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 <title>Computing Health Expectancies using IMaCh</title>  <title>Computing Health Expectancies using IMaCh</title>
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Line 29  color="#00006A">INED</font></a><font col Line 37  color="#00006A">INED</font></a><font col
 href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>  href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
   
 <p align="center"><font color="#00006A" size="4"><strong>Version  <p align="center"><font color="#00006A" size="4"><strong>Version
 0.7, February 2002</strong></font></p>  0.8, March 2002</strong></font></p>
   
 <hr size="3" color="#EC5E5E">  <hr size="3" color="#EC5E5E">
   
Line 58  color="#00006A">) </font></h4> Line 66  color="#00006A">) </font></h4>
   
 <ul>  <ul>
     <li><a href="#intro">Introduction</a> </li>      <li><a href="#intro">Introduction</a> </li>
     <li>The detailed statistical model (<a href="docmath.pdf">PDF  
         version</a>),(<a href="docmath.ps">ps version</a>) </li>  
     <li><a href="#data">On what kind of data can it be used?</a></li>      <li><a href="#data">On what kind of data can it be used?</a></li>
     <li><a href="#datafile">The data file</a> </li>      <li><a href="#datafile">The data file</a> </li>
     <li><a href="#biaspar">The parameter file</a> </li>      <li><a href="#biaspar">The parameter file</a> </li>
Line 80  monitor. In low mortality countries, the Line 86  monitor. In low mortality countries, the
 mortality declines, the increase in DFLE is not proportionate to  mortality declines, the increase in DFLE is not proportionate to
 the increase in total Life expectancy. This case is called the <em>Expansion  the increase in total Life expectancy. This case is called the <em>Expansion
 of morbidity</em>. Most of the data collected today, in  of morbidity</em>. Most of the data collected today, in
 particular by the international <a href="http://euroreves/reves">REVES</a>  particular by the international <a href="http://www.reves.org">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 273  weights or covariates, you must fill the Line 279  weights or covariates, you must fill the
 <h2><font color="#00006A">Your first example parameter file</font><a  <h2><font color="#00006A">Your first example parameter file</font><a
 href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>  href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
   
 <h2><a name="biaspar"></a>#Imach version 0.7, February 2002,  <h2><a name="biaspar"></a>#Imach version 0.8, March 2002,
 INED-EUROREVES </h2>  INED-EUROREVES </h2>
   
 <p>This is a comment. Comments start with a '#'.</p>  <p>This is a comment. Comments start with a '#'.</p>
Line 305  INED-EUROREVES </h2> Line 311  INED-EUROREVES </h2>
 <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented  <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
 line</font></a></h4>  line</font></a></h4>
   
 <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>  <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
   
 <ul>  <ul>
     <li><b>ftol=1e-8</b> Convergence tolerance on the function      <li><b>ftol=1e-8</b> Convergence tolerance on the function
Line 321  line</font></a></h4> Line 327  line</font></a></h4>
             <li>... </li>              <li>... </li>
         </ul>          </ul>
     </li>      </li>
     <li><b>ncov=2</b> Number of covariates in the datafile. The      <li><b>ncovcol=2</b> Number of covariate columns in the datafile
         intercept and the age parameter are counting for 2      which precede the date of birth. Here you can put variables that
         covariates.</li>      won't necessary be used during the run. It is not the number of
       covariates that will be specified by the model. The 'model'
       syntax describe the covariates to take into account. </li>
     <li><b>nlstate=2</b> Number of non-absorbing (alive) states.      <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
         Here we have two alive states: disability-free is coded 1          Here we have two alive states: disability-free is coded 1
         and disability is coded 2. </li>          and disability is coded 2. </li>
Line 349  line</font></a></h4> Line 357  line</font></a></h4>
 <h4><font color="#FF0000">Covariates</font></h4>  <h4><font color="#FF0000">Covariates</font></h4>
   
