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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
   64b, May 2001</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, quaterly 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 0.64b, May 2001,
 <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;: <br>
 derivatives. These derivatives are used to compute the hessian  <br>
 matrix of the parameters, that is the inverse of the covariance  <b>ij aij bij</b> </p>
 matrix, and the variances of health expectancies. Each line  
 consists in indices &quot;ij&quot; followed by the initial scales  <blockquote>
 (zero to simplify) associated with aij and bij. </p>      <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
   12 -14.155633  0.110794
 <ul>  13  -7.925360  0.032091
     <li>If mle=1 you can enter zeros:</li>  21  -1.890135 -0.029473
 </ul>  23  -6.234642  0.022315 </pre>
   </blockquote>
 <blockquote>  
     <pre># Scales (for hessian or gradient estimation)  <p>or, to simplify: </p>
 12 0. 0.   
 13 0. 0.   <blockquote>
 21 0. 0.       <pre>12 0.0 0.0
 23 0. 0. </pre>  13 0.0 0.0
 </blockquote>  21 0.0 0.0
   23 0.0 0.0</pre>
 <ul>  </blockquote>
     <li>If mle=0 you must enter a covariance matrix (usually  
         obtained from an earlier run).</li>  <h4><font color="#FF0000">Guess values for computing variances</font></h4>
 </ul>  
   <p>This is an output if <a href="#mle">mle</a>=1. But it can be
 <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>  used as an input to get the vairous output data files (Health
   expectancies, stationary prevalence etc.) and figures without
 <p>This is an output if <a href="#mle">mle</a>=1. But it can be  rerunning the rather long maximisation phase (mle=0). </p>
 used as an input to get the vairous output data files (Health  
 expectancies, stationary prevalence etc.) and figures without  <p>The scales are small values for the evaluation of numerical
 rerunning the rather long maximisation phase (mle=0). </p>  derivatives. These derivatives are used to compute the hessian
   matrix of the parameters, that is the inverse of the covariance
 <p>Each line starts with indices &quot;ijk&quot; followed by the  matrix, and the variances of health expectancies. Each line
 covariances between aij and bij: </p>  consists in indices &quot;ij&quot; followed by the initial scales
   (zero to simplify) associated with aij and bij. </p>
 <pre>  
    121 Var(a12)   <ul>
    122 Cov(b12,a12)  Var(b12)       <li>If mle=1 you can enter zeros:</li>
           ...  </ul>
    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>  
   <blockquote>
 <ul>      <pre># Scales (for hessian or gradient estimation)
     <li>If mle=1 you can enter zeros. </li>  12 0. 0.
 </ul>  13 0. 0.
   21 0. 0.
 <blockquote>  23 0. 0. </pre>
     <pre># Covariance matrix  </blockquote>
 121 0.  
 122 0. 0.  <ul>
 131 0. 0. 0.       <li>If mle=0 you must enter a covariance matrix (usually
 132 0. 0. 0. 0.           obtained from an earlier run).</li>
 211 0. 0. 0. 0. 0.   </ul>
 212 0. 0. 0. 0. 0. 0.   
 231 0. 0. 0. 0. 0. 0. 0.   <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>  
 </blockquote>  <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
 <ul>  expectancies, stationary prevalence etc.) and figures without
     <li>If mle=0 you must enter a covariance matrix (usually  rerunning the rather long maximisation phase (mle=0). </p>
         obtained from an earlier run).<br>  
         </li>  <p>Each line starts with indices &quot;ijk&quot; followed by the
 </ul>  covariances between aij and bij: </p>
   
 <h4><a name="biaspar-l"></a><font color="#FF0000">last  <pre>
 uncommented line</font></h4>     121 Var(a12)
      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  
 to calculated stationary prevalence, transitions probabilities  <ul>
 and life expectancies at any age. Choice of age ranges is useful      <li>If mle=1 you can enter zeros. </li>
 for extrapolation. In our data file, ages varies from age 70 to  </ul>
 102. Setting bage=50 and fage=100, makes the program computing  
 life expectancy from age bage to age fage. As we use a model, we  <blockquote>
 can compute life expectancy on a wider age range than the age      <pre># Covariance matrix
 range from the data. But the model can be rather wrong on big  121 0.
 intervals.</p>  122 0. 0.
   131 0. 0. 0.
 <p>Similarly, it is possible to get extrapolated stationary  132 0. 0. 0. 0.
 prevalence by age raning from agemin to agemax. </p>  211 0. 0. 0. 0. 0.
   212 0. 0. 0. 0. 0. 0.
 <ul>  231 0. 0. 0. 0. 0. 0. 0.
     <li><b>agemin=</b> Minimum age for calculation of the  232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
         stationary prevalence </li>  </blockquote>
     <li><b>agemax=</b> Maximum age for calculation of the  
         stationary prevalence </li>  <ul>
     <li><b>bage=</b> Minimum age for calculation of the health      <li>If mle=0 you must enter a covariance matrix (usually
         expectancies </li>          obtained from an earlier run).<br>
     <li><b>fage=</b> Maximum ages for calculation of the health          </li>
         expectancies </li>  </ul>
 </ul>  
   <h4><a name="biaspar-l"></a><font color="#FF0000">last
 <hr>  uncommented line</font></h4>
   
