Diff for /imach096d/doc/imach.htm between versions 1.2 and 1.7

version 1.2, 2001/03/14 08:24:41 version 1.7, 2002/03/10 15:54:47
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 <html>  <html>
   
 <head>  <head>
Line 28  src="euroreves2.gif" width="151" height= Line 29  src="euroreves2.gif" width="151" height=
 color="#00006A">INED</font></a><font color="#00006A"> and </font><a  color="#00006A">INED</font></a><font color="#00006A"> and </font><a
 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>March  <p align="center"><font color="#00006A" size="4"><strong>Version
 2000</strong></font></p>  0.71a, March 2002</strong></font></p>
   
 <hr size="3" color="#EC5E5E">  <hr size="3" color="#EC5E5E">
   
Line 58  color="#00006A">) </font></h4> Line 59  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 79  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 181  according to parameters: selection of a Line 180  according to parameters: selection of a
 absorbing and non-absorbing states, number of waves taken in  absorbing and non-absorbing states, number of waves taken in
 account (the user inputs the first and the last interview), a  account (the user inputs the first and the last interview), a
 tolerance level for the maximization function, the periodicity of  tolerance level for the maximization function, the periodicity of
 the transitions (we can compute annual, quaterly or monthly  the transitions (we can compute annual, quarterly or monthly
 transitions), covariates in the model. It works on Windows or on  transitions), covariates in the model. It works on Windows or on
 Unix.<br>  Unix.<br>
 </p>  </p>
Line 273  weights or covariates, you must fill the Line 272  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 0.63, February 2000,  <h2><a name="biaspar"></a>#Imach version 0.71a, 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 349  line</font></a></h4> Line 348  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 (actually two) can be included with the command: </p>
   
 <pre>model=<em>list of covariates</em></pre>  <pre>model=<em>list of covariates</em></pre>
   
Line 365  Additional covariates can be included wi Line 364  Additional covariates can be included wi
     <li>if <strong>model=V1*V2 </strong>the model includes the      <li>if <strong>model=V1*V2 </strong>the model includes the
         product of the first and the second covariate (fields 2          product of the first and the second covariate (fields 2
         and 3)</li>          and 3)</li>
       <li>if <strong>model=V1+V1*age</strong> the model includes
           the product covariate*age</li>
 </ul>  </ul>
   
 <h4><font color="#FF0000">Guess values for optimization</font><font  <h4><font color="#FF0000">Guess values for optimization</font><font
Line 385  initials values, a12, b12, a13, b13, a21 Line 386  initials values, a12, b12, a13, b13, a21
 start with zeros as in this example, but if you have a more  start with zeros as in this example, but if you have a more
 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;: <br>  Each of the four lines starts with indices &quot;ij&quot;: <b>ij
 <br>  aij bij</b> </p>
 <b>ij aij bij</b> </p>  
   
 <blockquote>  <blockquote>
     <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age      <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
Line 397  Each of the four lines starts with indic Line 397  Each of the four lines starts with indic
 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 409  Each of the four lines starts with indic Line 409  Each of the four lines starts with indic
 <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
 used as an input to get the vairous 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). </p>
   
Line 440  consists in indices &quot;ij&quot; follo Line 440  consists in indices &quot;ij&quot; follo
 <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>  <h4><font color="#FF0000">Covariance matrix of parameters</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
 used as an input to get the vairous 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). </p>
   
Line 475  covariances between aij and bij: </p> Line 475  covariances between aij and bij: </p>
         </li>          </li>
 </ul>  </ul>
   
 <h4><a name="biaspar-l"></a><font color="#FF0000">last  <h4><font color="#FF0000">Age range for calculation of stationary
 uncommented line</font></h4>  prevalences and health expectancies</font></h4>
   
 <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  <p>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 ranges 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
 life expectancy from age bage to age fage. As we use a model, we  prevalence by age ranging from agemin to agemax. </p>
 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  <p>Setting bage=50 (begin age) and fage=100 (final age), makes the program computing
 prevalence by age raning from agemin to agemax. </p>  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>
   