 <p>Intercept and age are systematically included in the model.  <p>Intercept and age are systematically included in the model.
 Additional covariates can be included with the command </p>  Additional covariates can be included with the command: </p>
   
 <pre>model=<em>list of covariates</em></pre>  <pre>model=<em>list of covariates</em></pre>
   
Line 369  Additional covariates can be included wi Line 377  Additional covariates can be included wi
         the product covariate*age</li>          the product covariate*age</li>
 </ul>  </ul>
   
   <p>In this example, we have two covariates in the data file
   (fields 2 and 3). The number of covariates included in the data file
   between the id and the date of birth is ncovcol=2 (it was named ncov
   in version prior to 0.8). If you have 3 covariates in the datafile
   (fields 2, 3 and 4), you will set ncovcol=3. Then you can run the
   programme with a new parametrisation taking into account the
   third covariate. For example, <strong>model=V1+V3 </strong>estimates
   a model with the first and third covariates. More complicated
   models can be used, but it will takes more time to converge. With
   a simple model (no covariates), the programme estimates 8
   parameters. Adding covariates increases the number of parameters
   : 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
   </strong>and 20 for <strong>model=V1+V2+V3.</strong></p>
   
 <h4><font color="#FF0000">Guess values for optimization</font><font  <h4><font color="#FF0000">Guess values for optimization</font><font
 color="#00006A"> </font></h4>  color="#00006A"> </font></h4>
   
Line 377  optimization. The number of parameters, Line 399  optimization. The number of parameters,
 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> +
 <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>  <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncovmodel</em>&nbsp;. <br>
 <br>  <br>
 Thus in the simple case with 2 covariates (the model is log  Thus in the simple case with 2 covariates (the model is log
 (pij/pii) = aij + bij * age where intercept and age are the two  (pij/pii) = aij + bij * age where intercept and age are the two
Line 398  aij bij</b> </p> Line 420  aij bij</b> </p>
 23  -6.234642  0.022315 </pre>  23  -6.234642  0.022315 </pre>
 </blockquote>  </blockquote>
   
 <p>or, to simplify: </p>  <p>or, to simplify (in most of cases it converges but there is no
   warranty!): </p>
   
 <blockquote>  <blockquote>
     <pre>12 0.0 0.0      <pre>12 0.0 0.0
Line 407  aij bij</b> </p> Line 430  aij bij</b> </p>
 23 0.0 0.0</pre>  23 0.0 0.0</pre>
 </blockquote>  </blockquote>
   
   <p> In order to speed up the convergence you can make a first run with
   a large stepm i.e stepm=12 or 24 and then decrease the stepm until
   stepm=1 month. If newstepm is the new shorter stepm and stepm can be
   expressed as a multiple of newstepm, like newstepm=n stepm, then the
   following approximation holds:
   <pre>aij(stepm) = aij(n . stepm) - ln(n)
   </pre> and
   <pre>bij(stepm) = bij(n . stepm) .</pre>
   
   <p> For example if you already ran for a 6 months interval and
   got:<br>
    <pre># Parameters
   12 -13.390179  0.126133
   13  -7.493460  0.048069
   21   0.575975 -0.041322
   23  -4.748678  0.030626
   </pre>
   If you now want to get the monthly estimates, you can guess the aij by
   substracting ln(6)= 1,7917<br> and running<br>
   <pre>12 -15.18193847  0.126133
   13 -9.285219469  0.048069
   21 -1.215784469 -0.041322
   23 -6.540437469  0.030626
   </pre>
   and get<br>
   <pre>12 -15.029768 0.124347
   13 -8.472981 0.036599
   21 -1.472527 -0.038394
   23 -6.553602 0.029856
   </br>
   which is closer to the results. The approximation is probably useful
   only for very small intervals and we don't have enough experience to
   know if you will speed up the convergence or not.
   <pre>         -ln(12)= -2.484
    -ln(6/1)=-ln(6)= -1.791
    -ln(3/1)=-ln(3)= -1.0986
   -ln(12/6)=-ln(2)= -0.693
   </pre>
   
