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 <h1 align="center"><font color="#00006A">Computing Health  
 Expectancies using IMaCh</font></h1>  <h1 align="center"><font color="#00006A">Computing Health
   Expectancies using IMaCh</font></h1>
 <h1 align="center"><font color="#00006A" size="5">(a Maximum  
 Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>  <h1 align="center"><font color="#00006A" size="5">(a Maximum
   Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
 <p align="center">&nbsp;</p>  
   <p align="center">&nbsp;</p>
 <p align="center"><a href="http://www.ined.fr/"><img  
 src="logo-ined.gif" border="0" width="151" height="76"></a><img  <p align="center"><a href="http://www.ined.fr/"><img
 src="euroreves2.gif" width="151" height="75"></p>  src="logo-ined.gif" border="0" width="151" height="76"></a><img
   src="euroreves2.gif" width="151" height="75"></p>
 <h3 align="center"><a href="http://www.ined.fr/"><font  
 color="#00006A">INED</font></a><font color="#00006A"> and </font><a  <h3 align="center"><a href="http://www.ined.fr/"><font
 href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>  color="#00006A">INED</font></a><font color="#00006A"> and </font><a
   href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
 <p align="center"><font color="#00006A" size="4"><strong>March  
 2000</strong></font></p>  <p align="center"><font color="#00006A" size="4"><strong>Version
   0.7, February 2002</strong></font></p>
 <hr size="3" color="#EC5E5E">  
   <hr size="3" color="#EC5E5E">
 <p align="center"><font color="#00006A"><strong>Authors of the  
 program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font  <p align="center"><font color="#00006A"><strong>Authors of the
 color="#00006A"><strong>Nicolas Brouard</strong></font></a><font  program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
 color="#00006A"><strong>, senior researcher at the </strong></font><a  color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
 href="http://www.ined.fr"><font color="#00006A"><strong>Institut  color="#00006A"><strong>, senior researcher at the </strong></font><a
 National d'Etudes Démographiques</strong></font></a><font  href="http://www.ined.fr"><font color="#00006A"><strong>Institut
 color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,  National d'Etudes Démographiques</strong></font></a><font
 Health and Epidemiology&quot; Research Unit </strong></font></p>  color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,
   Health and Epidemiology&quot; Research Unit </strong></font></p>
 <p align="center"><font color="#00006A"><strong>and Agnès  
 Lièvre<br clear="left">  <p align="center"><font color="#00006A"><strong>and Agnès
 </strong></font></p>  Lièvre<br clear="left">
   </strong></font></p>
 <h4><font color="#00006A">Contribution to the mathematics: C. R.  
 Heathcote </font><font color="#00006A" size="2">(Australian  <h4><font color="#00006A">Contribution to the mathematics: C. R.
 National University, Canberra).</font></h4>  Heathcote </font><font color="#00006A" size="2">(Australian
   National University, Canberra).</font></h4>
 <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a  
 href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font  <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
 color="#00006A">) </font></h4>  href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
   color="#00006A">) </font></h4>
 <hr>  
   <hr>
 <ul>  
     <li><a href="#intro">Introduction</a> </li>  <ul>
     <li>The detailed statistical model (<a href="docmath.pdf">PDF      <li><a href="#intro">Introduction</a> </li>
         version</a>),(<a href="docmath.ps">ps version</a>) </li>      <li>The detailed statistical model (<a href="docmath.pdf">PDF
     <li><a href="#data">On what kind of data can it be used?</a></li>          version</a>),(<a href="docmath.ps">ps version</a>) </li>
     <li><a href="#datafile">The data file</a> </li>      <li><a href="#data">On what kind of data can it be used?</a></li>
     <li><a href="#biaspar">The parameter file</a> </li>      <li><a href="#datafile">The data file</a> </li>
     <li><a href="#running">Running Imach</a> </li>      <li><a href="#biaspar">The parameter file</a> </li>
     <li><a href="#output">Output files and graphs</a> </li>      <li><a href="#running">Running Imach</a> </li>
     <li><a href="#example">Exemple</a> </li>      <li><a href="#output">Output files and graphs</a> </li>
 </ul>      <li><a href="#example">Exemple</a> </li>
   </ul>
 <hr>  
   <hr>
 <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>  
   <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
 <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal  
 data</b>. Within the family of Health Expectancies (HE),  <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
 Disability-free life expectancy (DFLE) is probably the most  data</b> using the methodology pioneered by Laditka and Wolf (1).
 important index to monitor. In low mortality countries, there is  Within the family of Health Expectancies (HE), Disability-free
 a fear that when mortality declines, the increase in DFLE is not  life expectancy (DFLE) is probably the most important index to
 proportionate to the increase in total Life expectancy. This case  monitor. In low mortality countries, there is a fear that when
 is called the <em>Expansion of morbidity</em>. Most of the data  mortality declines, the increase in DFLE is not proportionate to
 collected today, in particular by the international <a  the increase in total Life expectancy. This case is called the <em>Expansion
 href="http://euroreves/reves">REVES</a> network on Health  of morbidity</em>. Most of the data collected today, in
 expectancy, and most HE indices based on these data, are <em>cross-sectional</em>.  particular by the international <a href="http://euroreves/reves">REVES</a>
 It means that the information collected comes from a single  network on Health expectancy, and most HE indices based on these
 cross-sectional survey: people from various ages (but mostly old  data, are <em>cross-sectional</em>. It means that the information
 people) are surveyed on their health status at a single date.  collected comes from a single cross-sectional survey: people from
 Proportion of people disabled at each age, can then be measured  various ages (but mostly old people) are surveyed on their health
 at that date. This age-specific prevalence curve is then used to  status at a single date. Proportion of people disabled at each
 distinguish, within the stationary population (which, by  age, can then be measured at that date. This age-specific
 definition, is the life table estimated from the vital statistics  prevalence curve is then used to distinguish, within the
 on mortality at the same date), the disable population from the  stationary population (which, by definition, is the life table
 disability-free population. Life expectancy (LE) (or total  estimated from the vital statistics on mortality at the same
 population divided by the yearly number of births or deaths of  date), the disable population from the disability-free
 this stationary population) is then decomposed into DFLE and DLE.  population. Life expectancy (LE) (or total population divided by
 This method of computing HE is usually called the Sullivan method  the yearly number of births or deaths of this stationary
 (from the name of the author who first described it).</p>  population) is then decomposed into DFLE and DLE. This method of
   computing HE is usually called the Sullivan method (from the name
 <p>Age-specific proportions of people disable are very difficult  of the author who first described it).</p>
 to forecast because each proportion corresponds to historical  
 conditions of the cohort and it is the result of the historical  <p>Age-specific proportions of people disable are very difficult
 flows from entering disability and recovering in the past until  to forecast because each proportion corresponds to historical
 today. The age-specific intensities (or incidence rates) of  conditions of the cohort and it is the result of the historical
 entering disability or recovering a good health, are reflecting  flows from entering disability and recovering in the past until
 actual conditions and therefore can be used at each age to  today. The age-specific intensities (or incidence rates) of
 forecast the future of this cohort. For example if a country is  entering disability or recovering a good health, are reflecting
 improving its technology of prosthesis, the incidence of  actual conditions and therefore can be used at each age to
 recovering the ability to walk will be higher at each (old) age,  forecast the future of this cohort. For example if a country is
 but the prevalence of disability will only slightly reflect an  improving its technology of prosthesis, the incidence of
 improve because the prevalence is mostly affected by the history  recovering the ability to walk will be higher at each (old) age,
 of the cohort and not by recent period effects. To measure the  but the prevalence of disability will only slightly reflect an
 period improvement we have to simulate the future of a cohort of  improve because the prevalence is mostly affected by the history
 new-borns entering or leaving at each age the disability state or  of the cohort and not by recent period effects. To measure the
 dying according to the incidence rates measured today on  period improvement we have to simulate the future of a cohort of
 different cohorts. The proportion of people disabled at each age  new-borns entering or leaving at each age the disability state or
 in this simulated cohort will be much lower (using the exemple of  dying according to the incidence rates measured today on
 an improvement) that the proportions observed at each age in a  different cohorts. The proportion of people disabled at each age
 cross-sectional survey. This new prevalence curve introduced in a  in this simulated cohort will be much lower (using the exemple of
 life table will give a much more actual and realistic HE level  an improvement) that the proportions observed at each age in a
 than the Sullivan method which mostly measured the History of  cross-sectional survey. This new prevalence curve introduced in a
 health conditions in this country.</p>  life table will give a much more actual and realistic HE level
   than the Sullivan method which mostly measured the History of
 <p>Therefore, the main question is how to measure incidence rates  health conditions in this country.</p>
 from cross-longitudinal surveys? This is the goal of the IMaCH  
 program. From your data and using IMaCH you can estimate period  <p>Therefore, the main question is how to measure incidence rates
 HE and not only Sullivan's HE. Also the standard errors of the HE  from cross-longitudinal surveys? This is the goal of the IMaCH
 are computed.</p>  program. From your data and using IMaCH you can estimate period
   HE and not only Sullivan's HE. Also the standard errors of the HE
 <p>A cross-longitudinal survey consists in a first survey  are computed.</p>
 (&quot;cross&quot;) where individuals from different ages are  
 interviewed on their health status or degree of disability. At  <p>A cross-longitudinal survey consists in a first survey
 least a second wave of interviews (&quot;longitudinal&quot;)  (&quot;cross&quot;) where individuals from different ages are
 should measure each new individual health status. Health  interviewed on their health status or degree of disability. At
 expectancies are computed from the transitions observed between  least a second wave of interviews (&quot;longitudinal&quot;)
 waves and are computed for each degree of severity of disability  should measure each new individual health status. Health
 (number of life states). More degrees you consider, more time is  expectancies are computed from the transitions observed between
 necessary to reach the Maximum Likelihood of the parameters  waves and are computed for each degree of severity of disability
 involved in the model. Considering only two states of disability  (number of life states). More degrees you consider, more time is
 (disable and healthy) is generally enough but the computer  necessary to reach the Maximum Likelihood of the parameters
 program works also with more health statuses.<br>  involved in the model. Considering only two states of disability
 <br>  (disable and healthy) is generally enough but the computer
 The simplest model is the multinomial logistic model where <i>pij</i>  program works also with more health statuses.<br>
 is the probability to be observed in state <i>j</i> at the second  <br>
 wave conditional to be observed in state <em>i</em> at the first  The simplest model is the multinomial logistic model where <i>pij</i>
 wave. Therefore a simple model is: log<em>(pij/pii)= aij +  is the probability to be observed in state <i>j</i> at the second
 bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'  wave conditional to be observed in state <em>i</em> at the first
 is a covariate. The advantage that this computer program claims,  wave. Therefore a simple model is: log<em>(pij/pii)= aij +
 comes from that if the delay between waves is not identical for  bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
 each individual, or if some individual missed an interview, the  is a covariate. The advantage that this computer program claims,
 information is not rounded or lost, but taken into account using  comes from that if the delay between waves is not identical for
 an interpolation or extrapolation. <i>hPijx</i> is the  each individual, or if some individual missed an interview, the
 probability to be observed in state <i>i</i> at age <i>x+h</i>  information is not rounded or lost, but taken into account using
 conditional to the observed state <i>i</i> at age <i>x</i>. The  an interpolation or extrapolation. <i>hPijx</i> is the
 delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)  probability to be observed in state <i>i</i> at age <i>x+h</i>
 of unobserved intermediate states. This elementary transition (by  conditional to the observed state <i>i</i> at age <i>x</i>. The
 month or quarter trimester, semester or year) is modeled as a  delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
 multinomial logistic. The <i>hPx</i> matrix is simply the matrix  of unobserved intermediate states. This elementary transition (by
 product of <i>nh*stepm</i> elementary matrices and the  month or quarter trimester, semester or year) is modeled as a
 contribution of each individual to the likelihood is simply <i>hPijx</i>.  multinomial logistic. The <i>hPx</i> matrix is simply the matrix
 <br>  product of <i>nh*stepm</i> elementary matrices and the
 </p>  contribution of each individual to the likelihood is simply <i>hPijx</i>.
   <br>
 <p>The program presented in this manual is a quite general  </p>
 program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated  
 <strong>MA</strong>rkov <strong>CH</strong>ain), designed to  <p>The program presented in this manual is a quite general
 analyse transition data from longitudinal surveys. The first step  program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
 is the parameters estimation of a transition probabilities model  <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
 between an initial status and a final status. From there, the  analyse transition data from longitudinal surveys. The first step
 computer program produces some indicators such as observed and  is the parameters estimation of a transition probabilities model
 stationary prevalence, life expectancies and their variances and  between an initial status and a final status. From there, the
 graphs. Our transition model consists in absorbing and  computer program produces some indicators such as observed and
 non-absorbing states with the possibility of return across the  stationary prevalence, life expectancies and their variances and
 non-absorbing states. The main advantage of this package,  graphs. Our transition model consists in absorbing and
 compared to other programs for the analysis of transition data  non-absorbing states with the possibility of return across the
 (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole  non-absorbing states. The main advantage of this package,
 individual information is used even if an interview is missing, a  compared to other programs for the analysis of transition data
 status or a date is unknown or when the delay between waves is  (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
 not identical for each individual. The program can be executed  individual information is used even if an interview is missing, a
 according to parameters: selection of a sub-sample, number of  status or a date is unknown or when the delay between waves is
 absorbing and non-absorbing states, number of waves taken in  not identical for each individual. The program can be executed
 account (the user inputs the first and the last interview), a  according to parameters: selection of a sub-sample, number of
 tolerance level for the maximization function, the periodicity of  absorbing and non-absorbing states, number of waves taken in
 the transitions (we can compute annual, quaterly or monthly  account (the user inputs the first and the last interview), a
 transitions), covariates in the model. It works on Windows or on  tolerance level for the maximization function, the periodicity of
 Unix.<br>  the transitions (we can compute annual, quarterly or monthly
 </p>  transitions), covariates in the model. It works on Windows or on
   Unix.<br>
 <hr>  </p>
   
