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  <body><font size="2">Imach version 0.98q5, August 2015,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015 <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E">    <body><font size="7"><a href=http:/euroreves.ined.fr/imach>IMaCh for Interpolated Markov Chain</a> </font><br>
 Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=<br>  <font size="3">Sponsored by Copyright (C)  2002-2015 <a href=http://www.ined.fr>INED</a>-EUROREVES-Institut de longévité-2013-2016-Japan Society for the Promotion of Sciences 日本学術振興会 (<a href=https://www.jsps.go.jp/english/e-grants/>Grant-in-Aid for Scientific Research 25293121</a>) - <a href=https://software.intel.com/en-us>Intel Software 2015-2018</a></font><br>  <hr size="2" color="#EC5E5E"> 
   <font size="2">IMaCh-0.99r24 <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E"> 
   Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=1+age+<br>
   
 <hr  size="2" color="#EC5E5E"> <ul><li><h4>Parameter files</h4>  <hr  size="2" color="#EC5E5E"> <ul><li><h4>Parameter files</h4>
  - Parameter file: <a href="biaspar.imach">biaspar.imach</a><br>   - Parameter file: <a href="biaspar.imach">biaspar.imach</a><br>
  - Copy of the parameter file: <a href="orbiaspar.txt">orbiaspar.txt</a><br>   - Copy of the parameter file: <a href="orbiaspar.txt">orbiaspar.txt</a><br>
  - Log file of the run: <a href="biaspar.log">biaspar.log</a><br>   - Log file of the run: <a href="biaspar.log">biaspar.log</a><br>
  - Gnuplot file name: <a href="biaspar.gp">biaspar.gp</a><br>   - Gnuplot file name: <a href="biaspar.gp">biaspar.gp</a><br>
  - Date and time at start: Tue Aug 18 18:20:44 2015   - Date and time at start: Thu May 20 15:42:13 2021
 </ul>  </ul>
   
   <h4>Parameter line 2</h4><ul><li>Tolerance for the convergence of the likelihood: ftol=1e-08 
   <li>Interval for the elementary matrix (in month): stepm=1
   <li>Number of fixed dummy covariates: ncovcol=2 V1 V2 
   <li> Number of fixed quantitative variables: nqv=0 
   <li> Number of time varying (wave varying) dummy covariates: ntv=0 
   <li>Number of time varying  quantitative covariates: nqtv=0 
   <li>Weights column 
   <br>Number of alive states: nlstate=2 <br>Number of death states (not really implemented): ndeath=1 
   <li>Number of waves: maxwav=4 
   <li>Parameter for maximization (1), using parameter values (0), for design of parameters and variance-covariance matrix: mle=1 
   <li>Does the weight column be taken into account (1), or not (0): weight=0</ul>
   <h4> Diagram of states <a href="biaspar/D_biaspar_.svg">biaspar/D_biaspar_.svg</a></h4> 
   <img src="biaspar/D_biaspar_.svg">
   <h4>Some descriptive statistics </h4>
 <br>Total number of observations=8270 <br>  <br>Total number of observations=8270 <br>
 Youngest age at first (selected) pass 70.00, oldest age 104.17<br>  Youngest age at first (selected) pass 70.00, oldest age 104.17<br>
 Interval (in months) between two waves: Min=1 Max=74 Mean=24.04<br>  Interval (in months) between two waves: Min=1 Max=74 Mean=24.06<br>
   