 <h4><font color="#FF0000">Guess values for computing variances</font></h4>  <h4><font color="#FF0000">Guess values for computing variances</font></h4>
   
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
Line 420  matrix of the parameters, that is the in Line 482  matrix of the parameters, that is the in
 matrix, and the variances of health expectancies. Each line  matrix, and the variances of health expectancies. Each line
 consists in indices &quot;ij&quot; followed by the initial scales  consists in indices &quot;ij&quot; followed by the initial scales
 (zero to simplify) associated with aij and bij. </p>  (zero to simplify) associated with aij and bij. </p>
   <ul> <li>If mle=1 you can enter zeros:</li>
 <ul>  <blockquote><pre># Scales (for hessian or gradient estimation)
     <li>If mle=1 you can enter zeros:</li>  
 </ul>  
   
 <blockquote>  
     <pre># Scales (for hessian or gradient estimation)  
 12 0. 0.  12 0. 0.
 13 0. 0.  13 0. 0.
 21 0. 0.  21 0. 0.
 23 0. 0. </pre>  23 0. 0. </pre>
 </blockquote>  </blockquote>
   
 <ul>  
     <li>If mle=0 you must enter a covariance matrix (usually      <li>If mle=0 you must enter a covariance matrix (usually
         obtained from an earlier run).</li>          obtained from an earlier run).</li>
 </ul>  </ul>
Line 443  consists in indices &quot;ij&quot; follo Line 498  consists in indices &quot;ij&quot; follo
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  <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  used as an input to get the various output data files (Health
 expectancies, stationary prevalence etc.) and figures without  expectancies, stationary prevalence etc.) and figures without
 rerunning the rather long maximisation phase (mle=0). </p>  rerunning the rather long maximisation phase (mle=0). <br>
   Each line starts with indices &quot;ijk&quot; followed by the
 <p>Each line starts with indices &quot;ijk&quot; followed by the  covariances between aij and bij:<br>
 covariances between aij and bij: </p>  
   
 <pre>  <pre>
    121 Var(a12)     121 Var(a12)
    122 Cov(b12,a12)  Var(b12)     122 Cov(b12,a12)  Var(b12)
           ...            ...
    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>     232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>
   
 <ul>  <ul>
     <li>If mle=1 you can enter zeros. </li>      <li>If mle=1 you can enter zeros. </li>
 </ul>  
   
 <blockquote>  
     <pre># Covariance matrix      <pre># Covariance matrix
 121 0.  121 0.
 122 0. 0.  122 0. 0.
Line 468  covariances between aij and bij: </p> Line 517  covariances between aij and bij: </p>
 212 0. 0. 0. 0. 0. 0.  212 0. 0. 0. 0. 0. 0.
 231 0. 0. 0. 0. 0. 0. 0.  231 0. 0. 0. 0. 0. 0. 0.
 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>  232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
 </blockquote>  
   
 <ul>  
     <li>If mle=0 you must enter a covariance matrix (usually      <li>If mle=0 you must enter a covariance matrix (usually
         obtained from an earlier run).<br>          obtained from an earlier run). </li>
         </li>  
 </ul>  </ul>
   
 <h4><font color="#FF0000">Age range for calculation of stationary  <h4><font color="#FF0000">Age range for calculation of stationary
Line 481  prevalences and health expectancies</fon Line 526  prevalences and health expectancies</fon
   
 <pre>agemin=70 agemax=100 bage=50 fage=100</pre>  <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
   
 <p>Once we obtained the estimated parameters, the program is able  <br>Once we obtained the estimated parameters, the program is able
 to calculated stationary prevalence, transitions probabilities  to calculated stationary prevalence, transitions probabilities
 and life expectancies at any age. Choice of age range is useful  and life expectancies at any age. Choice of age range is useful
 for extrapolation. In our data file, ages varies from age 70 to  for extrapolation. In our data file, ages varies from age 70 to
 102. Setting bage=50 and fage=100, makes the program computing  102. It is possible to get extrapolated stationary prevalence by
 life expectancy from age bage to age fage. As we use a model, we  age ranging from agemin to agemax.
 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.</p>  
   
