the health expectancies and the total life  <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>
 expectancy with the confident interval in dashed curve. <o:p></o:p></span></p>  
   <p>Standard deviations (obtained from the information matrix of
 <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  the model) of these quantities are very useful.
 src="ebiaspar1.gif" width="400" height="300" id="_x0000_i1042"></pre>  Cross-longitudinal surveys are costly and do not involve huge
   samples, generally a few thousands; therefore it is very
 <p  important to have an idea of the standard deviation of our
 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  estimates. It has been a big challenge to compute the Health
 deviations (obtained from the information matrix of the model) of  Expectancy standard deviations. Don't be confuse: life expectancy
 these quantities are very useful. Cross-longitudinal surveys are  is, as any expected value, the mean of a distribution; but here
 costly and do not involve huge samples, generally a few  we are not computing the standard deviation of the distribution,
 thousands; therefore it is very important to have an idea of the  but the standard deviation of the estimate of the mean.</p>
 standard deviation of our estimates. It has been a big challenge  
 to compute the Health Expectancy standard deviations. Don't be  <p>Our health expectancies estimates vary according to the sample
 confuse: life expectancy is, as any expected value, the mean of a  size (and the standard deviations give confidence intervals of
 distribution; but here we are not computing the standard  the estimate) but also according to the model fitted. Let us
 deviation of the distribution, but the standard deviation of the  explain it in more details.</p>
 estimate of the mean.<o:p></o:p></span></p>  
   <p>Choosing a model means ar least two kind of choices. First we
 <p  have to decide the number of disability states. Second we have to
 style="text-align:justify;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Our  design, within the logit model family, the model: variables,
 health expectancies estimates vary according to the sample size  covariables, confonding factors etc. to be included.</p>
 (and the standard deviations give confidence intervals of the  
 estimate) but also according to the model fitted. Let us explain  <p>More disability states we have, better is our demographical
 it in more details.<o:p></o:p></span></p>  approach of the disability process, but smaller are the number of
   
 <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 1707  population. Our main purpose is not to m Line 877  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.<o:p></o:p></span></p>  measurement.</p>
   
 <p  <p>Incidences of disability or recovery are not affected by the
 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  number of states if these states are independant. But incidences
 of disability or recovery are not affected by the number of  estimates are dependant on the specification of the model. More
 states if these states are independant. But incidences estimates  covariates we added in the logit model better is the model, but
 are dependant on the specification of the model. More covariates  some covariates are not well measured, some are confounding
 we added in the logit model better is the model, but some  factors like in any statistical model. The procedure to &quot;fit
 covariates are not well measured, some are confounding factors  the best model' is similar to logistic regression which itself is
 like in any statistical model. The procedure to &quot;fit the  similar to regression analysis. We haven't yet been sofar because
 best model' is similar to logistic regression which itself is  we also have a severe limitation which is the speed of the
 similar to regression analysis. We haven't yet been so far  convergence. On a Pentium III, 500 MHz, even the simplest model,
 because we also have a severe limitation which is the speed of  estimated by month on 8,000 people may take 4 hours to converge.
 the convergence. On a Pentium III, 500 MHz, even the simplest  Also, the program is not yet a statistical package, which permits
 model, estimated by month on 8,000 people may take 4 hours to  a simple writing of the variables and the model to take into
 converge. Also, the program is not yet a statistical package,  account in the maximisation. The actual program allows only to
 which permits a simple writing of the variables and the model to  add simple variables like age+sex or age+sex+ age*sex but will
 take into account in the maximisation. The actual program allows  never be general enough. But what is to remember, is that
 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.<o:p></o:p></span></p>  affected by the variables specified into the model.</p>
   
 <p  <p>Also, the age range of the people interviewed has a link with
 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 life expectancy which can be estimated by
 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 probabilities of transition out of  range of 70-95 and estimating probabilties 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.<o:p></o:p></span></p>  probably not the case.</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">-  
 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  <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
 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</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
 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  <p>This copy of the parameter file can be useful to re-run the
 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">-  program while saving the old output files. </p>
 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  <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</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="mso-ansi-language:EN-GB">First,  </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
 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  <p>On a d'abord estimé la date moyenne des interviaew. ie
 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,  13/9/1995. This file contains </p>
 at date 1/1/1989 : <o:p></o:p></span></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>Example, at date 1/1/1989 : </p>
   
 <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>  <p>73 0.807 0.078 0.115 </p>
   
 <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>  <p>This means that at age 73, the probability for a person age 70
   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>
   
 <p  <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</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="mso-ansi-language:EN-GB">Since  </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
 the minimum age is 70 on the 13/9/1985, the youngest forecasted  
 age is 73. This means that at age a person aged 70 at 13/9/1989  
 has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.  
 Similarly, the probability to be in state 2 is 0.078 and the  
 probability to die is 0.115. Then, on the 1/1/1989, the  
 prevalence of disability at age 73 is estimated to be 0.088.<o:p></o:p></span></p>  
   
 <h5  <pre># Age P.1 P.2 P.3 [Population]
 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">-  # Forecasting at date 1/1/1989
 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:  75 572685.22 83798.08
 EN-GB">poprbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:  74 621296.51 79767.99
 EN-GB"><o:p></o:p></span></a></h5>  73 645857.70 69320.60 </pre>
   
 <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>  <pre># Forecasting at date 1/1/19909
   76 442986.68 92721.14 120775.48
   75 487781.02 91367.97 121915.51
   74 512892.07 85003.47 117282.76 </pre>
   
 <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>  <hr>
   
 <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>  
   
 <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>  
   
 <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>  <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
   