 <ul>  <ul>
     <li><b>agemin=</b> Minimum age for calculation of the      <li><b>agemin=</b> Minimum age for calculation of the
Line 500  prevalence by age raning from agemin to Line 501  prevalence by age raning from agemin to
         stationary prevalence </li>          stationary prevalence </li>
     <li><b>bage=</b> Minimum age for calculation of the health      <li><b>bage=</b> Minimum age for calculation of the health
         expectancies </li>          expectancies </li>
     <li><b>fage=</b> Maximum ages for calculation of the health      <li><b>fage=</b> Maximum age for calculation of the health
         expectancies </li>          expectancies </li>
 </ul>  </ul>
   
   <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
   color="#FF0000"> the observed prevalence</font></h4>
   
   <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
   select the period in which we calculate the observed prevalences
   in each state. In this example, the prevalences are calculated on
   data survey collected between 1 january 1984 and 1 june 1988. </p>
   
   <ul>
       <li><strong>begin-prev-date= </strong>Starting date
           (day/month/year)</li>
       <li><strong>end-prev-date= </strong>Final date
           (day/month/year)</li>
   </ul>
   
   <h4><font color="#FF0000">Population- or status-based health
   expectancies</font></h4>
   
   <pre>pop_based=0</pre>
   
   <p>The program computes status-based health expectancies, i.e health
   expectancies which depends on your initial health state.  If you are
   healthy your healthy life expectancy (e11) is higher than if you were
   disabled (e21, with e11 &gt; e21).<br>
   To compute a healthy life expectancy independant of the initial status
   we have to weight e11 and e21 according to the probability to be in
   each state at initial age or, with other word, according to the
   proportion of people in each state.<br>
   
   We prefer computing a 'pure' period healthy life expectancy based 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 "Sullivan prevalences") observed at the initial age during a
   period of time <a href="#Computing">defined just above</a>.
   
   <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>
   
   </p>
   
   <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>
   
   <p>Prevalence and population projections are only available if the
   interpolation unit is a month, i.e. stepm=1 and if there are no
   covariate. 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 centered at the mid-age of the five-age
   period. </p>
   
   <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>
   
   <h4><font color="#FF0000">Last uncommented line : Population
   forecasting </font></h4>
   
   <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
   month, i.e. stepm=1 and if popforecast=1. From a data file
   including age and number of persons alive at the precise date
   &#145;popfiledate&#146;, you can forecast the number of persons
   in each state until date &#145;last-popfiledate&#146;. In this
   example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
   includes real data which are the Japanese population in 1989.</p>
   
   <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.txt">1st_example  <p>We assume that you entered 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>. To
 run the program you should click on the imach.exe icon and enter  run the program you should 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
Line 533  and graphs</font> </a></h2> Line 638  and graphs</font> </a></h2>
   
 <p>Once the optimization is finished, some graphics can be made  <p>Once the optimization is finished, some graphics can be made
 with a grapher. We use Gnuplot which is an interactive plotting  with a grapher. We use Gnuplot which is an interactive plotting
 program copyrighted but freely distributed. Imach outputs the  program copyrighted but freely distributed. A gnuplot reference
 source of a gnuplot file, named 'graph.gp', which can be directly  manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
 input into gnuplot.<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>
   
Line 543  for plotting and output editing. </p> Line 647  for plotting and output editing. </p>
   
 <ul>  <ul>
     <li>'c' to start again the program from the beginning.</li>      <li>'c' to start again the program from the beginning.</li>
     <li>'g' to made graphics. The output graphs are in GIF format      <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
         and you have no control over which is produced. If you          file to edit the output files and graphs. </li>
         want to modify the graphics or make another one, you  
         should modify the parameters in the file <b>graph.gp</b>  
         located in imach\bin. A gnuplot reference manual is  
         available <a  
         href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.  
     </li>  
     <li>'e' opens the <strong>index.htm</strong> file to edit the  
         output files and graphs. </li>  
     <li>'q' for exiting.</li>      <li>'q' for exiting.</li>
 </ul>  </ul>
   