 <p>Similarly, it is possible to get extrapolated stationary  
 prevalence by age ranging from agemin to agemax. </p>  
   
   <br>Setting bage=50 (begin age) and fage=100 (final age), makes
   the program computing life expectancy from age 'bage' to age
   'fage'. As we use a model, we can interessingly compute life
   expectancy on a wider age range than the age range from the data.
   But the model can be rather wrong on much larger intervals.
   Program is limited to around 120 for upper age!
 <ul>  <ul>
     <li><b>agemin=</b> Minimum age for calculation of the      <li><b>agemin=</b> Minimum age for calculation of the
         stationary prevalence </li>          stationary prevalence </li>
Line 510  color="#FF0000"> the observed prevalence Line 555  color="#FF0000"> the observed prevalence
   
 <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>  <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
   
 <p>Statements 'begin-prev-date' and 'end-prev-date' allow to  <br>Statements 'begin-prev-date' and 'end-prev-date' allow to
 select the period in which we calculate the observed prevalences  select the period in which we calculate the observed prevalences
 in each state. In this example, the prevalences are calculated on  in each state. In this example, the prevalences are calculated on
 data survey collected between 1 january 1984 and 1 june 1988. </p>  data survey collected between 1 january 1984 and 1 june 1988.
   
 <ul>  <ul>
     <li><strong>begin-prev-date= </strong>Starting date      <li><strong>begin-prev-date= </strong>Starting date
         (day/month/year)</li>          (day/month/year)</li>
Line 527  expectancies</font></h4> Line 571  expectancies</font></h4>
   
 <pre>pop_based=0</pre>  <pre>pop_based=0</pre>
   
 <p>The user has the possibility to choose between  <p>The program computes status-based health expectancies, i.e
 population-based or status-based health expectancies. If  health expectancies which depends on your initial health state.
 pop_based=0 then status-based health expectancies are computed  If you are healthy your healthy life expectancy (e11) is higher
 and if pop_based=1, the programme computes population-based  than if you were disabled (e21, with e11 &gt; e21).<br>
 health expectancies. Health expectancies are weighted averages of  To compute a healthy life expectancy independant of the initial
 health expectancies respective of the initial state. For a  status we have to weight e11 and e21 according to the probability
 status-based index, the weights are the cross-sectional  to be in each state at initial age or, with other word, according
 prevalences observed between two dates, as <a href="#Computing">previously  to the proportion of people in each state.<br>
 explained</a>, whereas for a population-based index, the weights  We prefer computing a 'pure' period healthy life expectancy based
 are the stationary prevalences.</p>  only on the transtion forces. Then the weights are simply the
   stationnary prevalences or 'implied' prevalences at the initial
   age.<br>
   Some other people would like to use the cross-sectional
   prevalences (the &quot;Sullivan prevalences&quot;) observed at
   the initial age during a period of time <a href="#Computing">defined
   just above</a>. <br>
   
   <ul>
       <li><strong>popbased= 0 </strong>Health expectancies are
           computed at each age from stationary prevalences
           'expected' at this initial age.</li>
       <li><strong>popbased= 1 </strong>Health expectancies are
           computed at each age from cross-sectional 'observed'
           prevalence at this initial age. As all the population is
           not observed at the same exact date we define a short
           period were the observed prevalence is computed.</li>
   </ul>
   
 <h4><font color="#FF0000">Prevalence forecasting </font></h4>  <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
   
 <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>  <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
   