 <h2><a name="running"></a><font color="#00006A">Running Imach  <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
 with this example</font></h2>  
   <p>Once we obtained the estimated parameters, the program is able
 <p>We assume that you entered your <a href="biaspar.txt">1st_example  to calculated stationary prevalence, transitions probabilities
 parameter file</a> as explained <a href="#biaspar">above</a>. To  and life expectancies at any age. Choice of age ranges is useful
 run the program you should click on the imach.exe icon and enter  for extrapolation. In our data file, ages varies from age 70 to
 the name of the parameter file which is for example <a  102. Setting bage=50 and fage=100, makes the program computing
 href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>  life expectancy from age bage to age fage. As we use a model, we
 (you also can click on the biaspar.txt icon located in <br>  can compute life expectancy on a wider age range than the age
 <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with  range from the data. But the model can be rather wrong on big
 the mouse on the imach window).<br>  intervals.</p>
 </p>  
   <p>Similarly, it is possible to get extrapolated stationary
 <p>The time to converge depends on the step unit that you used (1  prevalence by age raning from agemin to agemax. </p>
 month is cpu consuming), on the number of cases, and on the  
 number of variables.</p>  <ul>
       <li><b>agemin=</b> Minimum age for calculation of the
 <p>The program outputs many files. Most of them are files which          stationary prevalence </li>
 will be plotted for better understanding.</p>      <li><b>agemax=</b> Maximum age for calculation of the
           stationary prevalence </li>
 <hr>      <li><b>bage=</b> Minimum age for calculation of the health
           expectancies </li>
 <h2><a name="output"><font color="#00006A">Output of the program      <li><b>fage=</b> Maximum ages for calculation of the health
 and graphs</font> </a></h2>          expectancies </li>
   </ul>
 <p>Once the optimization is finished, some graphics can be made  
 with a grapher. We use Gnuplot which is an interactive plotting  <hr>
 program copyrighted but freely distributed. Imach outputs the  
 source of a gnuplot file, named 'graph.gp', which can be directly  <h2><a name="running"></a><font color="#00006A">Running Imach
 input into gnuplot.<br>  with this example</font></h2>
 When the running is finished, the user should enter a caracter  
 for plotting and output editing. </p>  <p>We assume that you entered your <a href="biaspar.txt">1st_example
   parameter file</a> as explained <a href="#biaspar">above</a>. To
 <p>These caracters are:</p>  run the program you should click on the imach.exe icon and enter
   the name of the parameter file which is for example <a
 <ul>  href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
     <li>'c' to start again the program from the beginning.</li>  (you also can click on the biaspar.txt icon located in <br>
     <li>'g' to made graphics. The output graphs are in GIF format  <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
         and you have no control over which is produced. If you  the mouse on the imach window).<br>
         want to modify the graphics or make another one, you  </p>
         should modify the parameters in the file <b>graph.gp</b>  
         located in imach\bin. A gnuplot reference manual is  <p>The time to converge depends on the step unit that you used (1
         available <a  month is cpu consuming), on the number of cases, and on the
         href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.  number of variables.</p>
     </li>  
     <li>'e' opens the <strong>index.htm</strong> file to edit the  <p>The program outputs many files. Most of them are files which
         output files and graphs. </li>  will be plotted for better understanding.</p>
     <li>'q' for exiting.</li>  
 </ul>  <hr>
   
 <h5><font size="4"><strong>Results files </strong></font><br>  <h2><a name="output"><font color="#00006A">Output of the program
 <br>  and graphs</font> </a></h2>
 <font color="#EC5E5E" size="3"><strong>- </strong></font><a  
 name="Observed prevalence in each state"><font color="#EC5E5E"  <p>Once the optimization is finished, some graphics can be made
 size="3"><strong>Observed prevalence in each state</strong></font></a><font  with a grapher. We use Gnuplot which is an interactive plotting
 color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:  program copyrighted but freely distributed. A gnuplot reference
 </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>  manual is available <a href="http://www.gnuplot.org/">here</a>. <br>
 </h5>  When the running is finished, the user should enter a caracter
   for plotting and output editing. </p>
 <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  <p>These caracters are:</p>
 proportion of individuals in states 1 and 2 respectively as  
 observed during the first exam. Others fields are the numbers of  <ul>
 people in states 1, 2 or more. The number of columns increases if      <li>'c' to start again the program from the beginning.</li>
 the number of states is higher than 2.<br>      <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
 The header of the file is </p>          file to edit the output files and graphs. </li>
       <li>'q' for exiting.</li>
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  </ul>
 70 1.00000 631 631 70 0.00000 0 631  
 71 0.99681 625 627 71 0.00319 2 627   <h5><font size="4"><strong>Results files </strong></font><br>
 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>  <br>
   <font color="#EC5E5E" size="3"><strong>- </strong></font><a
 <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N  name="Observed prevalence in each state"><font color="#EC5E5E"
     70 0.95721 604 631 70 0.04279 27 631</pre>  size="3"><strong>Observed prevalence in each state</strong></font></a><font
   color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
 <p>It means that at age 70, the prevalence in state 1 is 1.000  </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
 and in state 2 is 0.00 . At age 71 the number of individuals in  </h5>
 state 1 is 625 and in state 2 is 2, hence the total number of  
 people aged 71 is 625+2=627. <br>  <p>The first line is the title and displays each field of the
 </p>  file. The first column is age. The fields 2 and 6 are the
   proportion of individuals in states 1 and 2 respectively as
 <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and  observed during the first exam. Others fields are the numbers of
 covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>  people in states 1, 2 or more. The number of columns increases if
   the number of states is higher than 2.<br>
 <p>This file contains all the maximisation results: </p>  The header of the file is </p>
   