 <h2><a name="data"><font color="#00006A">On what kind of data can  <hr>
 it be used?</font></a></h2>  
   <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New
 <p>The minimum data required for a transition model is the  Methods for Analyzing Active Life Expectancy&quot;. <i>Journal of
 recording of a set of individuals interviewed at a first date and  Aging and Health</i>. Vol 10, No. 2. </p>
 interviewed again at least one another time. From the  
 observations of an individual, we obtain a follow-up over time of  <hr>
 the occurrence of a specific event. In this documentation, the  
 event is related to health status at older ages, but the program  <h2><a name="data"><font color="#00006A">On what kind of data can
 can be applied on a lot of longitudinal studies in different  it be used?</font></a></h2>
 contexts. To build the data file explained into the next section,  
 you must have the month and year of each interview and the  <p>The minimum data required for a transition model is the
 corresponding health status. But in order to get age, date of  recording of a set of individuals interviewed at a first date and
 birth (month and year) is required (missing values is allowed for  interviewed again at least one another time. From the
 month). Date of death (month and year) is an important  observations of an individual, we obtain a follow-up over time of
 information also required if the individual is dead. Shorter  the occurrence of a specific event. In this documentation, the
 steps (i.e. a month) will more closely take into account the  event is related to health status at older ages, but the program
 survival time after the last interview.</p>  can be applied on a lot of longitudinal studies in different
   contexts. To build the data file explained into the next section,
 <hr>  you must have the month and year of each interview and the
   corresponding health status. But in order to get age, date of
 <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>  birth (month and year) is required (missing values is allowed for
   month). Date of death (month and year) is an important
 <p>In this example, 8,000 people have been interviewed in a  information also required if the individual is dead. Shorter
 cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).  steps (i.e. a month) will more closely take into account the
 Some people missed 1, 2 or 3 interviews. Health statuses are  survival time after the last interview.</p>
 healthy (1) and disable (2). The survey is not a real one. It is  
 a simulation of the American Longitudinal Survey on Aging. The  <hr>
 disability state is defined if the individual missed one of four  
 ADL (Activity of daily living, like bathing, eating, walking).  <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
 Therefore, even is the individuals interviewed in the sample are  
 virtual, the information brought with this sample is close to the  <p>In this example, 8,000 people have been interviewed in a
 situation of the United States. Sex is not recorded is this  cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
 sample.</p>  Some people missed 1, 2 or 3 interviews. Health statuses are
   healthy (1) and disable (2). The survey is not a real one. It is
 <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>  a simulation of the American Longitudinal Survey on Aging. The
 in this first example) is an individual record which fields are: </p>  disability state is defined if the individual missed one of four
   ADL (Activity of daily living, like bathing, eating, walking).
 <ul>  Therefore, even is the individuals interviewed in the sample are
     <li><b>Index number</b>: positive number (field 1) </li>  virtual, the information brought with this sample is close to the
     <li><b>First covariate</b> positive number (field 2) </li>  situation of the United States. Sex is not recorded is this
     <li><b>Second covariate</b> positive number (field 3) </li>  sample.</p>
     <li><a name="Weight"><b>Weight</b></a>: positive number  
         (field 4) . In most surveys individuals are weighted  <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
         according to the stratification of the sample.</li>  in this first example) is an individual record which fields are: </p>
     <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are  
         coded as 99/9999 (field 5) </li>  <ul>
     <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are      <li><b>Index number</b>: positive number (field 1) </li>
         coded as 99/9999 (field 6) </li>      <li><b>First covariate</b> positive number (field 2) </li>
     <li><b>Date of first interview</b>: coded as mm/yyyy. Missing      <li><b>Second covariate</b> positive number (field 3) </li>
         dates are coded as 99/9999 (field 7) </li>      <li><a name="Weight"><b>Weight</b></a>: positive number
     <li><b>Status at first interview</b>: positive number.          (field 4) . In most surveys individuals are weighted
         Missing values ar coded -1. (field 8) </li>          according to the stratification of the sample.</li>
     <li><b>Date of second interview</b>: coded as mm/yyyy.      <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
         Missing dates are coded as 99/9999 (field 9) </li>          coded as 99/9999 (field 5) </li>
     <li><strong>Status at second interview</strong> positive      <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
         number. Missing values ar coded -1. (field 10) </li>          coded as 99/9999 (field 6) </li>
     <li><b>Date of third interview</b>: coded as mm/yyyy. Missing      <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
         dates are coded as 99/9999 (field 11) </li>          dates are coded as 99/9999 (field 7) </li>
     <li><strong>Status at third interview</strong> positive      <li><b>Status at first interview</b>: positive number.
         number. Missing values ar coded -1. (field 12) </li>          Missing values ar coded -1. (field 8) </li>
     <li><b>Date of fourth interview</b>: coded as mm/yyyy.      <li><b>Date of second interview</b>: coded as mm/yyyy.
         Missing dates are coded as 99/9999 (field 13) </li>          Missing dates are coded as 99/9999 (field 9) </li>
     <li><strong>Status at fourth interview</strong> positive      <li><strong>Status at second interview</strong> positive
         number. Missing values are coded -1. (field 14) </li>          number. Missing values ar coded -1. (field 10) </li>
     <li>etc</li>      <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
 </ul>          dates are coded as 99/9999 (field 11) </li>
       <li><strong>Status at third interview</strong> positive
 <p>&nbsp;</p>          number. Missing values ar coded -1. (field 12) </li>
       <li><b>Date of fourth interview</b>: coded as mm/yyyy.
 <p>If your longitudinal survey do not include information about          Missing dates are coded as 99/9999 (field 13) </li>
 weights or covariates, you must fill the column with a number      <li><strong>Status at fourth interview</strong> positive
 (e.g. 1) because a missing field is not allowed.</p>          number. Missing values are coded -1. (field 14) </li>
       <li>etc</li>
 <hr>  </ul>
   