Line 578  The header of the file is </p> Line 674  The header of the file is </p>
 71 0.99681 625 627 71 0.00319 2 627  71 0.99681 625 627 71 0.00319 2 627
 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>  72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
   
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  
     70 0.95721 604 631 70 0.04279 27 631</pre>  
   
 <p>It means that at age 70, the prevalence in state 1 is 1.000  <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  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  state 1 is 625 and in state 2 is 2, hence the total number of
Line 592  covariance matrix</b></font><b>: </b><a Line 685  covariance matrix</b></font><b>: </b><a
   
 <p>This file contains all the maximisation results: </p>  <p>This file contains all the maximisation results: </p>
   
 <pre> Number of iterations=47  <pre> -2 log likelihood= 21660.918613445392
  -2 log likelihood=46553.005854373667     Estimated parameters: a12 = -12.290174 b12 = 0.092161
  Estimated parameters: a12 = -12.691743 b12 = 0.095819                         a13 = -9.155590  b13 = 0.046627
                        a13 = -7.815392   b13 = 0.031851                         a21 = -2.629849  b21 = -0.022030
                        a21 = -1.809895 b21 = -0.030470                         a23 = -7.958519  b23 = 0.042614  
                        a23 = -7.838248  b23 = 0.039490     Covariance matrix: Var(a12) = 1.47453e-001
  Covariance matrix: Var(a12) = 1.03611e-001                      Var(b12) = 2.18676e-005
                     Var(b12) = 1.51173e-005                      Var(a13) = 2.09715e-001
                     Var(a13) = 1.08952e-001                      Var(b13) = 3.28937e-005  
                     Var(b13) = 1.68520e-005                        Var(a21) = 9.19832e-001
                     Var(a21) = 4.82801e-001                      Var(b21) = 1.29229e-004
                     Var(b21) = 6.86392e-005                      Var(a23) = 4.48405e-001
                     Var(a23) = 2.27587e-001                      Var(b23) = 5.85631e-005
                     Var(b23) = 3.04465e-005  
  </pre>   </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>:  <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
 </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>  </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
   
Line 617  is a multiple of 2 years. The first colu Line 714  is a multiple of 2 years. The first colu
 the transition probabilities p11, p12, p13, p21, p22, p23. For  the transition probabilities p11, p12, p13, p21, p22, p23. For
 example, line 5 of the file is: </p>  example, line 5 of the file is: </p>
   
 <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>  <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
   
 <p>and this means: </p>  <p>and this means: </p>
   
 <pre>p11(100,106)=0.03286  <pre>p11(100,106)=0.02655
 p12(100,106)=0.23512  p12(100,106)=0.17622
 p13(100,106)=0.73202  p13(100,106)=0.79722
 p21(100,106)=0.02330  p21(100,106)=0.01809
 p22(100,106)=0.19210  p22(100,106)=0.13678
 p22(100,106)=0.78460 </pre>  p22(100,106)=0.84513 </pre>
   
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 name="Stationary prevalence in each state"><font color="#EC5E5E"  name="Stationary prevalence in each state"><font color="#EC5E5E"
 size="3"><b>Stationary prevalence in each state</b></font></a><b>:  size="3"><b>Stationary prevalence in each state</b></font></a><b>:
 </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>  </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
   
 <pre>#Age 1-1 2-2  <pre>#Prevalence
 70 0.92274 0.07726  #Age 1-1 2-2
 71 0.91420 0.08580  
 72 0.90481 0.09519  #************
 73 0.89453 0.10547</pre>  70 0.90134 0.09866
   71 0.89177 0.10823
   72 0.88139 0.11861
   73 0.87015 0.12985 </pre>
   