 <pre> Number of iterations=47  <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
  -2 log likelihood=46553.005854373667    70 1.00000 631 631 70 0.00000 0 631
  Estimated parameters: a12 = -12.691743 b12 = 0.095819   71 0.99681 625 627 71 0.00319 2 627
                        a13 = -7.815392   b13 = 0.031851   72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
                        a21 = -1.809895 b21 = -0.030470   
                        a23 = -7.838248  b23 = 0.039490    <p>It means that at age 70, the prevalence in state 1 is 1.000
  Covariance matrix: Var(a12) = 1.03611e-001  and in state 2 is 0.00 . At age 71 the number of individuals in
                     Var(b12) = 1.51173e-005  state 1 is 625 and in state 2 is 2, hence the total number of
                     Var(a13) = 1.08952e-001  people aged 71 is 625+2=627. <br>
                     Var(b13) = 1.68520e-005    </p>
                     Var(a21) = 4.82801e-001  
                     Var(b21) = 6.86392e-005  <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
                     Var(a23) = 2.27587e-001  covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
                     Var(b23) = 3.04465e-005   
  </pre>  <p>This file contains all the maximisation results: </p>
   
 <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:  <pre> -2 log likelihood= 21660.918613445392
 </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>   Estimated parameters: a12 = -12.290174 b12 = 0.092161
                          a13 = -9.155590  b13 = 0.046627
 <p>Here are the transitions probabilities Pij(x, x+nh) where nh                         a21 = -2.629849  b21 = -0.022030
 is a multiple of 2 years. The first column is the starting age x                         a23 = -7.958519  b23 = 0.042614  
 (from age 50 to 100), the second is age (x+nh) and the others are   Covariance matrix: Var(a12) = 1.47453e-001
 the transition probabilities p11, p12, p13, p21, p22, p23. For                      Var(b12) = 2.18676e-005
 example, line 5 of the file is: </p>                      Var(a13) = 2.09715e-001
                       Var(b13) = 3.28937e-005  
 <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>                      Var(a21) = 9.19832e-001
                       Var(b21) = 1.29229e-004
 <p>and this means: </p>                      Var(a23) = 4.48405e-001
                       Var(b23) = 5.85631e-005
 <pre>p11(100,106)=0.03286   </pre>
 p12(100,106)=0.23512  
 p13(100,106)=0.73202  <p>By substitution of these parameters in the regression model,
 p21(100,106)=0.02330  we obtain the elementary transition probabilities:</p>
 p22(100,106)=0.19210   
 p22(100,106)=0.78460 </pre>  <p><img src="pebiaspar1.gif" width="400" height="300"></p>
   
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
 name="Stationary prevalence in each state"><font color="#EC5E5E"  </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
 size="3"><b>Stationary prevalence in each state</b></font></a><b>:  
 </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>  <p>Here are the transitions probabilities Pij(x, x+nh) where nh
   is a multiple of 2 years. The first column is the starting age x
 <pre>#Age 1-1 2-2   (from age 50 to 100), the second is age (x+nh) and the others are
 70 0.92274 0.07726   the transition probabilities p11, p12, p13, p21, p22, p23. For
 71 0.91420 0.08580   example, line 5 of the file is: </p>
 72 0.90481 0.09519   
 73 0.89453 0.10547</pre>  <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
   
 <p>At age 70 the stationary prevalence is 0.92274 in state 1 and  <p>and this means: </p>
 0.07726 in state 2. This stationary prevalence differs from  
 observed prevalence. Here is the point. The observed prevalence  <pre>p11(100,106)=0.02655
 at age 70 results from the incidence of disability, incidence of  p12(100,106)=0.17622
 recovery and mortality which occurred in the past of the cohort.  p13(100,106)=0.79722
 Stationary prevalence results from a simulation with actual  p21(100,106)=0.01809
 incidences and mortality (estimated from this cross-longitudinal  p22(100,106)=0.13678
 survey). It is the best predictive value of the prevalence in the  p22(100,106)=0.84513 </pre>
 future if &quot;nothing changes in the future&quot;. This is  
 exactly what demographers do with a Life table. Life expectancy  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
 is the expected mean time to survive if observed mortality rates  name="Stationary prevalence in each state"><font color="#EC5E5E"
 (incidence of mortality) &quot;remains constant&quot; in the  size="3"><b>Stationary prevalence in each state</b></font></a><b>:
 future. </p>  </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
   