 <p>Prevalence and population projections are only available if  <p>Prevalence and population projections are only available if
 the interpolation unit is a month, i.e. stepm=1. The programme  the interpolation unit is a month, i.e. stepm=1 and if there are
 estimates the prevalence in each state at a precise date  no covariate. The programme estimates the prevalence in each
 expressed in day/month/year. The programme computes one  state at a precise date expressed in day/month/year. The
 forecasted prevalence a year from a starting date (1 january of  programme computes one forecasted prevalence a year from a
 1989 in this example) to a final date (1 january 1992). The  starting date (1 january of 1989 in this example) to a final date
 statement mov_average allows to compute smoothed forecasted  (1 january 1992). The statement mov_average allows to compute
 prevalences with a five-age moving average centered at the  smoothed forecasted prevalences with a five-age moving average
 mid-age of the five-age period. </p>  centered at the mid-age of the five-age period. <br>
   
 <ul>  <ul>
     <li><strong>starting-proj-date</strong>= starting date      <li><strong>starting-proj-date</strong>= starting date
Line 569  forecasting </font></h4> Line 630  forecasting </font></h4>
 <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>  <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
   
 <p>This command is available if the interpolation unit is a  <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>  month, i.e. stepm=1 and if popforecast=1. From a data file
   including age and number of persons alive at the precise date
 <p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>  &#145;popfiledate&#146;, you can forecast the number of persons
 : </b>age numbers</p>  in each state until date &#145;last-popfiledate&#146;. In this
   example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
 <p>&nbsp;</p>  includes real data which are the Japanese population in 1989.<br>
   
   <ul type="disc">
       <li class="MsoNormal"
       style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
           0 </b>Option for population forecasting. If
           popforecast=1, the programme does the forecasting<b>.</b></li>
       <li class="MsoNormal"
       style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
           </b>name of the population file</li>
       <li class="MsoNormal"
       style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
           date of the population population</li>
       <li class="MsoNormal"
       style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
           date of the last population projection&nbsp;</li>
   </ul>
   
 <hr>  <hr>
   
 <h2><a name="running"></a><font color="#00006A">Running Imach  <h2><a name="running"></a><font color="#00006A">Running Imach
 with this example</font></h2>  with this example</font></h2>
   
 <p>We assume that you entered your <a href="biaspar.imach">1st_example  We assume that you typed in your <a href="biaspar.imach">1st_example
 parameter file</a> as explained <a href="#biaspar">above</a>. To  parameter file</a> as explained <a href="#biaspar">above</a>.
 run the program you should click on the imach.exe icon and enter  <br>To run the program you should either:
   <ul> <li> click on the imach.exe icon and enter
 the name of the parameter file which is for example <a  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>  href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
 (you also can click on the biaspar.txt icon located in <br>  <li> You also can locate the biaspar.imach icon in
 <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with  <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with
 the mouse on the imach window).<br>  the mouse on the imach window).
 </p>  <li> With latest version (0.7 and higher) if you setup windows in order to
   understand ".imach" extension you can right click the
   biaspar.imach icon and either edit with notepad the parameter file or
   execute it with imach or whatever.
   </ul>  
   
 <p>The time to converge depends on the step unit that you used (1  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  month is cpu consuming), on the number of cases, and on the
 number of variables.</p>  number of variables.
   
 <p>The program outputs many files. Most of them are files which  <br>The program outputs many files. Most of them are files which
 will be plotted for better understanding.</p>  will be plotted for better understanding.
   
 <hr>  <hr>
   
Line 608  with a grapher. We use Gnuplot which is Line 690  with a grapher. We use Gnuplot which is
 program copyrighted but freely distributed. A gnuplot reference  program copyrighted but freely distributed. A gnuplot reference
 manual is available <a href="http://www.gnuplot.info/">here</a>. <br>  manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
 When the running is finished, the user should enter a caracter  When the running is finished, the user should enter a caracter
 for plotting and output editing. </p>  for plotting and output editing.
   