 <h2><font color="#00006A">Your first example parameter file</font><a  <p>&nbsp;</p>
 href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>  
   <p>If your longitudinal survey do not include information about
 <h2><a name="biaspar"></a>#Imach version 0.63, February 2000,  weights or covariates, you must fill the column with a number
 INED-EUROREVES </h2>  (e.g. 1) because a missing field is not allowed.</p>
   
 <p>This is a comment. Comments start with a '#'.</p>  <hr>
   
 <h4><font color="#FF0000">First uncommented line</font></h4>  <h2><font color="#00006A">Your first example parameter file</font><a
   href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
 <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>  
   <h2><a name="biaspar"></a>#Imach version 0.7, February 2002,
 <ul>  INED-EUROREVES </h2>
     <li><b>title=</b> 1st_example is title of the run. </li>  
     <li><b>datafile=</b>data1.txt is the name of the data set.  <p>This is a comment. Comments start with a '#'.</p>
         Our example is a six years follow-up survey. It consists  
         in a baseline followed by 3 reinterviews. </li>  <h4><font color="#FF0000">First uncommented line</font></h4>
     <li><b>lastobs=</b> 8600 the program is able to run on a  
         subsample where the last observation number is lastobs.  <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
         It can be set a bigger number than the real number of  
         observations (e.g. 100000). In this example, maximisation  <ul>
         will be done on the 8600 first records. </li>      <li><b>title=</b> 1st_example is title of the run. </li>
     <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more      <li><b>datafile=</b>data1.txt is the name of the data set.
         than two interviews in the survey, the program can be run          Our example is a six years follow-up survey. It consists
         on selected transitions periods. firstpass=1 means the          in a baseline followed by 3 reinterviews. </li>
         first interview included in the calculation is the      <li><b>lastobs=</b> 8600 the program is able to run on a
         baseline survey. lastpass=4 means that the information          subsample where the last observation number is lastobs.
         brought by the 4th interview is taken into account.</li>          It can be set a bigger number than the real number of
 </ul>          observations (e.g. 100000). In this example, maximisation
           will be done on the 8600 first records. </li>
 <p>&nbsp;</p>      <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
           than two interviews in the survey, the program can be run
 <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented          on selected transitions periods. firstpass=1 means the
 line</font></a></h4>          first interview included in the calculation is the
           baseline survey. lastpass=4 means that the information
 <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>          brought by the 4th interview is taken into account.</li>
   </ul>
 <ul>  
     <li><b>ftol=1e-8</b> Convergence tolerance on the function  <p>&nbsp;</p>
         value in the maximisation of the likelihood. Choosing a  
         correct value for ftol is difficult. 1e-8 is a correct  <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
         value for a 32 bits computer.</li>  line</font></a></h4>
     <li><b>stepm=1</b> Time unit in months for interpolation.  
         Examples:<ul>  <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
             <li>If stepm=1, the unit is a month </li>  
             <li>If stepm=4, the unit is a trimester</li>  <ul>
             <li>If stepm=12, the unit is a year </li>      <li><b>ftol=1e-8</b> Convergence tolerance on the function
             <li>If stepm=24, the unit is two years</li>          value in the maximisation of the likelihood. Choosing a
             <li>... </li>          correct value for ftol is difficult. 1e-8 is a correct
         </ul>          value for a 32 bits computer.</li>
     </li>      <li><b>stepm=1</b> Time unit in months for interpolation.
     <li><b>ncov=2</b> Number of covariates to be add to the          Examples:<ul>
         model. The intercept and the age parameter are counting              <li>If stepm=1, the unit is a month </li>
         for 2 covariates. For example, if you want to add gender              <li>If stepm=4, the unit is a trimester</li>
         in the covariate vector you must write ncov=3 else              <li>If stepm=12, the unit is a year </li>
         ncov=2. </li>              <li>If stepm=24, the unit is two years</li>
     <li><b>nlstate=2</b> Number of non-absorbing (live) states.              <li>... </li>
         Here we have two alive states: disability-free is coded 1          </ul>
         and disability is coded 2. </li>      </li>
     <li><b>ndeath=1</b> Number of absorbing states. The absorbing      <li><b>ncov=2</b> Number of covariates in the datafile. The
         state death is coded 3. </li>          intercept and the age parameter are counting for 2
     <li><b>maxwav=4</b> Maximum number of waves. The program can          covariates.</li>
         not include more than 4 interviews. </li>      <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
     <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the          Here we have two alive states: disability-free is coded 1
         Maximisation Likelihood Estimation. <ul>          and disability is coded 2. </li>
             <li>If mle=1 the program does the maximisation and      <li><b>ndeath=1</b> Number of absorbing states. The absorbing
                 the calculation of heath expectancies </li>          state death is coded 3. </li>
             <li>If mle=0 the program only does the calculation of      <li><b>maxwav=4</b> Number of waves in the datafile.</li>
                 the health expectancies. </li>      <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
         </ul>          Maximisation Likelihood Estimation. <ul>
     </li>              <li>If mle=1 the program does the maximisation and
     <li><b>weight=0</b> Possibility to add weights. <ul>                  the calculation of health expectancies </li>
             <li>If weight=0 no weights are included </li>              <li>If mle=0 the program only does the calculation of
             <li>If weight=1 the maximisation integrates the                  the health expectancies. </li>
                 weights which are in field <a href="#Weight">4</a></li>          </ul>
         </ul>      </li>
     </li>      <li><b>weight=0</b> Possibility to add weights. <ul>
 </ul>              <li>If weight=0 no weights are included </li>
               <li>If weight=1 the maximisation integrates the
 <h4><font color="#FF0000">Guess values for optimization</font><font                  weights which are in field <a href="#Weight">4</a></li>
 color="#00006A"> </font></h4>          </ul>
       </li>
 <p>You must write the initial guess values of the parameters for  </ul>
 optimization. The number of parameters, <em>N</em> depends on the  
 number of absorbing states and non-absorbing states and on the  <h4><font color="#FF0000">Covariates</font></h4>
 number of covariates. <br>  
 <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +  <p>Intercept and age are systematically included in the model.
 <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>  Additional covariates can be included with the command </p>
 <br>  
 Thus in the simple case with 2 covariates (the model is log  <pre>model=<em>list of covariates</em></pre>
 (pij/pii) = aij + bij * age where intercept and age are the two  
 covariates), and 2 health degrees (1 for disability-free and 2  <ul>
 for disability) and 1 absorbing state (3), you must enter 8      <li>if<strong> model=. </strong>then no covariates are
 initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can          included</li>
 start with zeros as in this example, but if you have a more      <li>if <strong>model=V1</strong> the model includes the first
 precise set (for example from an earlier run) you can enter it          covariate (field 2)</li>
 and it will speed up them<br>      <li>if <strong>model=V2 </strong>the model includes the
 Each of the four lines starts with indices &quot;ij&quot;: <br>          second covariate (field 3)</li>
 <br>      <li>if <strong>model=V1+V2 </strong>the model includes the
 <b>ij aij bij</b> </p>          first and the second covariate (fields 2 and 3)</li>
       <li>if <strong>model=V1*V2 </strong>the model includes the
 <blockquote>          product of the first and the second covariate (fields 2
     <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age          and 3)</li>
 12 -14.155633  0.110794       <li>if <strong>model=V1+V1*age</strong> the model includes
 13  -7.925360  0.032091           the product covariate*age</li>
 21  -1.890135 -0.029473   </ul>
 23  -6.234642  0.022315 </pre>  
 </blockquote>  <h4><font color="#FF0000">Guess values for optimization</font><font
   color="#00006A"> </font></h4>
 <p>or, to simplify: </p>  
   <p>You must write the initial guess values of the parameters for
 <blockquote>  optimization. The number of parameters, <em>N</em> depends on the
     <pre>12 0.0 0.0  number of absorbing states and non-absorbing states and on the
 13 0.0 0.0  number of covariates. <br>
 21 0.0 0.0  <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
 23 0.0 0.0</pre>  <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>
 </blockquote>  <br>
   Thus in the simple case with 2 covariates (the model is log
 <h4><font color="#FF0000">Guess values for computing variances</font></h4>  (pij/pii) = aij + bij * age where intercept and age are the two
   covariates), and 2 health degrees (1 for disability-free and 2
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  for disability) and 1 absorbing state (3), you must enter 8
 used as an input to get the vairous output data files (Health  initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
 expectancies, stationary prevalence etc.) and figures without  start with zeros as in this example, but if you have a more
 rerunning the rather long maximisation phase (mle=0). </p>  precise set (for example from an earlier run) you can enter it
   and it will speed up them<br>
 <p>The scales are small values for the evaluation of numerical  Each of the four lines starts with indices &quot;ij&quot;: <b>ij
 derivatives. These derivatives are used to compute the hessian  aij bij</b> </p>
 matrix of the parameters, that is the inverse of the covariance  
 matrix, and the variances of health expectancies. Each line  <blockquote>
 consists in indices &quot;ij&quot; followed by the initial scales      <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
 (zero to simplify) associated with aij and bij. </p>  12 -14.155633  0.110794
   13  -7.925360  0.032091
 <ul>  21  -1.890135 -0.029473
     <li>If mle=1 you can enter zeros:</li>  23  -6.234642  0.022315 </pre>
 </ul>  </blockquote>
   