 <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of  <pre>#Prevalence
 stationary prevalence</b></font><b>: </b><a  #Age 1-1 2-2
 href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>  
   #************
 <p>The stationary prevalence has to be compared with the observed  70 0.90134 0.09866
 prevalence by age. But both are statistical estimates and  71 0.89177 0.10823
 subjected to stochastic errors due to the size of the sample, the  72 0.88139 0.11861
 design of the survey, and, for the stationary prevalence to the  73 0.87015 0.12985 </pre>
 model used and fitted. It is possible to compute the standard  
 deviation of the stationary prevalence at each age.</p>  <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
   0.09866 in state 2. This stationary prevalence differs from
 <h6><font color="#EC5E5E" size="3">Observed and stationary  observed prevalence. Here is the point. The observed prevalence
 prevalence in state (2=disable) with the confident interval</font>:<b>  at age 70 results from the incidence of disability, incidence of
 vbiaspar2.gif</b></h6>  recovery and mortality which occurred in the past of the cohort.
   Stationary prevalence results from a simulation with actual
 <p><br>  incidences and mortality (estimated from this cross-longitudinal
 This graph exhibits the stationary prevalence in state (2) with  survey). It is the best predictive value of the prevalence in the
 the confidence interval in red. The green curve is the observed  future if &quot;nothing changes in the future&quot;. This is
 prevalence (or proportion of individuals in state (2)). Without  exactly what demographers do with a Life table. Life expectancy
 discussing the results (it is not the purpose here), we observe  is the expected mean time to survive if observed mortality rates
 that the green curve is rather below the stationary prevalence.  (incidence of mortality) &quot;remains constant&quot; in the
 It suggests an increase of the disability prevalence in the  future. </p>
 future.</p>  
   <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
 <p><img src="vbiaspar2.gif" width="400" height="300"></p>  stationary prevalence</b></font><b>: </b><a
   href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
 <h6><font color="#EC5E5E" size="3"><b>Convergence to the  
 stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>  <p>The stationary prevalence has to be compared with the observed
 <img src="pbiaspar1.gif" width="400" height="300"> </h6>  prevalence by age. But both are statistical estimates and
   subjected to stochastic errors due to the size of the sample, the
 <p>This graph plots the conditional transition probabilities from  design of the survey, and, for the stationary prevalence to the
 an initial state (1=healthy in red at the bottom, or 2=disable in  model used and fitted. It is possible to compute the standard
 green on top) at age <em>x </em>to the final state 2=disable<em> </em>at  deviation of the stationary prevalence at each age.</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  <h5><font color="#EC5E5E" size="3">-Observed and stationary
 curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>  prevalence in state (2=disable) with the confident interval</font>:<b>
 + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary  </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
 prevalence of disability</em>. In order to get the stationary  
 prevalence at age 70 we should start the process at an earlier  <p>This graph exhibits the stationary prevalence in state (2)
 age, i.e.50. If the disability state is defined by severe  with the confidence interval in red. The green curve is the
 disability criteria with only a few chance to recover, then the  observed prevalence (or proportion of individuals in state (2)).
 incidence of recovery is low and the time to convergence is  Without discussing the results (it is not the purpose here), we
 probably longer. But we don't have experience yet.</p>  observe that the green curve is rather below the stationary
   prevalence. It suggests an increase of the disability prevalence
 <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age  in the future.</p>
 and initial health status</b></font><b>: </b><a  
 href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>  <p><img src="vbiaspar21.gif" width="400" height="300"></p>
   
 <pre># Health expectancies   <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
 # Age 1-1 1-2 2-1 2-2   stationary prevalence of disability</b></font><b>: </b><a
 70 10.7297 2.7809 6.3440 5.9813   href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
 71 10.3078 2.8233 5.9295 5.9959   <img src="pbiaspar11.gif" width="400" height="300"> </h5>
 72 9.8927 2.8643 5.5305 6.0033   
 73 9.4848 2.9036 5.1474 6.0035 </pre>  <p>This graph plots the conditional transition probabilities from
   an initial state (1=healthy in red at the bottom, or 2=disable in
 <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:  green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
 e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>  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
 <pre><img src="exbiaspar1.gif" width="400" height="300"><img  curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
 src="exbiaspar2.gif" width="400" height="300"></pre>  + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
   prevalence of disability</em>. In order to get the stationary
 <p>For example, life expectancy of a healthy individual at age 70  prevalence at age 70 we should start the process at an earlier
 is 10.73 in the healthy state and 2.78 in the disability state  age, i.e.50. If the disability state is defined by severe
 (=13.51 years). If he was disable at age 70, his life expectancy  disability criteria with only a few chance to recover, then the
 will be shorter, 6.34 in the healthy state and 5.98 in the  incidence of recovery is low and the time to convergence is
 disability state (=12.32 years). The total life expectancy is a  probably longer. But we don't have experience yet.</p>
 weighted mean of both, 13.51 and 12.32; weight is the proportion  
 of people disabled at age 70. In order to get a pure period index  <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
 (i.e. based only on incidences) we use the <a  and initial health status</b></font><b>: </b><a
 href="#Stationary prevalence in each state">computed or  href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
 stationary prevalence</a> at age 70 (i.e. computed from  
 incidences at earlier ages) instead of the <a  <pre># Health expectancies
 href="#Observed prevalence in each state">observed prevalence</a>  # Age 1-1 1-2 2-1 2-2
 (for example at first exam) (<a href="#Health expectancies">see  70 10.9226 3.0401 5.6488 6.2122
 below</a>).</p>  71 10.4384 3.0461 5.2477 6.1599
   72 9.9667 3.0502 4.8663 6.1025
 <h5><font color="#EC5E5E" size="3"><b>- Variances of life  73 9.5077 3.0524 4.5044 6.0401 </pre>
 expectancies by age and initial health status</b></font><b>: </b><a  
 href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>  <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:
   e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>
 <p>For example, the covariances of life expectancies Cov(ei,ej)  
 at age 50 are (line 3) </p>  <pre><img src="expbiaspar21.gif" width="400" height="300"><img
   src="expbiaspar11.gif" width="400" height="300"></pre>
 <pre>   Cov(e1,e1)=0.4667  Cov(e1,e2)=0.0605=Cov(e2,e1)  Cov(e2,e2)=0.0183</pre>  
   <p>For example, life expectancy of a healthy individual at age 70
 <h5><font color="#EC5E5E" size="3"><b>- </b></font><a  is 10.92 in the healthy state and 3.04 in the disability state
 name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health  (=13.96 years). If he was disable at age 70, his life expectancy
 expectancies</b></font></a><font color="#EC5E5E" size="3"><b>  will be shorter, 5.64 in the healthy state and 6.21 in the
 with standard errors in parentheses</b></font><b>: </b><a  disability state (=11.85 years). The total life expectancy is a
 href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>  weighted mean of both, 13.96 and 11.85; weight is the proportion
   of people disabled at age 70. In order to get a pure period index
 <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>  (i.e. based only on incidences) we use the <a
   href="#Stationary prevalence in each state">computed or
 <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>  stationary prevalence</a> at age 70 (i.e. computed from
   incidences at earlier ages) instead of the <a
 <p>Thus, at age 70 the total life expectancy, e..=13.42 years is  href="#Observed prevalence in each state">observed prevalence</a>
 the weighted mean of e1.=13.51 and e2.=12.32 by the stationary  (for example at first exam) (<a href="#Health expectancies">see
 prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in  below</a>).</p>
 state 2, respectively (the sum is equal to one). e.1=10.39 is the  
 Disability-free life expectancy at age 70 (it is again a weighted  <h5><font color="#EC5E5E" size="3"><b>- Variances of life
 mean of e11 and e21). e.2=3.03 is also the life expectancy at age  expectancies by age and initial health status</b></font><b>: </b><a
 70 to be spent in the disability state.</p>  href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
   