 <p>These caracters are:</p>  <br>These caracters are:<br>
   
 <ul>  <ul>
     <li>'c' to start again the program from the beginning.</li>      <li>'c' to start again the program from the beginning.</li>
Line 648  people aged 71 is 625+2=627. <br> Line 730  people aged 71 is 625+2=627. <br>
 </p>  </p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and  <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>  covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>
   
 <p>This file contains all the maximisation results: </p>  <p>This file contains all the maximisation results: </p>
   
Line 775  href="erbiaspar.txt"><b>erbiaspar.txt</b Line 857  href="erbiaspar.txt"><b>erbiaspar.txt</b
 72 9.9667 3.0502 4.8663 6.1025  72 9.9667 3.0502 4.8663 6.1025
 73 9.5077 3.0524 4.5044 6.0401 </pre>  73 9.5077 3.0524 4.5044 6.0401 </pre>
   
 <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:  <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
 e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>  e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
   
 <pre><img src="expbiaspar21.gif" width="400" height="300"><img  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
 src="expbiaspar11.gif" width="400" height="300"></pre>  src="expbiaspar11.gif" width="400" height="300"></pre>
   
 <p>For example, life expectancy of a healthy individual at age 70  <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  is 10.42 in the healthy state and 3.04 in the disability state
 (=13.96 years). If he was disable at age 70, his life expectancy  (=13.46 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 5.71 in the
 disability state (=11.85 years). The total life expectancy is a  disability state (=11.35 years). The total life expectancy is a
 weighted mean of both, 13.96 and 11.85; weight is the proportion  weighted mean of both, 13.46 and 11.35; weight is the proportion
 of people disabled at age 70. In order to get a pure period index  of people disabled at age 70. In order to get a pure period index
 (i.e. based only on incidences) we use the <a  (i.e. based only on incidences) we use the <a
 href="#Stationary prevalence in each state">computed or  href="#Stationary prevalence in each state">computed or
Line 813  href="trbiaspar.txt"><font face="Courier Line 895  href="trbiaspar.txt"><font face="Courier
   
 <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>  <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
   
 <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>  <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
   
 <p>Thus, at age 70 the total life expectancy, e..=13.76years is  <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
 the weighted mean of e1.=13.96 and e2.=11.85 by the stationary  the weighted mean of e1.=13.46 and e2.=11.35 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=9.95 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=3.30 is also the life expectancy at age
 70 to be spent in the disability state.</p>  70 to be spent in the disability state.</p>
   
 <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by  <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
Line 921  program while saving the old output file Line 1003  program while saving the old output file
 <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:  <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
 </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>  </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
   
 <p>On a d'abord estimé la date moyenne des interviaew. ie  <p
 13/9/1995. This file contains </p>  style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,
   we have estimated the observed prevalence between 1/1/1984 and
 <p>Example, at date 1/1/1989 : </p>  1/6/1988. The mean date of interview (weighed average of the
   interviews performed between1/1/1984 and 1/6/1988) is estimated
 <p>73 0.807 0.078 0.115 </p>  to be 13/9/1985, as written on the top on the file. Then we
   forecast the probability to be in each state. </p>
 <p>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  <p
 to die is 0.115 at 1/1/1989.</p>  style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,
   at date 1/1/1989 : </p>
   
   <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
   # Forecasting at date 1/1/1989
     73 0.807 0.078 0.115</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">Since
   the minimum age is 70 on the 13/9/1985, the youngest forecasted
   age is 73. This means that at age a person aged 70 at 13/9/1989
   has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
   Similarly, the probability to be in state 2 is 0.078 and the
   probability to die is 0.115. Then, on the 1/1/1989, the
   prevalence of disability at age 73 is estimated to be 0.088.</p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:  <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
 </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>  </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
Line 946  to die is 0.115 at 1/1/1989.</p> Line 1042  to die is 0.115 at 1/1/1989.</p>
 75 487781.02 91367.97 121915.51  75 487781.02 91367.97 121915.51
 74 512892.07 85003.47 117282.76 </pre>  74 512892.07 85003.47 117282.76 </pre>
   