 <p>At age 70 the stationary prevalence is 0.92274 in state 1 and  <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
 0.07726 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
 recovery and mortality which occurred in the past of the cohort.  recovery and mortality which occurred in the past of the cohort.
Line 664  design of the survey, and, for the stati Line 764  design of the survey, and, for the stati
 model used and fitted. It is possible to compute the standard  model used and fitted. It is possible to compute the standard
 deviation of the stationary prevalence at each age.</p>  deviation of the stationary prevalence at each age.</p>
   
 <h6><font color="#EC5E5E" size="3">Observed and stationary  <h5><font color="#EC5E5E" size="3">-Observed and stationary
 prevalence in state (2=disable) with the confident interval</font>:<b>  prevalence in state (2=disable) with the confident interval</font>:<b>
 vbiaspar2.gif</b></h6>  </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
   
 <p><br>  <p>This graph exhibits the stationary prevalence in state (2)
 This graph exhibits the stationary prevalence in state (2) with  with the confidence interval in red. The green curve is the
 the confidence interval in red. The green curve is the observed  observed prevalence (or proportion of individuals in state (2)).
 prevalence (or proportion of individuals in state (2)). Without  Without discussing the results (it is not the purpose here), we
 discussing the results (it is not the purpose here), we observe  observe that the green curve is rather below the stationary
 that the green curve is rather below the stationary prevalence.  prevalence. It suggests an increase of the disability prevalence
 It suggests an increase of the disability prevalence in the  in the future.</p>
 future.</p>  
   <p><img src="vbiaspar21.gif" width="400" height="300"></p>
 <p><img src="vbiaspar2.gif" width="400" height="300"></p>  
   <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
 <h6><font color="#EC5E5E" size="3"><b>Convergence to the  stationary prevalence of disability</b></font><b>: </b><a
 stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>  href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
 <img src="pbiaspar1.gif" width="400" height="300"> </h6>  <img src="pbiaspar11.gif" width="400" height="300"> </h5>
   
 <p>This graph plots the conditional transition probabilities from  <p>This graph plots the conditional transition probabilities from
 an initial state (1=healthy in red at the bottom, or 2=disable in  an initial state (1=healthy in red at the bottom, or 2=disable in
Line 703  href="erbiaspar.txt"><b>erbiaspar.txt</b Line 803  href="erbiaspar.txt"><b>erbiaspar.txt</b
   
 <pre># Health expectancies  <pre># Health expectancies
 # Age 1-1 1-2 2-1 2-2  # Age 1-1 1-2 2-1 2-2
 70 10.7297 2.7809 6.3440 5.9813  70 10.9226 3.0401 5.6488 6.2122
 71 10.3078 2.8233 5.9295 5.9959  71 10.4384 3.0461 5.2477 6.1599
 72 9.8927 2.8643 5.5305 6.0033  72 9.9667 3.0502 4.8663 6.1025
 73 9.4848 2.9036 5.1474 6.0035 </pre>  73 9.5077 3.0524 4.5044 6.0401 </pre>
   
 <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:  <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
 e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>  e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
   
 <pre><img src="exbiaspar1.gif" width="400" height="300"><img  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
 src="exbiaspar2.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 10.73 in the healthy state and 2.78 in the disability state  is 10.42 in the healthy state and 3.04 in the disability state
 (=13.51 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, 6.34 in the healthy state and 5.98 in the  will be shorter, 5.64 in the healthy state and 5.71 in the
 disability state (=12.32 years). The total life expectancy is a  disability state (=11.35 years). The total life expectancy is a
 weighted mean of both, 13.51 and 12.32; 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 736  href="vrbiaspar.txt"><b>vrbiaspar.txt</b Line 836  href="vrbiaspar.txt"><b>vrbiaspar.txt</b
 <p>For example, the covariances of life expectancies Cov(ei,ej)  <p>For example, the covariances of life expectancies Cov(ei,ej)
 at age 50 are (line 3) </p>  at age 50 are (line 3) </p>
   