 <br>File of contributions to the likelihood: <a href="biaspar/ilkrbiaspar.txt">biaspar/ilkrbiaspar.txt</a><br>  <br>File of contributions to the likelihood computed with optimized parameters mle = 1. You should at least run with mle >= 1 to get starting values corresponding to the optimized parameters in order to visualize the real contribution of each individual/wave: <a href="biaspar/ILK_biaspar.txt">biaspar/ILK_biaspar.txt</a><br>
 <ul><li><a href='#firstorder'>Result files (first order: no variance)</a>  
   <br>Equation of the model: <b>model=1+age+</b><br>
   <br>- Probability p<sub>1j</sub> by origin 1 and destination j. Dot's sizes are related to corresponding weight: <a href="biaspar/ILK_biaspar-p1j.png">biaspar/ILK_biaspar-p1j.png</a><br> <img src="biaspar/ILK_biaspar-p1j.png"><br>- Probability p<sub>2j</sub> by origin 2 and destination j. Dot's sizes are related to corresponding weight: <a href="biaspar/ILK_biaspar-p2j.png">biaspar/ILK_biaspar-p2j.png</a><br> <img src="biaspar/ILK_biaspar-p2j.png"><br>- The function drawn is -2Log(L) in Log scale: by state of origin <a href="biaspar/ILK_biaspar-ori.png">biaspar/ILK_biaspar-ori.png</a><br> <img src="biaspar/ILK_biaspar-ori.png"><br>- and by state of destination <a href="biaspar/ILK_biaspar-dest.png">biaspar/ILK_biaspar-dest.png</a><br> <img src="biaspar/ILK_biaspar-dest.png"><ul><li><a href='#firstorder'>Result files (first order: no variance)</a>
     <li><a href='#secondorder'>Result files (second order (variance)</a>      <li><a href='#secondorder'>Result files (second order (variance)</a>
    </ul><ul><li> model=1+age+
  </ul><ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>   </ul><ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>
   - Observed prevalence in each state (during the period defined between 1/1/1984 and 1/6/1988): <a href="biaspar/prbiaspar.txt">biaspar/prbiaspar.txt</a> <br>  <li>- Observed frequency between two states (during the period defined between 1/1/1984 and 1/6/1988): <a href="biaspar/PHTMFR_biaspar.htm">biaspar/PHTMFR_biaspar.htm</a> (html file)<br/>
   - Estimated transition probabilities over 1 (stepm) months: <a href="biaspar/pijrbiaspar.txt">biaspar/pijrbiaspar.txt</a><br>  <li> - Observed prevalence in each state (during the period defined between 1/1/1984 and 1/6/1988): <a href="biaspar/PHTM_biaspar.htm">biaspar/PHTM_biaspar.htm</a> (html file) ,  <a href="biaspar/P_biaspar.txt">biaspar/P_biaspar.txt</a> (text file) <br>
   - Period (stable) prevalence in each health state: <a href="biaspar/plrbiaspar.txt">biaspar/plrbiaspar.txt</a> <br>   - Estimated transition probabilities over 1 (stepm) months: <a href="biaspar/PIJ_biaspar.txt">biaspar/PIJ_biaspar.txt</a><br>
  - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm= 1 months):    <a href="biaspar/erbiaspar.txt">biaspar/erbiaspar.txt</a> <br>    - Estimated back transition probabilities over 1 (stepm) months: <a href="biaspar/PIJB_biaspar.txt">biaspar/PIJB_biaspar.txt</a><br>
  - Population projections by age and states:    <a href="biaspar/frbiaspar.txt">biaspar/frbiaspar.txt</a> <br>    - Period (forward) prevalence in each health state: <a href="biaspar/PL_biaspar.txt">biaspar/PL_biaspar.txt</a> <br>
    - Backward prevalence in each health state: <a href="biaspar/PLB_biaspar.txt">biaspar/PLB_biaspar.txt</a> <br>
    - (a) Life expectancies by health status at initial age, e<sub>i.</sub> (b) health expectancies by health status at initial age, e<sub>ij</sub> . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm= 1 months):    <a href="biaspar/E_biaspar.txt">biaspar/E_biaspar.txt</a> <br>
    - Prevalence projections by age and states:                               <a href="biaspar/F_biaspar.txt">biaspar/F_biaspar.txt</a> <br>
 </li>   </li> 
 <ul><li><b>Graphs</b></li><p><br>- Pij or Conditional probabilities to be observed in state j being in state i, 1 (stepm) months before: <a href="biaspar/pebiaspar1_1.png">biaspar/pebiaspar1_1.png</a><br> <img src="biaspar/pebiaspar1_1.png"><br>- Pij or Conditional probabilities to be observed in state j being in state i 1 (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href="biaspar/pebiaspar1_2.png">biaspar/pebiaspar1_2.png</a><br> <img src="biaspar/pebiaspar1_2.png"><br>- Convergence to period (stable) prevalence in state 1. Or probability to be in state 1 being in state (1 to 2) at different ages. <a href="biaspar/pbiaspar1_1.png">biaspar/pbiaspar1_1.png</a><br> <img src="biaspar/pbiaspar1_1.png"><br>- Convergence to period (stable) prevalence in state 2. Or probability to be in state 2 being in state (1 to 2) at different ages. <a href="biaspar/pbiaspar2_1.png">biaspar/pbiaspar2_1.png</a><br> <img src="biaspar/pbiaspar2_1.png">  <ul><li><b>Graphs</b></li><p> 