   <p>From the population file, we estimate the number of people in
   each state. At age 73, 645857 persons are in state 1 and 69320
   are in state 2. One year latter, 512892 are still in state 1,
   85003 are in state 2 and 117282 died before 1/1/1990.</p>
   
 <hr>  <hr>
   
 <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>  <h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>
   
 <p>Since you know how to run the program, it is time to test it  <p>Since you know how to run the program, it is time to test it
 on your own computer. Try for example on a parameter file named <a  on your own computer. Try for example on a parameter file named <a
 href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font  href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of <font
 size="2" face="Courier New">mypar.txt</font> included in the  size="2" face="Courier New">mypar.imach</font> included in the
 subdirectory of imach, <font size="2" face="Courier New">mytry</font>.  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"  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  face="Courier New">..\data\mydata.txt</font> if you don't want to
Line 965  question:'<strong>Enter the parameter fi Line 1066  question:'<strong>Enter the parameter fi
   
 <table border="1">  <table border="1">
     <tr>      <tr>
         <td width="100%"><strong>IMACH, Version 0.7</strong><p><strong>Enter          <td width="100%"><strong>IMACH, Version 0.8</strong><p><strong>Enter
         the parameter file name: ..\mytry\imachpar.txt</strong></p>          the parameter file name: ..\mytry\imachpar.imach</strong></p>
         </td>          </td>
     </tr>      </tr>
 </table>  </table>
Line 984  href="imachrun.LOG">this Log file</a> Line 1085  href="imachrun.LOG">this Log file</a>
 #  #
   
 title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3  title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
 ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>  ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
     </li>      </li>
     <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92      <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
   
Line 1089  edit the master file mypar.htm. </font>< Line 1190  edit the master file mypar.htm. </font><
         - Observed prevalence in each state: <a          - Observed prevalence in each state: <a
         href="..\mytry\prmypar.txt">pmypar.txt</a> <br>          href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
         - Estimated parameters and the covariance matrix: <a          - Estimated parameters and the covariance matrix: <a
         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>          href="..\mytry\rmypar.txt">rmypar.imach</a> <br>
         - Stationary prevalence in each state: <a          - Stationary prevalence in each state: <a
         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>          href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
         - Transition probabilities: <a          - Transition probabilities: <a
Line 1112  edit the master file mypar.htm. </font>< Line 1213  edit the master file mypar.htm. </font><
         </li>          </li>
     <li><u>Graphs</u> <br>      <li><u>Graphs</u> <br>
         <br>          <br>
         -<a href="../mytry/pemypar1.gif">One-step transition          -<a href="../mytry/pemypar1.gif">One-step transition probabilities</a><br>
         probabilities</a><br>          -<a href="../mytry/pmypar11.gif">Convergence to the stationary prevalence</a><br>
         -<a href="../mytry/pmypar11.gif">Convergence to the          -<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> <br>
         stationary prevalence</a><br>          -<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> <br>
         -<a href="..\mytry\vmypar11.gif">Observed and stationary          -<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> <br>
         prevalence in state (1) with the confident interval</a> <br>          -<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> <br>
         -<a href="..\mytry\vmypar21.gif">Observed and stationary          -<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li>
         prevalence in state (2) with the confident interval</a> <br>  
         -<a href="..\mytry\expmypar11.gif">Health life  
         expectancies by age and initial health state (1)</a> <br>  
         -<a href="..\mytry\expmypar21.gif">Health life  
         expectancies by age and initial health state (2)</a> <br>  
         -<a href="..\mytry\emypar1.gif">Total life expectancy by  
         age and health expectancies in states (1) and (2).</a> </li>  
 </ul>  </ul>
   
 <p>This software have been partly granted by <a  <p>This software have been partly granted by <a
Line 1138  simple justification (name, email, insti Line 1232  simple justification (name, email, insti
 href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a  href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
 href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>  href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
   
 <p>Latest version (0.7 of February 2002) can be accessed at <a  <p>Latest version (0.8 of March 2002) can be accessed at <a
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>  href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
 </p>  </p>
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