 <pre>   Cov(e1,e1)=0.4667  Cov(e1,e2)=0.0605=Cov(e2,e1)  Cov(e2,e2)=0.0183</pre>  <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</pre>
   
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health  name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
Line 746  href="trbiaspar.txt"><font face="Courier Line 846  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 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09) </pre>  <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..=13.42 years is  <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
 the weighted mean of e1.=13.51 and e2.=12.32 by the stationary  the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
 prevalence at age 70 which are 0.92274 in state 1 and 0.07726 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=10.39 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=3.03 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>
   
 <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by  <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
 age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:  age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
 ebiaspar.gif</b></h6>  </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
   
 <p>This figure represents the health expectancies and the total  <p>This figure represents the health expectancies and the total
 life expectancy with the confident interval in dashed curve. </p>  life expectancy with the confident interval in dashed curve. </p>
   
 <pre>        <img src="ebiaspar.gif" width="400" height="300"></pre>  <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>
   
 <p>Standard deviations (obtained from the information matrix of  <p>Standard deviations (obtained from the information matrix of
 the model) of these quantities are very useful.  the model) of these quantities are very useful.
Line 826  estimated by month on 8,000 people may t Line 926  estimated by month on 8,000 people may t
 Also, the program is not yet a statistical package, which permits  Also, the program is not yet a statistical package, which permits
 a simple writing of the variables and the model to take into  a simple writing of the variables and the model to take into
 account in the maximisation. The actual program allows only to  account in the maximisation. The actual program allows only to
 add simple variables without covariations, like age+sex but  add simple variables like age+sex or age+sex+ age*sex but will
 without age+sex+ age*sex . This can be done from the source code  
 (you have to change three lines in the source code) but will  
 never be general enough. But what is to remember, is that  never be general enough. But what is to remember, is that
 incidences or probability of change from one state to another is  incidences or probability of change from one state to another is
 affected by the variables specified into the model.</p>  affected by the variables specified into the model.</p>
Line 853  file</b></font><b>: </b><a href="orbiasp Line 951  file</b></font><b>: </b><a href="orbiasp
 <p>This copy of the parameter file can be useful to re-run the  <p>This copy of the parameter file can be useful to re-run the
 program while saving the old output files. </p>  program while saving the old output files. </p>
   
   <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
   </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></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">First,
   we have estimated the observed prevalence between 1/1/1984 and
   1/6/1988. 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. </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">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>:
   </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
   
   <pre># Age P.1 P.2 P.3 [Population]
   # Forecasting at date 1/1/1989
   75 572685.22 83798.08
   74 621296.51 79767.99
   73 645857.70 69320.60 </pre>
   
   <pre># Forecasting at date 1/1/19909
   76 442986.68 92721.14 120775.48
   75 487781.02 91367.97 121915.51
   74 512892.07 85003.47 117282.76 </pre>
   
   <p>From the population file, we estimate the number of people in
   each state. At age 73, 645857 persons are in state 1 and 69320
   are in state 2. One year latter, 512892 are still in state 1,
   85003 are in state 2 and 117282 died before 1/1/1990.</p>
   
 <hr>  <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></a></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="file://../mytry/imachpar.txt">imachpar.txt</a> which is a  href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
 copy of <font size="2" face="Courier New">mypar.txt</font>  size="2" face="Courier New">mypar.txt</font> included in the
 included in the subdirectory of imach, <font size="2"  subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
 face="Courier New">mytry</font>. Edit it to change the name of  Edit it to change the name of the data file to <font size="2"
 the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>  face="Courier New">..\data\mydata.txt</font> if you don't want to
 if you don't want to copy it on the same directory. The file <font  copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
 face="Courier New">mydata.txt</font> is a smaller file of 3,000  is a smaller file of 3,000 people but still with 4 waves. </p>
 people but still with 4 waves. </p>  
   