 <br>- Life expectancy by health state (1) at initial age and its decomposition into health expectancies in each alive state (1 to 2) : <a href="biaspar/expbiaspar11.png">biaspar/expbiaspar11.png</a> <br> <img src="biaspar/expbiaspar11.png">  <ul> 
 <br>- Life expectancy by health state (2) at initial age and its decomposition into health expectancies in each alive state (1 to 2) : <a href="biaspar/expbiaspar21.png">biaspar/expbiaspar21.png</a> <br> <img src="biaspar/expbiaspar21.png"></ul>  </ul><br>- Logit model (yours is: logit(pij)=log(pij/pii)= aij+ bij age+) as a function of age: <a href="biaspar/PE_biaspar_1-1-1.svg">biaspar/PE_biaspar_1-1-1.svg</a><br> <img src="biaspar/PE_biaspar_1-1-1.svg"><br>
   - P<sub>ij</sub> or conditional probabilities to be observed in state j being in state i, 1 (stepm) months before: <a href="biaspar/PE_biaspar_1-2-1.svg">biaspar/PE_biaspar_1-2-1.svg</a><br> <img src="biaspar/PE_biaspar_1-2-1.svg"><br>
   - I<sub>ij</sub> or Conditional probabilities to be observed in state j being in state i 1 (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too,  incidence (rates) are the limit when h tends to zero of the ratio of the probability  <sub>h</sub>P<sub>ij</sub> divided by h: <sub>h</sub>P<sub>ij</sub>/h : <a href="biaspar/PE_biaspar_1-3-1.svg">biaspar/PE_biaspar_1-3-1.svg</a><br> <img src="biaspar/PE_biaspar_1-3-1.svg"><br>
   - Survival functions in state 1. And probability to be observed in state 1 being in state (1 to 2) at different ages. <a href="biaspar/LIJ_biaspar_1-1-1.svg">biaspar/LIJ_biaspar_1-1-1.svg</a><br> <img src="biaspar/LIJ_biaspar_1-1-1.svg"><br>
   - Survival functions in state 2. And probability to be observed in state 2 being in state (1 to 2) at different ages. <a href="biaspar/LIJ_biaspar_2-1-1.svg">biaspar/LIJ_biaspar_2-1-1.svg</a><br> <img src="biaspar/LIJ_biaspar_2-1-1.svg"><br>
   - Survival functions in state 1 and in any other live state (total). And probability to be observed in various states (up to 2) being in state 1 at different ages.      <a href="biaspar/LIJT_biaspar_1-1-1.svg">biaspar/LIJT_biaspar_1-1-1.svg</a><br> <img src="biaspar/LIJT_biaspar_1-1-1.svg"><br>
   - Survival functions in state 2 and in any other live state (total). And probability to be observed in various states (up to 2) being in state 2 at different ages.      <a href="biaspar/LIJT_biaspar_2-1-1.svg">biaspar/LIJT_biaspar_2-1-1.svg</a><br> <img src="biaspar/LIJT_biaspar_2-1-1.svg"><br>
   - Convergence to period (stable) prevalence in state 1. Or probability for a person being in state (1 to 2) at different ages, to be in state 1 some years after. <a href="biaspar/P_biaspar_1-1-1.svg">biaspar/P_biaspar_1-1-1.svg</a><br> <img src="biaspar/P_biaspar_1-1-1.svg"><br>
   - Convergence to period (stable) prevalence in state 2. Or probability for a person being in state (1 to 2) at different ages, to be in state 2 some years after. <a href="biaspar/P_biaspar_2-1-1.svg">biaspar/P_biaspar_2-1-1.svg</a><br> <img src="biaspar/P_biaspar_2-1-1.svg"><br>
   - Projection of cross-sectional prevalence (estimated with cases observed from 1984.0 to 1988.4 and mobil_average=0), from year 1989.0 up to year 2000.0 tending to period (stable) forward prevalence in state 1. Or probability to be in state 1 being in an observed weighted state (from 1 to 2). <a href="biaspar/PROJ_biaspar_1-1-1.svg">biaspar/PROJ_biaspar_1-1-1.svg</a><br> <img src="biaspar/PROJ_biaspar_1-1-1.svg"><br>
   - Projection of cross-sectional prevalence (estimated with cases observed from 1984.0 to 1988.4 and mobil_average=0), from year 1989.0 up to year 2000.0 tending to period (stable) forward prevalence in state 2. Or probability to be in state 2 being in an observed weighted state (from 1 to 2). <a href="biaspar/PROJ_biaspar_2-1-1.svg">biaspar/PROJ_biaspar_2-1-1.svg</a><br> <img src="biaspar/PROJ_biaspar_2-1-1.svg">
   <br>- Life expectancy by health state (1) at initial age and its decomposition into health expectancies in each alive state (1 to 2) (or area under each survival functions): <a href="biaspar/EXP_biaspar_1-1-1.svg">biaspar/EXP_biaspar_1-1-1.svg</a> <br> <img src="biaspar/EXP_biaspar_1-1-1.svg">
   <br>- Life expectancy by health state (2) at initial age and its decomposition into health expectancies in each alive state (1 to 2) (or area under each survival functions): <a href="biaspar/EXP_biaspar_2-1-1.svg">biaspar/EXP_biaspar_2-1-1.svg</a> <br> <img src="biaspar/EXP_biaspar_2-1-1.svg"></ul>
 <br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>  <br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>