 <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by  <p>For example, the covariances of life expectancies Cov(ei,ej)
 age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:  at age 50 are (line 3) </p>
 ebiaspar.gif</b></h6>  
   <pre>   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424</pre>
 <p>This figure represents the health expectancies and the total  
 life expectancy with the confident interval in dashed curve. </p>  <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
   name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
 <pre>        <img src="ebiaspar.gif" width="400" height="300"></pre>  expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
   with standard errors in parentheses</b></font><b>: </b><a
 <p>Standard deviations (obtained from the information matrix of  href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
 the model) of these quantities are very useful.  
 Cross-longitudinal surveys are costly and do not involve huge  <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
 samples, generally a few thousands; therefore it is very  
 important to have an idea of the standard deviation of our  <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>
 estimates. It has been a big challenge to compute the Health  
 Expectancy standard deviations. Don't be confuse: life expectancy  <p>Thus, at age 70 the total life expectancy, e..=13.76years is
 is, as any expected value, the mean of a distribution; but here  the weighted mean of e1.=13.96 and e2.=11.85 by the stationary
 we are not computing the standard deviation of the distribution,  prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
 but the standard deviation of the estimate of the mean.</p>  state 2, respectively (the sum is equal to one). e.1=10.40 is the
   Disability-free life expectancy at age 70 (it is again a weighted
 <p>Our health expectancies estimates vary according to the sample  mean of e11 and e21). e.2=3.35 is also the life expectancy at age
 size (and the standard deviations give confidence intervals of  70 to be spent in the disability state.</p>
 the estimate) but also according to the model fitted. Let us  
 explain it in more details.</p>  <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
   age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
 <p>Choosing a model means ar least two kind of choices. First we  </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
 have to decide the number of disability states. Second we have to  
 design, within the logit model family, the model: variables,  <p>This figure represents the health expectancies and the total
 covariables, confonding factors etc. to be included.</p>  life expectancy with the confident interval in dashed curve. </p>
   