 <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">From the population file, we estimate the  <p>Since you know how to run the program, it is time to test it
 number of people in each state. At age 73, 645857 persons are in  on your own computer. Try for example on a parameter file named <a
 state 1 and 69320 are in state 2. One year latter, 512892 are  href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
 still in state 1, 85003 are in state 2 and 117282 died before  size="2" face="Courier New">mypar.txt</font> included in the
 1/1/1990.<o:p></o:p></span></p>  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>
   
 <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>  <p>Click on the imach.exe icon to open a window. Answer to the
   question:'<strong>Enter the parameter file name:'</strong></p>
   
 <hr>  <table border="1">
   
 <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%"          <td width="100%"><strong>IMACH, Version 0.7</strong><p><strong>Enter
         style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">IMACH,          the parameter file name: ..\mytry\imachpar.txt</strong></p>
         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  <p>Most of the data files or image files generated, will use the
 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 </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>  the same as the mypar files initially included in the directory <font
   size="2" face="Courier New">mytry</font>.</p>
 <pre  
 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"><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>  
   
 <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>  
   
 <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>  
   
 <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>  
   
 <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>  
   
 <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<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: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>  
   
 <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>
       <li><pre><u>Output on the screen</u> The output screen looks like <a
   href="imachrun.LOG">this Log file</a>
   #
   
 <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>  title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
   ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
 <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>      </li>
       <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
   
 <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>  Warning, no any valid information for:126 line=126
   Warning, no any valid information for:2307 line=2307
   Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
   <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
   Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
    prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
   Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
       </li>
   </ul>
   
 <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>  <p>&nbsp;</p>
   
 <ul type="disc">  <ul>
     <li class="MsoNormal"      <li>Maximisation with the Powell algorithm. 8 directions are
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          given corresponding to the 8 parameters. this can be
      mso-list:l6 level1 lfo46;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Maximisation          rather long to get convergence.<br>
         with the Powell algorithm. 8 directions are given          <font size="1" face="Courier New"><br>
         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 1925  href="imachrun.LOG"><span lang="EN-GB" s Line 1025  href="imachrun.LOG"><span lang="EN-GB" s
         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 </span><span lang="EN-GB" style="mso-ansi-language:          23 -5.051297 0.051271 </font><br>
      EN-GB"><o:p></o:p></span></li>          </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>
   
 <pre  <p><font size="3">Once the running is finished, the program
 style="margin-left:36.0pt;text-align:justify;text-indent:-18.0pt;  requires a caracter:</font></p>
 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>  
   
 <pre style="margin-left:18.0pt;text-align:justify">#Hessian matrix#</pre>  <table border="1">
   
 <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%"          <td width="100%"><strong>Type e to edit output files, c
         style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Type          to start again, and q for exiting:</strong></td>
         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  <p><font size="3">First you should enter <strong>e </strong>to
 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  edit the master file mypar.htm. </font></p>
 you should enter <strong>e </strong>to edit the master file  
 mypar.htm. <o:p></o:p></span></p>  <ul>
       <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: </span><a          - Observed prevalence in each state: <a
         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>          href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
         - Estimated parameters and the covariance matrix: </span><a          - Estimated parameters and the covariance matrix: <a
         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>          href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
         - Stationary prevalence in each state: </span><a          - Stationary prevalence in each state: <a
         href="..\mytry\plrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:          href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
      EN-GB">plrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:          - Transition probabilities: <a
      EN-GB"></a> <br>          href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
         - Transition probabilities: </span><a          - Copy of the parameter file: <a
         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>          href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
         - Copy of the parameter file: </span><a          - Life expectancies by age and initial health status: <a
         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>          href="..\mytry\ermypar.txt">ermypar.txt</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: </span><a href="..\mytry\vrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:          health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
      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>
         - Population forecasting (if popforecast=1): </span><a          - Health expectancies with their variances: <a
         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>          href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
     <li class="MsoNormal"          - Standard deviation of stationary prevalence: <a
     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;          href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
      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>          - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
         <br>          <br>
           - Population forecasting (if popforecast=1): <a
           href="poprmypar.txt">poprmypar.txt</a> <br>
           </li>
       <li><u>Graphs</u> <br>
         <br>          <br>
         -</span><a href="..\mytry\pemypar1.gif"><span lang="EN-GB" style="mso-ansi-language:          -<a href="../mytry/pemypar1.gif">One-step transition
      EN-GB">One-step transition          probabilities</a><br>
         probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>          -<a href="../mytry/pmypar11.gif">Convergence to the
         -</span><a href="..\mytry\pmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:          stationary prevalence</a><br>
      EN-GB">Convergence to the          -<a href="..\mytry\vmypar11.gif">Observed and stationary
         stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>          prevalence in state (1) with the confident interval</a> <br>
         -</span><a href="..\mytry\vmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:          -<a href="..\mytry\vmypar21.gif">Observed and stationary
      EN-GB">Observed and stationary          prevalence in state (2) with the confident interval</a> <br>
         prevalence in state (1) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>          -<a href="..\mytry\expmypar11.gif">Health life
         -</span><a href="..\mytry\vmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:          expectancies by age and initial health state (1)</a> <br>
      EN-GB">Observed and stationary          -<a href="..\mytry\expmypar21.gif">Health life
         prevalence in state (2) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>          expectancies by age and initial health state (2)</a> <br>
         -</span><a href="..\mytry\expmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life          -<a href="..\mytry\emypar1.gif">Total life expectancy by
         expectancies by age and initial health state (1)</span><span lang="EN-GB" style="mso-ansi-language:          age and health expectancies in states (1) and (2).</a> </li>
      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  <p>This software have been partly granted by <a
 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  href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
 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) </span><a  simple justification (name, email, institute) <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:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
 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>  href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
   
 <p  <p>Latest version (0.7 of February 2002) can be accessed at <a
 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  href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
 version (0.7 of February 2002) can be accessed at </span><a  </p>
 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>  
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