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<title>Computing Health Expectancies using IMaCh</title>\r
-<!-- Changed by: Agnes Lievre, 12-Oct-2000 -->\r
<html>\r
\r
<head>\r
href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>\r
\r
<p align="center"><font color="#00006A" size="4"><strong>Version\r
-0.8a, May 2002</strong></font></p>\r
+0.97, June 2004</strong></font></p>\r
\r
<hr size="3" color="#EC5E5E">\r
\r
computing HE is usually called the Sullivan method (from the name\r
of the author who first described it).</p>\r
\r
-<p>Age-specific proportions of people disable are very difficult\r
-to forecast because each proportion corresponds to historical\r
-conditions of the cohort and it is the result of the historical\r
-flows from entering disability and recovering in the past until\r
-today. The age-specific intensities (or incidence rates) of\r
-entering disability or recovering a good health, are reflecting\r
-actual conditions and therefore can be used at each age to\r
-forecast the future of this cohort. For example if a country is\r
-improving its technology of prosthesis, the incidence of\r
-recovering the ability to walk will be higher at each (old) age,\r
-but the prevalence of disability will only slightly reflect an\r
-improve because the prevalence is mostly affected by the history\r
-of the cohort and not by recent period effects. To measure the\r
-period improvement we have to simulate the future of a cohort of\r
-new-borns entering or leaving at each age the disability state or\r
-dying according to the incidence rates measured today on\r
-different cohorts. The proportion of people disabled at each age\r
-in this simulated cohort will be much lower (using the exemple of\r
-an improvement) that the proportions observed at each age in a\r
-cross-sectional survey. This new prevalence curve introduced in a\r
-life table will give a much more actual and realistic HE level\r
-than the Sullivan method which mostly measured the History of\r
-health conditions in this country.</p>\r
+<p>Age-specific proportions of people disabled (prevalence of\r
+disability) are dependent on the historical flows from entering\r
+disability and recovering in the past until today. The age-specific\r
+forces (or incidence rates), estimated over a recent period of time\r
+(like for period forces of mortality), of entering disability or\r
+recovering a good health, are reflecting current conditions and\r
+therefore can be used at each age to forecast the future of this\r
+cohort<em>if nothing changes in the future</em>, i.e to forecast the\r
+prevalence of disability of each cohort. Our finding (2) is that the period\r
+prevalence of disability (computed from period incidences) is lower\r
+than the cross-sectional prevalence. For example if a country is\r
+improving its technology of prosthesis, the incidence of recovering\r
+the ability to walk will be higher at each (old) age, but the\r
+prevalence of disability will only slightly reflect an improve because\r
+the prevalence is mostly affected by the history of the cohort and not\r
+by recent period effects. To measure the period improvement we have to\r
+simulate the future of a cohort of new-borns entering or leaving at\r
+each age the disability state or dying according to the incidence\r
+rates measured today on different cohorts. The proportion of people\r
+disabled at each age in this simulated cohort will be much lower that\r
+the proportions observed at each age in a cross-sectional survey. This\r
+new prevalence curve introduced in a life table will give a more\r
+realistic HE level than the Sullivan method which mostly measured the\r
+History of health conditions in this country.</p>\r
\r
<p>Therefore, the main question is how to measure incidence rates\r
from cross-longitudinal surveys? This is the goal of the IMaCH\r
<p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New\r
Methods for Analyzing Active Life Expectancy". <i>Journal of\r
Aging and Health</i>. Vol 10, No. 2. </p>\r
+<p>(2) <a href=http://taylorandfrancis.metapress.com/app/home/contribution.asp?wasp=1f99bwtvmk5yrb7hlhw3&referrer=parent&backto=issue,1,2;journal,2,5;linkingpublicationresults,1:300265,1\r
+>Lièvre A., Brouard N. and Heathcote Ch. (2003) Estimating Health Expectancies \r
+from Cross-longitudinal surveys. <em>Mathematical Population Studies</em>.- 10(4), pp. 211-248</a>\r
\r
<hr>\r
\r
<h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>\r
\r
<p>In this example, 8,000 people have been interviewed in a\r
-cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).\r
-Some people missed 1, 2 or 3 interviews. Health statuses are\r
-healthy (1) and disable (2). The survey is not a real one. It is\r
-a simulation of the American Longitudinal Survey on Aging. The\r
-disability state is defined if the individual missed one of four\r
-ADL (Activity of daily living, like bathing, eating, walking).\r
-Therefore, even is the individuals interviewed in the sample are\r
-virtual, the information brought with this sample is close to the\r
-situation of the United States. Sex is not recorded is this\r
-sample.</p>\r
+cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). Some\r