 <p>More disability states we have, better is our demographical  <pre>        <img src="ebiaspar1.gif" width="400" height="300"></pre>
 approach of the disability process, but smaller are the number of  
 transitions between each state and higher is the noise in the  <p>Standard deviations (obtained from the information matrix of
 measurement. We do not have enough experiments of the various  the model) of these quantities are very useful.
 models to summarize the advantages and disadvantages, but it is  Cross-longitudinal surveys are costly and do not involve huge
 important to say that even if we had huge and unbiased samples,  samples, generally a few thousands; therefore it is very
 the total life expectancy computed from a cross-longitudinal  important to have an idea of the standard deviation of our
 survey, varies with the number of states. If we define only two  estimates. It has been a big challenge to compute the Health
 states, alive or dead, we find the usual life expectancy where it  Expectancy standard deviations. Don't be confuse: life expectancy
 is assumed that at each age, people are at the same risk to die.  is, as any expected value, the mean of a distribution; but here
 If we are differentiating the alive state into healthy and  we are not computing the standard deviation of the distribution,
 disable, and as the mortality from the disability state is higher  but the standard deviation of the estimate of the mean.</p>
 than the mortality from the healthy state, we are introducing  
 heterogeneity in the risk of dying. The total mortality at each  <p>Our health expectancies estimates vary according to the sample
 age is the weighted mean of the mortality in each state by the  size (and the standard deviations give confidence intervals of
 prevalence in each state. Therefore if the proportion of people  the estimate) but also according to the model fitted. Let us
 at each age and in each state is different from the stationary  explain it in more details.</p>
 equilibrium, there is no reason to find the same total mortality  
 at a particular age. Life expectancy, even if it is a very useful  <p>Choosing a model means ar least two kind of choices. First we
 tool, has a very strong hypothesis of homogeneity of the  have to decide the number of disability states. Second we have to
 population. Our main purpose is not to measure differential  design, within the logit model family, the model: variables,
 mortality but to measure the expected time in a healthy or  covariables, confonding factors etc. to be included.</p>
 disability state in order to maximise the former and minimize the  
 latter. But the differential in mortality complexifies the  <p>More disability states we have, better is our demographical
 measurement.</p>  approach of the disability process, but smaller are the number of
   transitions between each state and higher is the noise in the
 <p>Incidences of disability or recovery are not affected by the  measurement. We do not have enough experiments of the various
 number of states if these states are independant. But incidences  models to summarize the advantages and disadvantages, but it is
 estimates are dependant on the specification of the model. More  important to say that even if we had huge and unbiased samples,
 covariates we added in the logit model better is the model, but  the total life expectancy computed from a cross-longitudinal
 some covariates are not well measured, some are confounding  survey, varies with the number of states. If we define only two
 factors like in any statistical model. The procedure to &quot;fit  states, alive or dead, we find the usual life expectancy where it
 the best model' is similar to logistic regression which itself is  is assumed that at each age, people are at the same risk to die.
 similar to regression analysis. We haven't yet been sofar because  If we are differentiating the alive state into healthy and
 we also have a severe limitation which is the speed of the  disable, and as the mortality from the disability state is higher
 convergence. On a Pentium III, 500 MHz, even the simplest model,  than the mortality from the healthy state, we are introducing
 estimated by month on 8,000 people may take 4 hours to converge.  heterogeneity in the risk of dying. The total mortality at each
 Also, the program is not yet a statistical package, which permits  age is the weighted mean of the mortality in each state by the
 a simple writing of the variables and the model to take into  prevalence in each state. Therefore if the proportion of people
 account in the maximisation. The actual program allows only to  at each age and in each state is different from the stationary
 add simple variables without covariations, like age+sex but  equilibrium, there is no reason to find the same total mortality
 without age+sex+ age*sex . This can be done from the source code  at a particular age. Life expectancy, even if it is a very useful
 (you have to change three lines in the source code) but will  tool, has a very strong hypothesis of homogeneity of the
 never be general enough. But what is to remember, is that  population. Our main purpose is not to measure differential
 incidences or probability of change from one state to another is  mortality but to measure the expected time in a healthy or
 affected by the variables specified into the model.</p>  disability state in order to maximise the former and minimize the
   latter. But the differential in mortality complexifies the
 <p>Also, the age range of the people interviewed has a link with  measurement.</p>
 the age range of the life expectancy which can be estimated by  
 extrapolation. If your sample ranges from age 70 to 95, you can  <p>Incidences of disability or recovery are not affected by the
 clearly estimate a life expectancy at age 70 and trust your  number of states if these states are independant. But incidences
 confidence interval which is mostly based on your sample size,  estimates are dependant on the specification of the model. More
 but if you want to estimate the life expectancy at age 50, you  covariates we added in the logit model better is the model, but
 should rely in your model, but fitting a logistic model on a age  some covariates are not well measured, some are confounding
 range of 70-95 and estimating probabilties of transition out of  factors like in any statistical model. The procedure to &quot;fit
 this age range, say at age 50 is very dangerous. At least you  the best model' is similar to logistic regression which itself is
 should remember that the confidence interval given by the  similar to regression analysis. We haven't yet been sofar because
 standard deviation of the health expectancies, are under the  we also have a severe limitation which is the speed of the
 strong assumption that your model is the 'true model', which is  convergence. On a Pentium III, 500 MHz, even the simplest model,
 probably not the case.</p>  estimated by month on 8,000 people may take 4 hours to converge.
   Also, the program is not yet a statistical package, which permits
 <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter  a simple writing of the variables and the model to take into
 file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>  account in the maximisation. The actual program allows only to
   add simple variables like age+sex or age+sex+ age*sex but will
 <p>This copy of the parameter file can be useful to re-run the  never be general enough. But what is to remember, is that
 program while saving the old output files. </p>  incidences or probability of change from one state to another is
   affected by the variables specified into the model.</p>
 <hr>  
   <p>Also, the age range of the people interviewed has a link with
 <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>  the age range of the life expectancy which can be estimated by
   extrapolation. If your sample ranges from age 70 to 95, you can
 <p>Since you know how to run the program, it is time to test it  clearly estimate a life expectancy at age 70 and trust your
 on your own computer. Try for example on a parameter file named <a  confidence interval which is mostly based on your sample size,
 href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a  but if you want to estimate the life expectancy at age 50, you
 copy of <font size="2" face="Courier New">mypar.txt</font>  should rely in your model, but fitting a logistic model on a age
 included in the subdirectory of imach, <font size="2"  range of 70-95 and estimating probabilties of transition out of
 face="Courier New">mytry</font>. Edit it to change the name of  this age range, say at age 50 is very dangerous. At least you
 the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>  should remember that the confidence interval given by the
 if you don't want to copy it on the same directory. The file <font  standard deviation of the health expectancies, are under the
 face="Courier New">mydata.txt</font> is a smaller file of 3,000  strong assumption that your model is the 'true model', which is
 people but still with 4 waves. </p>  probably not the case.</p>
   