  - Parameter file with estimated parameters and covariance matrix: <a href="rbiaspar.imach">rbiaspar.imach</a> <br>  - 95% confidence intervals and T statistics are in the log file.<br>   - Parameter file with estimated parameters and covariance matrix: <a href="rbiaspar.imach">rbiaspar.imach</a> <br>  - 95% confidence intervals and Wald tests of the estimated parameters are in the log file if optimization has been done (mle != 0).<br> But because parameters are usually highly correlated (a higher incidence of disability and a higher incidence of recovery can give very close observed transition) it might be very useful to look not only at linear confidence intervals estimated from the variances but at the covariance matrix. And instead of looking at the estimated coefficients (parameters) of the logistic regression, it might be more meaningful to visualize the covariance matrix of the one-step probabilities. See page 'Matrix of variance-covariance of one-step probabilities' below. 
  - Standard deviation of one-step probabilities: <a href="biaspar/probrbiaspar.txt">biaspar/probrbiaspar.txt</a> <br>   - Standard deviation of one-step probabilities: <a href="biaspar/PROB_biaspar.txt">biaspar/PROB_biaspar.txt</a> <br>
  - Variance-covariance of one-step probabilities: <a href="biaspar/probcovrbiaspar.txt">biaspar/probcovrbiaspar.txt</a> <br>   - Variance-covariance of one-step probabilities: <a href="biaspar/PROBCOV_biaspar.txt">biaspar/PROBCOV_biaspar.txt</a> <br>
  - Correlation matrix of one-step probabilities: <a href="biaspar/probcorrbiaspar.txt">biaspar/probcorrbiaspar.txt</a> <br>   - Correlation matrix of one-step probabilities: <a href="biaspar/PROBCOR_biaspar.txt">biaspar/PROBCOR_biaspar.txt</a> <br>
  - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm= 1 months):    <a href="biaspar/cverbiaspar.txt">biaspar/cverbiaspar.txt</a> <br>   - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm= 1 months):    <a href="biaspar/CVE_biaspar.txt">biaspar/CVE_biaspar.txt</a> <br>
 </li> - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm= 1 months):    <a href="biaspar/stderbiaspar.txt">biaspar/stderbiaspar.txt</a> <br>  </li> - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm= 1 months):    <a href="biaspar/STDE_biaspar.txt">biaspar/STDE_biaspar.txt</a> <br>
 </li> - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=1 months): <a href="biaspar/vrbiaspar.txt">biaspar/vrbiaspar.txt</a><br>  </li> - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the forward (period) prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=1 months): <a href="biaspar/V_biaspar.txt">biaspar/V_biaspar.txt</a><br>
  - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=1 months): <a href="biaspar/trbiaspar.txt">biaspar/trbiaspar.txt</a> <br>   - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=1 months): <a href="biaspar/T_biaspar.txt">biaspar/T_biaspar.txt</a> <br>
  - Standard deviation of period (stable) prevalences: <a href="biaspar/vplrbiaspar.txt">biaspar/vplrbiaspar.txt</a> <br>   - Standard deviation of forward (period) prevalences: <a href="biaspar/VPL_biaspar.txt">biaspar/VPL_biaspar.txt</a> <br>
  <ul><li><b>Graphs</b></li><p><br>- Observed (cross-sectional) and period (incidence based) prevalence (with 95% confidence interval) in state (1): biaspar/vbiaspar1_1.png <br><img src="biaspar/vbiaspar1_1.png"><br>- Observed (cross-sectional) and period (incidence based) prevalence (with 95% confidence interval) in state (2): biaspar/vbiaspar2_1.png <br><img src="biaspar/vbiaspar2_1.png">   <ul><li><b>Graphs</b></li><p>
 <br>- Total life expectancy by age and health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) true period expectancies (those weighted with period prevalences are also drawn in addition to the population based expectancies computed using observed and cahotic prevalences: biaspar/ebiaspar1.png<br><img src="biaspar/ebiaspar1.png"></ul>  <br>- Observed (cross-sectional with mov_average=0) and period (incidence based) prevalence (with 95% confidence interval) in state (1): <a href="biaspar/V_biaspar_1-1-1.svg"> biaspar/V_biaspar_1-1-1.svg</a>
    <br><img src="biaspar/V_biaspar_1-1-1.svg">
   <br>- Observed (cross-sectional with mov_average=0) and period (incidence based) prevalence (with 95% confidence interval) in state (2): <a href="biaspar/V_biaspar_2-1-1.svg"> biaspar/V_biaspar_2-1-1.svg</a>
    <br><img src="biaspar/V_biaspar_2-1-1.svg">
   <br>- Total life expectancy by age and health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) true period expectancies (those weighted with period prevalences are also drawn in addition to the population based expectancies computed using observed and cahotic prevalences:  <a href="biaspar/E_biaspar_1-1.svg">biaspar/E_biaspar_1-1.svg</a>
   <br><img src="biaspar/E_biaspar_1-1.svg"></ul>
 <li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>  <li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>
   
