Diff for /imach096d/doc/imach.htm between versions 1.7 and 1.12

version 1.7, 2002/03/10 15:54:47 version 1.12, 2002/03/13 17:27:44
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 <title>Computing Health Expectancies using IMaCh</title>  <title>Computing Health Expectancies using IMaCh</title>
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Line 30  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
 0.71a, March 2002</strong></font></p>  0.8, March 2002</strong></font></p>
   
 <hr size="3" color="#EC5E5E">  <hr size="3" color="#EC5E5E">
   
Line 272  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 0.71a, March 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 304  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 320  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 348  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 (actually two) 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 368  Additional covariates (actually two) can Line 377  Additional covariates (actually two) can
         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 376  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 397  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 (in most of cases it converges but there is no warranty!): </p>  <p>or, to simplify (in most of cases it converges but there is no
   warranty!): </p>
   
 <blockquote>  <blockquote>
     <pre>12 0.0 0.0      <pre>12 0.0 0.0
Line 406  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 419  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 442  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 467  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 480  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. It is possible to get extrapolated stationary  102. It is possible to get extrapolated stationary prevalence by
 prevalence by age ranging from agemin to agemax. </p>  age ranging from agemin to agemax.
   
   
 <p>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!</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 program computes status-based health expectancies, i.e health  <p>The program computes status-based health expectancies, i.e
 expectancies which depends on your initial health state.  If you are  health expectancies which depends on your initial health state.
 healthy your healthy life expectancy (e11) is higher than if you were  If you are healthy your healthy life expectancy (e11) is higher
 disabled (e21, with e11 &gt; e21).<br>  than if you were disabled (e21, with e11 &gt; e21).<br>
 To compute a healthy life expectancy independant of the initial status  To compute a healthy life expectancy independant of the initial
 we have to weight e11 and e21 according to the probability to be in  status we have to weight e11 and e21 according to the probability
 each state at initial age or, with other word, according to the  to be in each state at initial age or, with other word, according
 proportion of people in each state.<br>  to the proportion of people in each state.<br>
   We prefer computing a 'pure' period healthy life expectancy based
 We prefer computing a 'pure' period healthy life expectancy based only  only on the transtion forces. Then the weights are simply the
 on the transtion forces. Then the weights are simply the stationnary  stationnary prevalences or 'implied' prevalences at the initial
 prevalences or 'implied' prevalences at the initial age.<br>  age.<br>
   Some other people would like to use the cross-sectional
 Some other people would like to use the cross-sectional prevalences  prevalences (the &quot;Sullivan prevalences&quot;) observed at
 (the "Sullivan prevalences") observed at the initial age during a  the initial age during a period of time <a href="#Computing">defined
 period of time <a href="#Computing">defined just above</a>.  just above</a>. <br>
   
 <ul>  <ul>
     <li><strong>popbased= 0 </strong> Health expectancies are computed      <li><strong>popbased= 0 </strong>Health expectancies are
     at each age from stationary prevalences 'expected' at this initial age.</li>          computed at each age from stationary prevalences
     <li><strong>popbased= 1 </strong> Health expectancies are computed          'expected' at this initial age.</li>
     at each age from cross-sectional 'observed' prevalence at this      <li><strong>popbased= 1 </strong>Health expectancies are
     initial age. As all the population is not observed at the same exact date we          computed at each age from cross-sectional 'observed'
     define a short period were the observed prevalence is computed.</li>          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>  </ul>
   
 </p>  
   
 <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</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 the  <p>Prevalence and population projections are only available if
 interpolation unit is a month, i.e. stepm=1 and if there are no  the interpolation unit is a month, i.e. stepm=1 and if there are
 covariate. The programme estimates the prevalence in each state at a  no covariate. The programme estimates the prevalence in each
 precise date 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 1989  programme computes one forecasted prevalence a year from a
 in this example) to a final date (1 january 1992). The statement  starting date (1 january of 1989 in this example) to a final date
 mov_average allows to compute smoothed forecasted prevalences with a  (1 january 1992). The statement mov_average allows to compute
 five-age moving average centered at the mid-age of the five-age  smoothed forecasted prevalences with a five-age moving average
 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 591  including age and number of persons aliv Line 635  including age and number of persons aliv
 &#145;popfiledate&#146;, you can forecast the number of persons  &#145;popfiledate&#146;, you can forecast the number of persons
 in each state until date &#145;last-popfiledate&#146;. In this  in each state until date &#145;last-popfiledate&#146;. In this
 example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>  example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
 includes real data which are the Japanese population in 1989.</p>  includes real data which are the Japanese population in 1989.<br>
   
 <ul type="disc">  <ul type="disc">
     <li class="MsoNormal"      <li class="MsoNormal"
Line 614  includes real data which are the Japanes Line 658  includes real data which are the Japanes
 <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 641  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 681  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 1000  are in state 2. One year latter, 512892 Line 1049  are in state 2. One year latter, 512892
   
 <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 1017  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 0.71</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 1036  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 1141  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 1164  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 1190  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 (0.71a of March 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>
 </body>  </body>
 </html>  </html>

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