 <p>Click on the imach.exe icon to open a window. Answer to the  <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
 question:'<strong>Enter the parameter file name:'</strong></p>  file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
   
 <table border="1">  <p>This copy of the parameter file can be useful to re-run the
     <tr>  program while saving the old output files. </p>
         <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter  
         the parameter file name: ..\mytry\imachpar.txt</strong></p>  <hr>
         </td>  
     </tr>  <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
 </table>  
   <p>Since you know how to run the program, it is time to test it
 <p>Most of the data files or image files generated, will use the  on your own computer. Try for example on a parameter file named <a
 'imachpar' string into their name. The running time is about 2-3  href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
 minutes on a Pentium III. If the execution worked correctly, the  size="2" face="Courier New">mypar.txt</font> included in the
 outputs files are created in the current directory, and should be  subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
 the same as the mypar files initially included in the directory <font  Edit it to change the name of the data file to <font size="2"
 size="2" face="Courier New">mytry</font>.</p>  face="Courier New">..\data\mydata.txt</font> if you don't want to
   copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
 <ul>  is a smaller file of 3,000 people but still with 4 waves. </p>
     <li><pre><u>Output on the screen</u> The output screen looks like <a  
 href="imachrun.LOG">this Log file</a>  <p>Click on the imach.exe icon to open a window. Answer to the
 #  question:'<strong>Enter the parameter file name:'</strong></p>
   
 title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3  <table border="1">
 ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>      <tr>
     </li>          <td width="100%"><strong>IMACH, Version 0.64b</strong><p><strong>Enter
     <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92          the parameter file name: ..\mytry\imachpar.txt</strong></p>
           </td>
 Warning, no any valid information for:126 line=126      </tr>
 Warning, no any valid information for:2307 line=2307  </table>
 Delay (in months) between two waves Min=21 Max=51 Mean=24.495826  
 <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>  <p>Most of the data files or image files generated, will use the
 Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14  'imachpar' string into their name. The running time is about 2-3
  prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1  minutes on a Pentium III. If the execution worked correctly, the
 Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>  outputs files are created in the current directory, and should be
     </li>  the same as the mypar files initially included in the directory <font
 </ul>  size="2" face="Courier New">mytry</font>.</p>
   