   
 <li><h4> <a href="biaspar-cov.htm">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>  <li><h4> <a href="biaspar-cov.htm">Matrix of variance-covariance of one-step probabilities (drawings)</a></h4> this page is important in order to visualize confidence intervals and especially correlation between disability and recovery, or more generally, way in and way back. File biaspar-cov.htm</li>
   
   <li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>
   
   <br>-STABLBASED_  <br>
   
   <br> File (multiple files are possible if covariates are present): <A href="biaspar/PRMORPREV-1-STABLBASED_biaspar.txt">biaspar/PRMORPREV-1-STABLBASED_biaspar.txt</a>
   
   <br> Probability is computed over estepm=1 months. <br> <img src="biaspar/VARMUPTJGR--STABLBASED_biaspar1.svg"> <br>
   
 <li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>  <li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>
   
 <br>-stablbased-  <br>  <br>-POPULBASED-NOMOBIL_  <br>
   
 <br> File (multiple files are possible if covariates are present): <A href="biaspar/prmorprev1-stablbased-rbiaspar.txt">biaspar/prmorprev1-stablbased-rbiaspar.txt</a>  <br> File (multiple files are possible if covariates are present): <A href="biaspar/PRMORPREV-1-POPULBASED-NOMOBIL_biaspar.txt">biaspar/PRMORPREV-1-POPULBASED-NOMOBIL_biaspar.txt</a>
   
 <br> Probability is computed over estepm=1 months. <br> <img src="biaspar/varmuptjgr-stablbased-biaspar1.png"> <br>  <br> Probability is computed over estepm=1 months. <br> <img src="biaspar/VARMUPTJGR--POPULBASED-NOMOBIL_biaspar1.svg"> <br>
 <br>Local time at start Tue Aug 18 18:20:44 2015  <br>Local time at start Thu May 20 15:42:13 2021
 <br>Local time at end   Tue Aug 18 18:26:33 2015  <br>Local time at end   Thu May 20 15:43:12 2021
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