 <blockquote>  <p>or, to simplify: </p>
     <pre># Scales (for hessian or gradient estimation)  
 12 0. 0.   <blockquote>
 13 0. 0.       <pre>12 0.0 0.0
 21 0. 0.   13 0.0 0.0
 23 0. 0. </pre>  21 0.0 0.0
 </blockquote>  23 0.0 0.0</pre>
   </blockquote>
 <ul>  
     <li>If mle=0 you must enter a covariance matrix (usually  <h4><font color="#FF0000">Guess values for computing variances</font></h4>
         obtained from an earlier run).</li>  
 </ul>  <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
 <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>  expectancies, stationary prevalence etc.) and figures without
   rerunning the rather long maximisation phase (mle=0). </p>
 <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  <p>The scales are small values for the evaluation of numerical
 expectancies, stationary prevalence etc.) and figures without  derivatives. These derivatives are used to compute the hessian
 rerunning the rather long maximisation phase (mle=0). </p>  matrix of the parameters, that is the inverse of the covariance
   matrix, and the variances of health expectancies. Each line
 <p>Each line starts with indices &quot;ijk&quot; followed by the  consists in indices &quot;ij&quot; followed by the initial scales
 covariances between aij and bij: </p>  (zero to simplify) associated with aij and bij. </p>
   
 <pre>  <ul>
    121 Var(a12)       <li>If mle=1 you can enter zeros:</li>
    122 Cov(b12,a12)  Var(b12)   </ul>
           ...  
    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>  <blockquote>
       <pre># Scales (for hessian or gradient estimation)
 <ul>  12 0. 0.
     <li>If mle=1 you can enter zeros. </li>  13 0. 0.
 </ul>  21 0. 0.
   23 0. 0. </pre>
 <blockquote>  </blockquote>
     <pre># Covariance matrix  
 121 0.  <ul>
 122 0. 0.      <li>If mle=0 you must enter a covariance matrix (usually
 131 0. 0. 0.           obtained from an earlier run).</li>
 132 0. 0. 0. 0.   </ul>
 211 0. 0. 0. 0. 0.   
 212 0. 0. 0. 0. 0. 0.   <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
 231 0. 0. 0. 0. 0. 0. 0.   
 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>  <p>This is an output if <a href="#mle">mle</a>=1. But it can be
 </blockquote>  used as an input to get the various output data files (Health
   expectancies, stationary prevalence etc.) and figures without
 <ul>  rerunning the rather long maximisation phase (mle=0). </p>
     <li>If mle=0 you must enter a covariance matrix (usually  
         obtained from an earlier run).<br>  <p>Each line starts with indices &quot;ijk&quot; followed by the
         </li>  covariances between aij and bij: </p>
 </ul>  
   <pre>
 <h4><a name="biaspar-l"></a><font color="#FF0000">last     121 Var(a12)
 uncommented line</font></h4>     122 Cov(b12,a12)  Var(b12)
             ...
 <pre>agemin=70 agemax=100 bage=50 fage=100</pre>     232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>
   
 <p>Once we obtained the estimated parameters, the program is able  <ul>
 to calculated stationary prevalence, transitions probabilities      <li>If mle=1 you can enter zeros. </li>
 and life expectancies at any age. Choice of age ranges is useful  </ul>
 for extrapolation. In our data file, ages varies from age 70 to  
 102. Setting bage=50 and fage=100, makes the program computing  <blockquote>
 life expectancy from age bage to age fage. As we use a model, we      <pre># Covariance matrix
 can compute life expectancy on a wider age range than the age  121 0.
 range from the data. But the model can be rather wrong on big  122 0. 0.
 intervals.</p>  131 0. 0. 0.
   132 0. 0. 0. 0.
 <p>Similarly, it is possible to get extrapolated stationary  211 0. 0. 0. 0. 0.
 prevalence by age raning from agemin to agemax. </p>  212 0. 0. 0. 0. 0. 0.
   231 0. 0. 0. 0. 0. 0. 0.
 <ul>  232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
     <li><b>agemin=</b> Minimum age for calculation of the  </blockquote>
         stationary prevalence </li>  
     <li><b>agemax=</b> Maximum age for calculation of the  <ul>
         stationary prevalence </li>      <li>If mle=0 you must enter a covariance matrix (usually
     <li><b>bage=</b> Minimum age for calculation of the health          obtained from an earlier run).<br>
         expectancies </li>          </li>
     <li><b>fage=</b> Maximum ages for calculation of the health  </ul>
         expectancies </li>  
 </ul>  <h4><font color="#FF0000">Age range for calculation of stationary
   prevalences and health expectancies</font></h4>
 <hr>  
   <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
 <h2><a name="running"></a><font color="#00006A">Running Imach  
 with this example</font></h2>  <p>Once we obtained the estimated parameters, the program is able
   to calculated stationary prevalence, transitions probabilities
 <p>We assume that you entered your <a href="biaspar.txt">1st_example  and life expectancies at any age. Choice of age range is useful
 parameter file</a> as explained <a href="#biaspar">above</a>. To  for extrapolation. In our data file, ages varies from age 70 to
 run the program you should click on the imach.exe icon and enter  102. Setting bage=50 and fage=100, makes the program computing
 the name of the parameter file which is for example <a  life expectancy from age bage to age fage. As we use a model, we
 href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>  can compute life expectancy on a wider age range than the age
 (you also can click on the biaspar.txt icon located in <br>  range from the data. But the model can be rather wrong on big
 <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with  intervals.</p>
 the mouse on the imach window).<br>  
 </p>  <p>Similarly, it is possible to get extrapolated stationary
   prevalence by age ranging from agemin to agemax. </p>
 <p>The time to converge depends on the step unit that you used (1  
 month is cpu consuming), on the number of cases, and on the  <ul>
 number of variables.</p>      <li><b>agemin=</b> Minimum age for calculation of the
           stationary prevalence </li>
 <p>The program outputs many files. Most of them are files which      <li><b>agemax=</b> Maximum age for calculation of the
 will be plotted for better understanding.</p>          stationary prevalence </li>
       <li><b>bage=</b> Minimum age for calculation of the health
 <hr>          expectancies </li>
       <li><b>fage=</b> Maximum age for calculation of the health
 <h2><a name="output"><font color="#00006A">Output of the program          expectancies </li>
 and graphs</font> </a></h2>  </ul>
   
 <p>Once the optimization is finished, some graphics can be made  <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
 with a grapher. We use Gnuplot which is an interactive plotting  color="#FF0000"> the observed prevalence</font></h4>
 program copyrighted but freely distributed. Imach outputs the  
 source of a gnuplot file, named 'graph.gp', which can be directly  <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
 input into gnuplot.<br>  
 When the running is finished, the user should enter a caracter  <p>Statements 'begin-prev-date' and 'end-prev-date' allow to
 for plotting and output editing. </p>  select the period in which we calculate the observed prevalences
   in each state. In this example, the prevalences are calculated on
 <p>These caracters are:</p>  data survey collected between 1 january 1984 and 1 june 1988. </p>
   