 <p>&nbsp;</p>  <ul>
       <li><pre><u>Output on the screen</u> The output screen looks like <a
 <ul>  href="imachrun.LOG">this Log file</a>
     <li>Maximisation with the Powell algorithm. 8 directions are  #
         given corresponding to the 8 parameters. this can be  
         rather long to get convergence.<br>  title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
         <font size="1" face="Courier New"><br>  ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2      </li>
         0.000000000000 3<br>      <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
         0.000000000000 4 0.000000000000 5 0.000000000000 6  
         0.000000000000 7 <br>  Warning, no any valid information for:126 line=126
         0.000000000000 8 0.000000000000<br>  Warning, no any valid information for:2307 line=2307
         1..........2.................3..........4.................5.........<br>  Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
         6................7........8...............<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>
         Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283  Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
         <br>   prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
         2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>  Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
         5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>      </li>
         8 0.051272038506<br>  </ul>
         1..............2...........3..............4...........<br>  
         5..........6................7...........8.........<br>  <p>&nbsp;</p>
         #Number of iterations = 23, -2 Log likelihood =  
         6744.954042573691<br>  <ul>
         # Parameters<br>      <li>Maximisation with the Powell algorithm. 8 directions are
         12 -12.966061 0.135117 <br>          given corresponding to the 8 parameters. this can be
         13 -7.401109 0.067831 <br>          rather long to get convergence.<br>
         21 -0.672648 -0.006627 <br>          <font size="1" face="Courier New"><br>
         23 -5.051297 0.051271 </font><br>          Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
         </li>          0.000000000000 3<br>
     <li><pre><font size="2">Calculation of the hessian matrix. Wait...          0.000000000000 4 0.000000000000 5 0.000000000000 6
 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          0.000000000000 7 <br>
           0.000000000000 8 0.000000000000<br>
 Inverting the hessian to get the covariance matrix. Wait...          1..........2.................3..........4.................5.........<br>
           6................7........8...............<br>
 #Hessian matrix#          Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001           <br>
 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003           2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
 -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001           5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
 -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003           8 0.051272038506<br>
 -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..............2...........3..............4...........<br>
 -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005           5..........6................7...........8.........<br>
 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004           #Number of iterations = 23, -2 Log likelihood =
 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006           6744.954042573691<br>
 # Scales          # Parameters<br>
 12 1.00000e-004 1.00000e-006          12 -12.966061 0.135117 <br>
 13 1.00000e-004 1.00000e-006          13 -7.401109 0.067831 <br>
 21 1.00000e-003 1.00000e-005          21 -0.672648 -0.006627 <br>
 23 1.00000e-004 1.00000e-005          23 -5.051297 0.051271 </font><br>
 # Covariance          </li>
   1 5.90661e-001      <li><pre><font size="2">Calculation of the hessian matrix. Wait...
   2 -7.26732e-003 8.98810e-005  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
   3 8.80177e-002 -1.12706e-003 5.15824e-001  
   4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005  Inverting the hessian to get the covariance matrix. Wait...
   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  #Hessian matrix#
   7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000  3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
   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  2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
 # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).  -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
 agemin=70 agemax=100 bage=50 fage=100  -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
 Computing prevalence limit: result on file 'plrmypar.txt'   3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
 Computing pij: result on file 'pijrmypar.txt'   3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
 Computing Health Expectancies: result on file 'ermypar.txt'   # Scales
 Computing Variance-covariance of DFLEs: file 'vrmypar.txt'   12 1.00000e-004 1.00000e-006
 Computing Total LEs with variances: file 'trmypar.txt'   13 1.00000e-004 1.00000e-006
 Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'   21 1.00000e-003 1.00000e-005
 End of Imach  23 1.00000e-004 1.00000e-005
 </font></pre>  # Covariance
     </li>    1 5.90661e-001
 </ul>    2 -7.26732e-003 8.98810e-005
     3 8.80177e-002 -1.12706e-003 5.15824e-001
 <p><font size="3">Once the running is finished, the program    4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
 requires a caracter:</font></p>    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
 <table border="1">    7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
     <tr>    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
         <td width="100%"><strong>Type g for plotting (available  # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
         if mle=1), e to edit output files, c to start again,</strong><p><strong>and  
         q for exiting:</strong></p>  
         </td>  agemin=70 agemax=100 bage=50 fage=100
     </tr>  Computing prevalence limit: result on file 'plrmypar.txt'
 </table>  Computing pij: result on file 'pijrmypar.txt'
   Computing Health Expectancies: result on file 'ermypar.txt'
 <p><font size="3">First you should enter <strong>g</strong> to  Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
 make the figures and then you can edit all the results by typing <strong>e</strong>.  Computing Total LEs with variances: file 'trmypar.txt'
 </font></p>  Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
   End of Imach
 <ul>  </font></pre>
     <li><u>Outputs files</u> <br>      </li>
         - index.htm, this file is the master file on which you  </ul>
         should click first.<br>  
         - Observed prevalence in each state: <a  <p><font size="3">Once the running is finished, the program
         href="..\mytry\prmypar.txt">mypar.txt</a> <br>  requires a caracter:</font></p>
         - Estimated parameters and the covariance matrix: <a  
         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>  <table border="1">
         - Stationary prevalence in each state: <a      <tr>
         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>          <td width="100%"><strong>Type e to edit output files, c
         - Transition probabilities: <a          to start again, and q for exiting:</strong></td>
         href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>      </tr>
         - Copy of the parameter file: <a  </table>
         href="..\mytry\ormypar.txt">ormypar.txt</a> <br>  
         - Life expectancies by age and initial health status: <a  <p><font size="3">First you should enter <strong>e </strong>to
         href="..\mytry\ermypar.txt">ermypar.txt</a> <br>  edit the master file mypar.htm. </font></p>
         - Variances of life expectancies by age and initial  
         health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>  <ul>
         <br>      <li><u>Outputs files</u> <br>
         - Health expectancies with their variances: <a          <br>
         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>          - Observed prevalence in each state: <a
         - Standard deviation of stationary prevalence: <a          href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>          - Estimated parameters and the covariance matrix: <a
         <br>          href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
         </li>          - Stationary prevalence in each state: <a
     <li><u>Graphs</u> <br>          href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
         <br>          - Transition probabilities: <a
         -<a href="..\mytry\vmypar1.gif">Observed and stationary          href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
         prevalence in state (1) with the confident interval</a> <br>          - Copy of the parameter file: <a
         -<a href="..\mytry\vmypar2.gif">Observed and stationary          href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
         prevalence in state (2) with the confident interval</a> <br>          - Life expectancies by age and initial health status: <a
         -<a href="..\mytry\exmypar1.gif">Health life expectancies          href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
         by age and initial health state (1)</a> <br>          - Variances of life expectancies by age and initial
         -<a href="..\mytry\exmypar2.gif">Health life expectancies          health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
         by age and initial health state (2)</a> <br>          <br>
         -<a href="..\mytry\emypar.gif">Total life expectancy by          - Health expectancies with their variances: <a
         age and health expectancies in states (1) and (2).</a> </li>          href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
 </ul>          - Standard deviation of stationary prevalence: <a
           href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>
 <p>This software have been partly granted by <a          <br>
 href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted          </li>
 action from the European Union. It will be copyrighted      <li><u>Graphs</u> <br>
 identically to a GNU software product, i.e. program and software          <br>
 can be distributed freely for non commercial use. Sources are not          -<a href="../mytry/pemypar1.gif">One-step transition
 widely distributed today. You can get them by asking us with a          probabilities</a><br>
 simple justification (name, email, institute) <a          -<a href="../mytry/pmypar11.gif">Convergence to the
 href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a          stationary prevalence</a><br>
 href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>          -<a href="..\mytry\vmypar11.gif">Observed and stationary
           prevalence in state (1) with the confident interval</a> <br>
 <p>Latest version (0.63 of 16 march 2000) can be accessed at <a          -<a href="..\mytry\vmypar21.gif">Observed and stationary
 href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>          prevalence in state (2) with the confident interval</a> <br>
 </p>          -<a href="..\mytry\expmypar11.gif">Health life
 </body>          expectancies by age and initial health state (1)</a> <br>
 </html>          -<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 (0.64b of may 2001) can be accessed at <a
   href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
   </p>
   </body>
   </html>

Removed from v.1.1.1.1  
changed lines
  Added in v.1.3


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