 <p>Click on the imach.exe icon to open a window. Answer to the  <p>Click on the imach.exe icon to open a window. Answer to the
 question:'<strong>Enter the parameter file name:'</strong></p>  question:'<strong>Enter the parameter file name:'</strong></p>
   
 <table border="1">  <table border="1">
     <tr>      <tr>
         <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter          <td width="100%"><strong>IMACH, Version 0.71</strong><p><strong>Enter
         the parameter file name: ..\mytry\imachpar.txt</strong></p>          the parameter file name: ..\mytry\imachpar.txt</strong></p>
         </td>          </td>
     </tr>      </tr>
Line 983  requires a caracter:</font></p> Line 1127  requires a caracter:</font></p>
   
 <table border="1">  <table border="1">
     <tr>      <tr>
         <td width="100%"><strong>Type g for plotting (available          <td width="100%"><strong>Type e to edit output files, c
         if mle=1), e to edit output files, c to start again,</strong><p><strong>and          to start again, and q for exiting:</strong></td>
         q for exiting:</strong></p>  
         </td>  
     </tr>      </tr>
 </table>  </table>
   
 <p><font size="3">First you should enter <strong>g</strong> to  <p><font size="3">First you should enter <strong>e </strong>to
 make the figures and then you can edit all the results by typing <strong>e</strong>.  edit the master file mypar.htm. </font></p>
 </font></p>  
   
 <ul>  <ul>
     <li><u>Outputs files</u> <br>      <li><u>Outputs files</u> <br>
         - index.htm, this file is the master file on which you          <br>
         should click first.<br>  
         - Observed prevalence in each state: <a          - Observed prevalence in each state: <a
         href="..\mytry\prmypar.txt">mypar.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.txt</a> <br>
         - Stationary prevalence in each state: <a          - Stationary prevalence in each state: <a
Line 1016  make the figures and then you can edit a Line 1156  make the figures and then you can edit a
         - Health expectancies with their variances: <a          - Health expectancies with their variances: <a
         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>          href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
         - Standard deviation of stationary prevalence: <a          - Standard deviation of stationary prevalence: <a
         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>          href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
           - 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>
     <li><u>Graphs</u> <br>      <li><u>Graphs</u> <br>
         <br>          <br>
         -<a href="..\mytry\vmypar1.gif">Observed and stationary          -<a href="../mytry/pemypar1.gif">One-step transition
           probabilities</a><br>
           -<a href="../mytry/pmypar11.gif">Convergence to the
           stationary prevalence</a><br>
           -<a href="..\mytry\vmypar11.gif">Observed and stationary
         prevalence in state (1) with the confident interval</a> <br>          prevalence in state (1) with the confident interval</a> <br>
         -<a href="..\mytry\vmypar2.gif">Observed and stationary          -<a href="..\mytry\vmypar21.gif">Observed and stationary
         prevalence in state (2) with the confident interval</a> <br>          prevalence in state (2) with the confident interval</a> <br>
         -<a href="..\mytry\exmypar1.gif">Health life expectancies          -<a href="..\mytry\expmypar11.gif">Health life
         by age and initial health state (1)</a> <br>          expectancies by age and initial health state (1)</a> <br>
         -<a href="..\mytry\exmypar2.gif">Health life expectancies          -<a href="..\mytry\expmypar21.gif">Health life
         by age and initial health state (2)</a> <br>          expectancies by age and initial health state (2)</a> <br>
         -<a href="..\mytry\emypar.gif">Total life expectancy by          -<a href="..\mytry\emypar1.gif">Total life expectancy by
         age and health expectancies in states (1) and (2).</a> </li>          age and health expectancies in states (1) and (2).</a> </li>
 </ul>  </ul>
   
Line 1043  simple justification (name, email, insti Line 1190  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 (0.63 of 16 march 2000) can be accessed at <a  <p>Latest version (0.71a of March 2002) can be accessed at <a
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>  href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
 </p>  </p>
 </body>  </body>

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