 <ul>  <ul>
     <li>'c' to start again the program from the beginning.</li>      <li><strong>begin-prev-date= </strong>Starting date
     <li>'g' to made graphics. The output graphs are in GIF format          (day/month/year)</li>
         and you have no control over which is produced. If you      <li><strong>end-prev-date= </strong>Final date
         want to modify the graphics or make another one, you          (day/month/year)</li>
         should modify the parameters in the file <b>graph.gp</b>  </ul>
         located in imach\bin. A gnuplot reference manual is  
         available <a  <h4><font color="#FF0000">Population- or status-based health
         href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.  expectancies</font></h4>
     </li>  
     <li>'e' opens the <strong>index.htm</strong> file to edit the  <pre>pop_based=0</pre>
         output files and graphs. </li>  
     <li>'q' for exiting.</li>  <p>The user has the possibility to choose between
 </ul>  population-based or status-based health expectancies. If
   pop_based=0 then status-based health expectancies are computed
 <h5><font size="4"><strong>Results files </strong></font><br>  and if pop_based=1, the programme computes population-based
 <br>  health expectancies. Health expectancies are weighted averages of
 <font color="#EC5E5E" size="3"><strong>- </strong></font><a  health expectancies respective of the initial state. For a
 name="Observed prevalence in each state"><font color="#EC5E5E"  status-based index, the weights are the cross-sectional
 size="3"><strong>Observed prevalence in each state</strong></font></a><font  prevalences observed between two dates, as <a href="#Computing">previously
 color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:  explained</a>, whereas for a population-based index, the weights
 </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>  are the stationary prevalences.</p>
 </h5>  
   <h4><font color="#FF0000">Prevalence forecasting </font></h4>
 <p>The first line is the title and displays each field of the  
 file. The first column is age. The fields 2 and 6 are the  <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
 proportion of individuals in states 1 and 2 respectively as  
 observed during the first exam. Others fields are the numbers of  <p>Prevalence and population projections are only available if
 people in states 1, 2 or more. The number of columns increases if  the interpolation unit is a month, i.e. stepm=1. The programme
 the number of states is higher than 2.<br>  estimates the prevalence in each state at a precise date
 The header of the file is </p>  expressed in day/month/year. The programme computes one
   forecasted prevalence a year from a starting date (1 january of
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  1989 in this example) to a final date (1 january 1992). The
 70 1.00000 631 631 70 0.00000 0 631  statement mov_average allows to compute smoothed forecasted
 71 0.99681 625 627 71 0.00319 2 627   prevalences with a five-age moving average centered at the
 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>  mid-age of the five-age period. </p>
   
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  <ul>
     70 0.95721 604 631 70 0.04279 27 631</pre>      <li><strong>starting-proj-date</strong>= starting date
           (day/month/year) of forecasting</li>
 <p>It means that at age 70, the prevalence in state 1 is 1.000      <li><strong>final-proj-date= </strong>final date
 and in state 2 is 0.00 . At age 71 the number of individuals in          (day/month/year) of forecasting</li>
 state 1 is 625 and in state 2 is 2, hence the total number of      <li><strong>mov_average</strong>= smoothing with a five-age
 people aged 71 is 625+2=627. <br>          moving average centered at the mid-age of the five-age
 </p>          period. The command<strong> mov_average</strong> takes
           value 1 if the prevalences are smoothed and 0 otherwise.</li>
 <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and  </ul>
 covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>  
   <h4><font color="#FF0000">Last uncommented line : Population
 <p>This file contains all the maximisation results: </p>  forecasting </font></h4>
   
 <pre> Number of iterations=47  <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
  -2 log likelihood=46553.005854373667    
  Estimated parameters: a12 = -12.691743 b12 = 0.095819   <p>This command is available if the interpolation unit is a
                        a13 = -7.815392   b13 = 0.031851   month, i.e. stepm=1 and if popforecast=1. From a data file </p>
                        a21 = -1.809895 b21 = -0.030470   
                        a23 = -7.838248  b23 = 0.039490    <p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>
  Covariance matrix: Var(a12) = 1.03611e-001  : </b>age numbers</p>
                     Var(b12) = 1.51173e-005  
                     Var(a13) = 1.08952e-001  <p>&nbsp;</p>
                     Var(b13) = 1.68520e-005    
                     Var(a21) = 4.82801e-001  <hr>
                     Var(b21) = 6.86392e-005  
                     Var(a23) = 2.27587e-001  <h2><a name="running"></a><font color="#00006A">Running Imach
                     Var(b23) = 3.04465e-005   with this example</font></h2>
  </pre>  
   <p>We assume that you entered your <a href="biaspar.imach">1st_example
 <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:  parameter file</a> as explained <a href="#biaspar">above</a>. To
 </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>  run the program you should click on the imach.exe icon and enter
   the name of the parameter file which is for example <a
 <p>Here are the transitions probabilities Pij(x, x+nh) where nh  href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
 is a multiple of 2 years. The first column is the starting age x  (you also can click on the biaspar.txt icon located in <br>
 (from age 50 to 100), the second is age (x+nh) and the others are  <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
 the transition probabilities p11, p12, p13, p21, p22, p23. For  the mouse on the imach window).<br>
 example, line 5 of the file is: </p>  </p>
   
 <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>  <p>The time to converge depends on the step unit that you used (1
   month is cpu consuming), on the number of cases, and on the
 <p>and this means: </p>  number of variables.</p>
   
 <pre>p11(100,106)=0.03286  <p>The program outputs many files. Most of them are files which
 p12(100,106)=0.23512  will be plotted for better understanding.</p>
 p13(100,106)=0.73202  
 p21(100,106)=0.02330  <hr>
 p22(100,106)=0.19210   
 p22(100,106)=0.78460 </pre>  <h2><a name="output"><font color="#00006A">Output of the program
   and graphs</font> </a></h2>
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  
 name="Stationary prevalence in each state"><font color="#EC5E5E"  <p>Once the optimization is finished, some graphics can be made
 size="3"><b>Stationary prevalence in each state</b></font></a><b>:  with a grapher. We use Gnuplot which is an interactive plotting
 </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>  program copyrighted but freely distributed. A gnuplot reference
   manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
 <pre>#Age 1-1 2-2   When the running is finished, the user should enter a caracter
 70 0.92274 0.07726   for plotting and output editing. </p>
 71 0.91420 0.08580   
 72 0.90481 0.09519   <p>These caracters are:</p>
 73 0.89453 0.10547</pre>  
   <ul>
 <p>At age 70 the stationary prevalence is 0.92274 in state 1 and      <li>'c' to start again the program from the beginning.</li>
 0.07726 in state 2. This stationary prevalence differs from      <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
 observed prevalence. Here is the point. The observed prevalence          file to edit the output files and graphs. </li>
 at age 70 results from the incidence of disability, incidence of      <li>'q' for exiting.</li>
 recovery and mortality which occurred in the past of the cohort.  </ul>
 Stationary prevalence results from a simulation with actual  
 incidences and mortality (estimated from this cross-longitudinal  <h5><font size="4"><strong>Results files </strong></font><br>
 survey). It is the best predictive value of the prevalence in the  <br>
 future if &quot;nothing changes in the future&quot;. This is  <font color="#EC5E5E" size="3"><strong>- </strong></font><a
 exactly what demographers do with a Life table. Life expectancy  name="Observed prevalence in each state"><font color="#EC5E5E"
 is the expected mean time to survive if observed mortality rates  size="3"><strong>Observed prevalence in each state</strong></font></a><font
 (incidence of mortality) &quot;remains constant&quot; in the  color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
 future. </p>  </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
   </h5>
 <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of  
 stationary prevalence</b></font><b>: </b><a  <p>The first line is the title and displays each field of the
 href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>  file. The first column is age. The fields 2 and 6 are the
   proportion of individuals in states 1 and 2 respectively as
 <p>The stationary prevalence has to be compared with the observed  observed during the first exam. Others fields are the numbers of
 prevalence by age. But both are statistical estimates and  people in states 1, 2 or more. The number of columns increases if
 subjected to stochastic errors due to the size of the sample, the  the number of states is higher than 2.<br>
 design of the survey, and, for the stationary prevalence to the  The header of the file is </p>
 model used and fitted. It is possible to compute the standard  
 deviation of the stationary prevalence at each age.</p>  <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
   70 1.00000 631 631 70 0.00000 0 631
 <h6><font color="#EC5E5E" size="3">Observed and stationary  71 0.99681 625 627 71 0.00319 2 627
 prevalence in state (2=disable) with the confident interval</font>:<b>  72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
 vbiaspar2.gif</b></h6>  
   <p>It means that at age 70, the prevalence in state 1 is 1.000
 <p><br>  and in state 2 is 0.00 . At age 71 the number of individuals in
 This graph exhibits the stationary prevalence in state (2) with  state 1 is 625 and in state 2 is 2, hence the total number of
 the confidence interval in red. The green curve is the observed  people aged 71 is 625+2=627. <br>
 prevalence (or proportion of individuals in state (2)). Without  </p>
 discussing the results (it is not the purpose here), we observe  
 that the green curve is rather below the stationary prevalence.  <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
 It suggests an increase of the disability prevalence in the  covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
 future.</p>  
   <p>This file contains all the maximisation results: </p>
 <p><img src="vbiaspar2.gif" width="400" height="300"></p>  
   <pre> -2 log likelihood= 21660.918613445392
 <h6><font color="#EC5E5E" size="3"><b>Convergence to the   Estimated parameters: a12 = -12.290174 b12 = 0.092161
 stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>                         a13 = -9.155590  b13 = 0.046627
 <img src="pbiaspar1.gif" width="400" height="300"> </h6>                         a21 = -2.629849  b21 = -0.022030
                          a23 = -7.958519  b23 = 0.042614  
 <p>This graph plots the conditional transition probabilities from   Covariance matrix: Var(a12) = 1.47453e-001
 an initial state (1=healthy in red at the bottom, or 2=disable in                      Var(b12) = 2.18676e-005
 green on top) at age <em>x </em>to the final state 2=disable<em> </em>at                      Var(a13) = 2.09715e-001
 age <em>x+h. </em>Conditional means at the condition to be alive                      Var(b13) = 3.28937e-005  
 at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The                      Var(a21) = 9.19832e-001
 curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>                      Var(b21) = 1.29229e-004
 + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary                      Var(a23) = 4.48405e-001
 prevalence of disability</em>. In order to get the stationary                      Var(b23) = 5.85631e-005
 prevalence at age 70 we should start the process at an earlier   </pre>
 age, i.e.50. If the disability state is defined by severe  
 disability criteria with only a few chance to recover, then the  <p>By substitution of these parameters in the regression model,
 incidence of recovery is low and the time to convergence is  we obtain the elementary transition probabilities:</p>
 probably longer. But we don't have experience yet.</p>  
   <p><img src="pebiaspar1.gif" width="400" height="300"></p>
 <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age  
 and initial health status</b></font><b>: </b><a  <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
 href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>  </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
   
 <pre># Health expectancies   <p>Here are the transitions probabilities Pij(x, x+nh) where nh
 # Age 1-1 1-2 2-1 2-2   is a multiple of 2 years. The first column is the starting age x
 70 10.7297 2.7809 6.3440 5.9813   (from age 50 to 100), the second is age (x+nh) and the others are
 71 10.3078 2.8233 5.9295 5.9959   the transition probabilities p11, p12, p13, p21, p22, p23. For
 72 9.8927 2.8643 5.5305 6.0033   example, line 5 of the file is: </p>
 73 9.4848 2.9036 5.1474 6.0035 </pre>  
   <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
 <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:  
 e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>  <p>and this means: </p>
   
 <pre><img src="exbiaspar1.gif" width="400" height="300"><img  <pre>p11(100,106)=0.02655
 src="exbiaspar2.gif" width="400" height="300"></pre>  p12(100,106)=0.17622
   p13(100,106)=0.79722
 <p>For example, life expectancy of a healthy individual at age 70  p21(100,106)=0.01809
 is 10.73 in the healthy state and 2.78 in the disability state  p22(100,106)=0.13678
 (=13.51 years). If he was disable at age 70, his life expectancy  p22(100,106)=0.84513 </pre>
 will be shorter, 6.34 in the healthy state and 5.98 in the  
 disability state (=12.32 years). The total life expectancy is a  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 weighted mean of both, 13.51 and 12.32; weight is the proportion  name="Stationary prevalence in each state"><font color="#EC5E5E"
 of people disabled at age 70. In order to get a pure period index  size="3"><b>Stationary prevalence in each state</b></font></a><b>:
 (i.e. based only on incidences) we use the <a  </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
 href="#Stationary prevalence in each state">computed or  
 stationary prevalence</a> at age 70 (i.e. computed from  <pre>#Prevalence
 incidences at earlier ages) instead of the <a  #Age 1-1 2-2
 href="#Observed prevalence in each state">observed prevalence</a>  
 (for example at first exam) (<a href="#Health expectancies">see  #************
 below</a>).</p>  70 0.90134 0.09866
   71 0.89177 0.10823
 <h5><font color="#EC5E5E" size="3"><b>- Variances of life  72 0.88139 0.11861
 expectancies by age and initial health status</b></font><b>: </b><a  73 0.87015 0.12985 </pre>
 href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>  
   <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
 <p>For example, the covariances of life expectancies Cov(ei,ej)  0.09866 in state 2. This stationary prevalence differs from
 at age 50 are (line 3) </p>  observed prevalence. Here is the point. The observed prevalence
   at age 70 results from the incidence of disability, incidence of
 <pre>   Cov(e1,e1)=0.4667  Cov(e1,e2)=0.0605=Cov(e2,e1)  Cov(e2,e2)=0.0183</pre>  recovery and mortality which occurred in the past of the cohort.
   Stationary prevalence results from a simulation with actual
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  incidences and mortality (estimated from this cross-longitudinal
 name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health  survey). It is the best predictive value of the prevalence in the
 expectancies</b></font></a><font color="#EC5E5E" size="3"><b>  future if &quot;nothing changes in the future&quot;. This is
 with standard errors in parentheses</b></font><b>: </b><a  exactly what demographers do with a Life table. Life expectancy
 href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>  is the expected mean time to survive if observed mortality rates
   (incidence of mortality) &quot;remains constant&quot; in the
 <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>  future. </p>
   
 <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>  <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
   stationary prevalence</b></font><b>: </b><a
 <p>Thus, at age 70 the total life expectancy, e..=13.42 years is  href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
 the weighted mean of e1.=13.51 and e2.=12.32 by the stationary  
 prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in  <p>The stationary prevalence has to be compared with the observed
 state 2, respectively (the sum is equal to one). e.1=10.39 is the  prevalence by age. But both are statistical estimates and
 Disability-free life expectancy at age 70 (it is again a weighted  subjected to stochastic errors due to the size of the sample, the
 mean of e11 and e21). e.2=3.03 is also the life expectancy at age  design of the survey, and, for the stationary prevalence to the
 70 to be spent in the disability state.</p>  model used and fitted. It is possible to compute the standard
   deviation of the stationary prevalence at each age.</p>
 <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by  
 age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:  <h5><font color="#EC5E5E" size="3">-Observed and stationary
 ebiaspar.gif</b></h6>  prevalence in state (2=disable) with the confident interval</font>:<b>
   </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
 <p>This figure represents the health expectancies and the total  
 life expectancy with the confident interval in dashed curve. </p>  <p>This graph exhibits the stationary prevalence in state (2)
   with the confidence interval in red. The green curve is the
 <pre>        <img src="ebiaspar.gif" width="400" height="300"></pre>  observed prevalence (or proportion of individuals in state (2)).
   Without discussing the results (it is not the purpose here), we
 <p>Standard deviations (obtained from the information matrix of  observe that the green curve is rather below the stationary
 the model) of these quantities are very useful.  prevalence. It suggests an increase of the disability prevalence
 Cross-longitudinal surveys are costly and do not involve huge  in the future.</p>
 samples, generally a few thousands; therefore it is very  
 important to have an idea of the standard deviation of our  <p><img src="vbiaspar21.gif" width="400" height="300"></p>
 estimates. It has been a big challenge to compute the Health  
 Expectancy standard deviations. Don't be confuse: life expectancy  <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
 is, as any expected value, the mean of a distribution; but here  stationary prevalence of disability</b></font><b>: </b><a
 we are not computing the standard deviation of the distribution,  href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
 but the standard deviation of the estimate of the mean.</p>  <img src="pbiaspar11.gif" width="400" height="300"> </h5>
   
 <p>Our health expectancies estimates vary according to the sample  <p>This graph plots the conditional transition probabilities from
 size (and the standard deviations give confidence intervals of  an initial state (1=healthy in red at the bottom, or 2=disable in
 the estimate) but also according to the model fitted. Let us  green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
 explain it in more details.</p>  age <em>x+h. </em>Conditional means at the condition to be alive
   at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
 <p>Choosing a model means ar least two kind of choices. First we  curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
 have to decide the number of disability states. Second we have to  + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
 design, within the logit model family, the model: variables,  prevalence of disability</em>. In order to get the stationary
 covariables, confonding factors etc. to be included.</p>  prevalence at age 70 we should start the process at an earlier
   age, i.e.50. If the disability state is defined by severe
 <p>More disability states we have, better is our demographical  disability criteria with only a few chance to recover, then the
 approach of the disability process, but smaller are the number of  incidence of recovery is low and the time to convergence is
 transitions between each state and higher is the noise in the  probably longer. But we don't have experience yet.</p>
 measurement. We do not have enough experiments of the various  
 models to summarize the advantages and disadvantages, but it is  <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
 important to say that even if we had huge and unbiased samples,  and initial health status</b></font><b>: </b><a
 the total life expectancy computed from a cross-longitudinal  href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
 survey, varies with the number of states. If we define only two  
 states, alive or dead, we find the usual life expectancy where it  <pre># Health expectancies
 is assumed that at each age, people are at the same risk to die.  # Age 1-1 1-2 2-1 2-2
 If we are differentiating the alive state into healthy and  70 10.9226 3.0401 5.6488 6.2122
 disable, and as the mortality from the disability state is higher  71 10.4384 3.0461 5.2477 6.1599
 than the mortality from the healthy state, we are introducing  72 9.9667 3.0502 4.8663 6.1025
 heterogeneity in the risk of dying. The total mortality at each  73 9.5077 3.0524 4.5044 6.0401 </pre>
 age is the weighted mean of the mortality in each state by the  
 prevalence in each state. Therefore if the proportion of people  <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:
 at each age and in each state is different from the stationary  e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>
 equilibrium, there is no reason to find the same total mortality  
 at a particular age. Life expectancy, even if it is a very useful  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
 tool, has a very strong hypothesis of homogeneity of the  src="expbiaspar11.gif" width="400" height="300"></pre>
 population. Our main purpose is not to measure differential  
 mortality but to measure the expected time in a healthy or  <p>For example, life expectancy of a healthy individual at age 70
 disability state in order to maximise the former and minimize the  is 10.92 in the healthy state and 3.04 in the disability state
 latter. But the differential in mortality complexifies the  (=13.96 years). If he was disable at age 70, his life expectancy
 measurement.</p>  will be shorter, 5.64 in the healthy state and 6.21 in the
   disability state (=11.85 years). The total life expectancy is a
 <p>Incidences of disability or recovery are not affected by the  weighted mean of both, 13.96 and 11.85; weight is the proportion
 number of states if these states are independant. But incidences  of people disabled at age 70. In order to get a pure period index
 estimates are dependant on the specification of the model. More  (i.e. based only on incidences) we use the <a
 covariates we added in the logit model better is the model, but  href="#Stationary prevalence in each state">computed or
 some covariates are not well measured, some are confounding  stationary prevalence</a> at age 70 (i.e. computed from
 factors like in any statistical model. The procedure to &quot;fit  incidences at earlier ages) instead of the <a
 the best model' is similar to logistic regression which itself is  href="#Observed prevalence in each state">observed prevalence</a>
 similar to regression analysis. We haven't yet been sofar because  (for example at first exam) (<a href="#Health expectancies">see
 we also have a severe limitation which is the speed of the  below</a>).</p>
 convergence. On a Pentium III, 500 MHz, even the simplest model,  
 estimated by month on 8,000 people may take 4 hours to converge.  <h5><font color="#EC5E5E" size="3"><b>- Variances of life
 Also, the program is not yet a statistical package, which permits  expectancies by age and initial health status</b></font><b>: </b><a
 a simple writing of the variables and the model to take into  href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
 account in the maximisation. The actual program allows only to  
 add simple variables without covariations, like age+sex but  <p>For example, the covariances of life expectancies Cov(ei,ej)
 without age+sex+ age*sex . This can be done from the source code  at age 50 are (line 3) </p>
 (you have to change three lines in the source code) but will  
 never be general enough. But what is to remember, is that  <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</pre>
 incidences or probability of change from one state to another is  
 affected by the variables specified into the model.</p>  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
   name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
 <p>Also, the age range of the people interviewed has a link with  expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
 the age range of the life expectancy which can be estimated by  with standard errors in parentheses</b></font><b>: </b><a
 extrapolation. If your sample ranges from age 70 to 95, you can  href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
 clearly estimate a life expectancy at age 70 and trust your  
 confidence interval which is mostly based on your sample size,  <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
 but if you want to estimate the life expectancy at age 50, you  
 should rely in your model, but fitting a logistic model on a age  <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>
 range of 70-95 and estimating probabilties of transition out of  
 this age range, say at age 50 is very dangerous. At least you  <p>Thus, at age 70 the total life expectancy, e..=13.76years is
 should remember that the confidence interval given by the  the weighted mean of e1.=13.96 and e2.=11.85 by the stationary
 standard deviation of the health expectancies, are under the  prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
 strong assumption that your model is the 'true model', which is  state 2, respectively (the sum is equal to one). e.1=10.40 is the
 probably not the case.</p>  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
 <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter  70 to be spent in the disability state.</p>
 file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>  
   <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
 <p>This copy of the parameter file can be useful to re-run the  age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
 program while saving the old output files. </p>  </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
   
 <hr>  <p>This figure represents the health expectancies and the total
   life expectancy with the confident interval in dashed curve. </p>
 <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>  
   <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>
 <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  <p>Standard deviations (obtained from the information matrix of
 href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a  the model) of these quantities are very useful.
 copy of <font size="2" face="Courier New">mypar.txt</font>  Cross-longitudinal surveys are costly and do not involve huge
 included in the subdirectory of imach, <font size="2"  samples, generally a few thousands; therefore it is very
 face="Courier New">mytry</font>. Edit it to change the name of  important to have an idea of the standard deviation of our
 the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>  estimates. It has been a big challenge to compute the Health
 if you don't want to copy it on the same directory. The file <font  Expectancy standard deviations. Don't be confuse: life expectancy
 face="Courier New">mydata.txt</font> is a smaller file of 3,000  is, as any expected value, the mean of a distribution; but here
 people but still with 4 waves. </p>  we are not computing the standard deviation of the distribution,
   but the standard deviation of the estimate of the mean.</p>
 <p>Click on the imach.exe icon to open a window. Answer to the  
 question:'<strong>Enter the parameter file name:'</strong></p>  <p>Our health expectancies estimates vary according to the sample
   size (and the standard deviations give confidence intervals of
 <table border="1">  the estimate) but also according to the model fitted. Let us
     <tr>  explain it in more details.</p>
         <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter  
         the parameter file name: ..\mytry\imachpar.txt</strong></p>  <p>Choosing a model means ar least two kind of choices. First we
         </td>  have to decide the number of disability states. Second we have to
     </tr>  design, within the logit model family, the model: variables,
 </table>  covariables, confonding factors etc. to be included.</p>
   
 <p>Most of the data files or image files generated, will use the  <p>More disability states we have, better is our demographical
 'imachpar' string into their name. The running time is about 2-3  approach of the disability process, but smaller are the number of
 minutes on a Pentium III. If the execution worked correctly, the  transitions between each state and higher is the noise in the
 outputs files are created in the current directory, and should be  measurement. We do not have enough experiments of the various
 the same as the mypar files initially included in the directory <font  models to summarize the advantages and disadvantages, but it is
 size="2" face="Courier New">mytry</font>.</p>  important to say that even if we had huge and unbiased samples,
   the total life expectancy computed from a cross-longitudinal
 <ul>  survey, varies with the number of states. If we define only two
     <li><pre><u>Output on the screen</u> The output screen looks like <a  states, alive or dead, we find the usual life expectancy where it
 href="imachrun.LOG">this Log file</a>  is assumed that at each age, people are at the same risk to die.
 #  If we are differentiating the alive state into healthy and
   disable, and as the mortality from the disability state is higher
 title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3  than the mortality from the healthy state, we are introducing
 ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>  heterogeneity in the risk of dying. The total mortality at each
     </li>  age is the weighted mean of the mortality in each state by the
     <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92  prevalence in each state. Therefore if the proportion of people
   at each age and in each state is different from the stationary
 Warning, no any valid information for:126 line=126  equilibrium, there is no reason to find the same total mortality
 Warning, no any valid information for:2307 line=2307  at a particular age. Life expectancy, even if it is a very useful
 Delay (in months) between two waves Min=21 Max=51 Mean=24.495826  tool, has a very strong hypothesis of homogeneity of the
 <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>  population. Our main purpose is not to measure differential
 Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14  mortality but to measure the expected time in a healthy or
  prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1  disability state in order to maximise the former and minimize the
 Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>  latter. But the differential in mortality complexifies the
     </li>  measurement.</p>
 </ul>  
   <p>Incidences of disability or recovery are not affected by the
 <p>&nbsp;</p>  number of states if these states are independant. But incidences
   estimates are dependant on the specification of the model. More
 <ul>  covariates we added in the logit model better is the model, but
     <li>Maximisation with the Powell algorithm. 8 directions are  some covariates are not well measured, some are confounding
         given corresponding to the 8 parameters. this can be  factors like in any statistical model. The procedure to &quot;fit
         rather long to get convergence.<br>  the best model' is similar to logistic regression which itself is
         <font size="1" face="Courier New"><br>  similar to regression analysis. We haven't yet been sofar because
         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2  we also have a severe limitation which is the speed of the
         0.000000000000 3<br>  convergence. On a Pentium III, 500 MHz, even the simplest model,
         0.000000000000 4 0.000000000000 5 0.000000000000 6  estimated by month on 8,000 people may take 4 hours to converge.
         0.000000000000 7 <br>  Also, the program is not yet a statistical package, which permits
         0.000000000000 8 0.000000000000<br>  a simple writing of the variables and the model to take into
         1..........2.................3..........4.................5.........<br>  account in the maximisation. The actual program allows only to
         6................7........8...............<br>  add simple variables like age+sex or age+sex+ age*sex but will
         Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283  never be general enough. But what is to remember, is that
         <br>  incidences or probability of change from one state to another is
         2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>  affected by the variables specified into the model.</p>
         5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>  
         8 0.051272038506<br>  <p>Also, the age range of the people interviewed has a link with
         1..............2...........3..............4...........<br>  the age range of the life expectancy which can be estimated by
         5..........6................7...........8.........<br>  extrapolation. If your sample ranges from age 70 to 95, you can
         #Number of iterations = 23, -2 Log likelihood =  clearly estimate a life expectancy at age 70 and trust your
         6744.954042573691<br>  confidence interval which is mostly based on your sample size,
         # Parameters<br>  but if you want to estimate the life expectancy at age 50, you
         12 -12.966061 0.135117 <br>  should rely in your model, but fitting a logistic model on a age
         13 -7.401109 0.067831 <br>  range of 70-95 and estimating probabilties of transition out of
         21 -0.672648 -0.006627 <br>  this age range, say at age 50 is very dangerous. At least you
         23 -5.051297 0.051271 </font><br>  should remember that the confidence interval given by the
         </li>  standard deviation of the health expectancies, are under the
     <li><pre><font size="2">Calculation of the hessian matrix. Wait...  strong assumption that your model is the 'true model', which is
 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78  probably not the case.</p>
   
 Inverting the hessian to get the covariance matrix. Wait...  <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
   file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
 #Hessian matrix#  
 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001   <p>This copy of the parameter file can be useful to re-run the
 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003   program while saving the old output files. </p>
 -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001   
 -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003   <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
 -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003   </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
 -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005   
 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004   <p>On a d'abord estimé la date moyenne des interviaew. ie
 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006   13/9/1995. This file contains </p>
 # Scales  
 12 1.00000e-004 1.00000e-006  <p>Example, at date 1/1/1989 : </p>
 13 1.00000e-004 1.00000e-006  
 21 1.00000e-003 1.00000e-005  <p>73 0.807 0.078 0.115 </p>
 23 1.00000e-004 1.00000e-005  
 # Covariance  <p>This means that at age 73, the probability for a person age 70
   1 5.90661e-001  at 13/9/1989 to be in state 1 is 0.807, in state 2 is 0.078 and
   2 -7.26732e-003 8.98810e-005  to die is 0.115 at 1/1/1989.</p>
   3 8.80177e-002 -1.12706e-003 5.15824e-001  
   4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005  <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
   5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000  </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
   6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004  
   7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000  <pre># Age P.1 P.2 P.3 [Population]
   8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004  # Forecasting at date 1/1/1989
 # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).  75 572685.22 83798.08
   74 621296.51 79767.99
   73 645857.70 69320.60 </pre>
 agemin=70 agemax=100 bage=50 fage=100  
 Computing prevalence limit: result on file 'plrmypar.txt'   <pre># Forecasting at date 1/1/19909
 Computing pij: result on file 'pijrmypar.txt'   76 442986.68 92721.14 120775.48
 Computing Health Expectancies: result on file 'ermypar.txt'   75 487781.02 91367.97 121915.51
 Computing Variance-covariance of DFLEs: file 'vrmypar.txt'   74 512892.07 85003.47 117282.76 </pre>
 Computing Total LEs with variances: file 'trmypar.txt'   
 Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'   <hr>
 End of Imach  
 </font></pre>  <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
     </li>  
 </ul>  <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
 <p><font size="3">Once the running is finished, the program  href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
 requires a caracter:</font></p>  size="2" face="Courier New">mypar.txt</font> included in the
   subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
 <table border="1">  Edit it to change the name of the data file to <font size="2"
     <tr>  face="Courier New">..\data\mydata.txt</font> if you don't want to
         <td width="100%"><strong>Type g for plotting (available  copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
         if mle=1), e to edit output files, c to start again,</strong><p><strong>and  is a smaller file of 3,000 people but still with 4 waves. </p>
         q for exiting:</strong></p>  
         </td>  <p>Click on the imach.exe icon to open a window. Answer to the
     </tr>  question:'<strong>Enter the parameter file name:'</strong></p>
 </table>  
   <table border="1">
 <p><font size="3">First you should enter <strong>g</strong> to      <tr>
 make the figures and then you can edit all the results by typing <strong>e</strong>.          <td width="100%"><strong>IMACH, Version 0.7</strong><p><strong>Enter
 </font></p>          the parameter file name: ..\mytry\imachpar.txt</strong></p>
           </td>
 <ul>      </tr>
     <li><u>Outputs files</u> <br>  </table>
         - index.htm, this file is the master file on which you  
         should click first.<br>  <p>Most of the data files or image files generated, will use the
         - Observed prevalence in each state: <a  'imachpar' string into their name. The running time is about 2-3
         href="..\mytry\prmypar.txt">mypar.txt</a> <br>  minutes on a Pentium III. If the execution worked correctly, the
         - Estimated parameters and the covariance matrix: <a  outputs files are created in the current directory, and should be
         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>  the same as the mypar files initially included in the directory <font
         - Stationary prevalence in each state: <a  size="2" face="Courier New">mytry</font>.</p>
         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>  
         - Transition probabilities: <a  <ul>
         href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>      <li><pre><u>Output on the screen</u> The output screen looks like <a
         - Copy of the parameter file: <a  href="imachrun.LOG">this Log file</a>
         href="..\mytry\ormypar.txt">ormypar.txt</a> <br>  #
         - Life expectancies by age and initial health status: <a  
         href="..\mytry\ermypar.txt">ermypar.txt</a> <br>  title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
         - Variances of life expectancies by age and initial  ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
         health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>      </li>
         <br>      <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
         - Health expectancies with their variances: <a  
         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>  Warning, no any valid information for:126 line=126
         - Standard deviation of stationary prevalence: <a  Warning, no any valid information for:2307 line=2307
         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>  Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
         <br>  <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
         </li>  Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
     <li><u>Graphs</u> <br>   prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
         <br>  Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
         -<a href="..\mytry\vmypar1.gif">Observed and stationary      </li>
         prevalence in state (1) with the confident interval</a> <br>  </ul>
         -<a href="..\mytry\vmypar2.gif">Observed and stationary  
         prevalence in state (2) with the confident interval</a> <br>  <p>&nbsp;</p>
         -<a href="..\mytry\exmypar1.gif">Health life expectancies  
         by age and initial health state (1)</a> <br>  <ul>
         -<a href="..\mytry\exmypar2.gif">Health life expectancies      <li>Maximisation with the Powell algorithm. 8 directions are
         by age and initial health state (2)</a> <br>          given corresponding to the 8 parameters. this can be
         -<a href="..\mytry\emypar.gif">Total life expectancy by          rather long to get convergence.<br>
         age and health expectancies in states (1) and (2).</a> </li>          <font size="1" face="Courier New"><br>
 </ul>          Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
           0.000000000000 3<br>
 <p>This software have been partly granted by <a          0.000000000000 4 0.000000000000 5 0.000000000000 6
 href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted          0.000000000000 7 <br>
 action from the European Union. It will be copyrighted          0.000000000000 8 0.000000000000<br>
 identically to a GNU software product, i.e. program and software          1..........2.................3..........4.................5.........<br>
 can be distributed freely for non commercial use. Sources are not          6................7........8...............<br>
 widely distributed today. You can get them by asking us with a          Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
 simple justification (name, email, institute) <a          <br>
 href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a          2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
 href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>          5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
           8 0.051272038506<br>
 <p>Latest version (0.63 of 16 march 2000) can be accessed at <a          1..............2...........3..............4...........<br>
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>          5..........6................7...........8.........<br>
 </p>          #Number of iterations = 23, -2 Log likelihood =
 </body>          6744.954042573691<br>
 </html>          # Parameters<br>
           12 -12.966061 0.135117 <br>
           13 -7.401109 0.067831 <br>
           21 -0.672648 -0.006627 <br>
           23 -5.051297 0.051271 </font><br>
           </li>
       <li><pre><font size="2">Calculation of the hessian matrix. Wait...
   12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78
   
   Inverting the hessian to get the covariance matrix. Wait...
   
   #Hessian matrix#
   3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
   2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
   -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
   -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
   -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
   -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
   3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
   3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
   # Scales
   12 1.00000e-004 1.00000e-006
   13 1.00000e-004 1.00000e-006
   21 1.00000e-003 1.00000e-005
   23 1.00000e-004 1.00000e-005
   # Covariance
     1 5.90661e-001
     2 -7.26732e-003 8.98810e-005
     3 8.80177e-002 -1.12706e-003 5.15824e-001
     4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
     5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
     6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
     7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
     8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004
   # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
   
   
   agemin=70 agemax=100 bage=50 fage=100
   Computing prevalence limit: result on file 'plrmypar.txt'
   Computing pij: result on file 'pijrmypar.txt'
   Computing Health Expectancies: result on file 'ermypar.txt'
   Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
   Computing Total LEs with variances: file 'trmypar.txt'
   Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
   End of Imach
   </font></pre>
       </li>
   </ul>
   
   <p><font size="3">Once the running is finished, the program
   requires a caracter:</font></p>
   
   <table border="1">
       <tr>
           <td width="100%"><strong>Type e to edit output files, c
           to start again, and q for exiting:</strong></td>
       </tr>
   </table>
   
   <p><font size="3">First you should enter <strong>e </strong>to
   edit the master file mypar.htm. </font></p>
   
   <ul>
       <li><u>Outputs files</u> <br>
           <br>
           - Observed prevalence in each state: <a
           href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
           - Estimated parameters and the covariance matrix: <a
           href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
           - Stationary prevalence in each state: <a
           href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
           - Transition probabilities: <a
           href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
           - Copy of the parameter file: <a
           href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
           - Life expectancies by age and initial health status: <a
           href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
           - Variances of life expectancies by age and initial
           health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
           <br>
           - Health expectancies with their variances: <a
           href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
           - Standard deviation of stationary prevalence: <a
           href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
           - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
           <br>
           - Population forecasting (if popforecast=1): <a
           href="poprmypar.txt">poprmypar.txt</a> <br>
           </li>
       <li><u>Graphs</u> <br>
           <br>
           -<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>
           -<a href="..\mytry\vmypar21.gif">Observed and stationary
           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>
   
   <p>This software have been partly granted by <a
   href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
   action from the European Union. It will be copyrighted
   identically to a GNU software product, i.e. program and software
   can be distributed freely for non commercial use. Sources are not
   widely distributed today. You can get them by asking us with a
   simple justification (name, email, institute) <a
   href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
   href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
   
   <p>Latest version (0.7 of February 2002) can be accessed at <a
   href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
   </p>
   </body>
   </html>

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  Added in v.1.6


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