+people missed 1, 2 or 3 interviews. Health statuses are healthy (1)\r
+and disable (2). The survey is not a real one. It is a simulation of\r
+the American Longitudinal Survey on Aging. The disability state is\r
+defined if the individual missed one of four ADL (Activity of daily\r
+living, like bathing, eating, walking). Therefore, even if the\r
+individuals interviewed in the sample are virtual, the information\r
+brought with this sample is close to the situation of the United\r
+States. Sex is not recorded is this sample. The LSOA survey is biased\r
+in the sense that people living in an institution were not surveyed at\r
+first pass in 1984. Thus the prevalence of disability in 1984 is\r
+biased downwards at old ages. But when people left their household to\r
+an institution, they have been surveyed in their institution in 1986,\r
+1988 or 1990. Thus incidences are not biased. But cross-sectional\r
+prevalences of disability at old ages are thus artificially increasing\r
+in 1986, 1988 and 1990 because of a higher weight of people\r
+institutionalized in the sample. Our article shows the\r
+opposite: the period prevalence is lower at old ages than the\r
+adjusted cross-sectional prevalence proving important current progress\r
+against disability.</p>\r
\r
<p>Each line of the data set (named <a href="data1.txt">data1.txt</a>\r
-in this first example) is an individual record which fields are: </p>\r
+in this first example) is an individual record. Fields are separated\r
+by blanks: </p>\r
\r
<ul>\r
<li><b>Index number</b>: positive number (field 1) </li>\r
<h2><font color="#00006A">Your first example parameter file</font><a\r
href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>\r
\r
-<h2><a name="biaspar"></a>#Imach version 0.8a, May 2002,\r
+<h2><a name="biaspar"></a>#Imach version 0.97b, June 2004,\r
INED-EUROREVES </h2>\r
\r
-<p>This is a comment. Comments start with a '#'.</p>\r
+<p>This first line was a comment. Comments line start with a '#'.</p>\r
\r
<h4><font color="#FF0000">First uncommented line</font></h4>\r
\r
<li>... </li>\r
</ul>\r
</li>\r
- <li><b>ncovcol=2</b> Number of covariate columns in the\r
- datafile which precede the date of birth. Here you can\r
- put variables that won't necessary be used during the\r
+ <li><b>ncovcol=2</b> Number of covariate columns included in the\r
+ datafile before the column of the date of birth. You can have\r
+covariates that won't necessary be used during the\r
run. It is not the number of covariates that will be\r
- specified by the model. The 'model' syntax describe the\r
- covariates to take into account. </li>\r
+ specified by the model. The 'model' syntax describes the\r
+ covariates to be taken into account during the run. </li>\r
<li><b>nlstate=2</b> Number of non-absorbing (alive) states.\r
Here we have two alive states: disability-free is coded 1\r
and disability is coded 2. </li>\r
<li>If mle=1 the program does the maximisation and\r
the calculation of health expectancies </li>\r
<li>If mle=0 the program only does the calculation of\r
- the health expectancies. </li>\r
+ the health expectancies and other indices and graphs\r
+but without the maximization.. </li>\r
+ There also other possible values:\r
+ <ul>\r
+ <li>If mle=-1 you get a template which can be useful if\r
+your model is complex with many covariates.</li>\r
+ <li> If mle=-3 IMaCh computes the mortality but without\r
+ any health status (May 2004)</li> <li>If mle=2 IMach\r
+ likelihood corresponds to a linear interpolation</li> <li>\r
+ If mle=3 IMach likelihood corresponds to an exponential\r
+ inter-extrapolation</li> \r
+ <li> If mle=4 IMach likelihood\r
+ corresponds to no inter-extrapolation, and thus biasing\r
+ the results. </li> \r
+ <li> If mle=5 IMach likelihood\r
+ corresponds to no inter-extrapolation, and before the\r
+ correction of the Jackson's bug (avoid this).</li>\r
+ </ul>\r
</ul>\r
</li>\r
<li><b>weight=0</b> Possibility to add weights. <ul>\r
-ln(12/6)=-ln(2)= -0.693\r
</pre>\r
\r
+In version 0.9 and higher you can still have valuable results even if\r
+your stepm parameter is bigger than a month. The idea is to run with\r
+bigger stepm in order to have a quicker convergence at the price of a\r
+small bias. Once you know which model you want to fit, you can put\r
+stepm=1 and wait hours or days to get the convergence!\r
+\r
+To get unbiased results even with large stepm we introduce the idea of\r
+pseudo likelihood by interpolating two exact likelihoods. Let us\r
+detail this:\r
+<p>\r
+If the interval of <em>d</em> months between two waves is not a\r
+mutliple of 'stepm', but is comprised between <em>(n-1) stepm</em> and\r
+<em>n stepm</em> then both exact likelihoods are computed (the\r
+contribution to the likelihood at <em>n stepm</em> requires one matrix\r
+product more) (let us remember that we are modelling the probability\r
+to be observed in a particular state after <em>d</em> months being\r
+observed at a particular state at 0). The distance, (<em>bh</em> in\r
+the program), from the month of interview to the rounded date of <em>n\r
+stepm</em> is computed. It can be negative (interview occurs before\r
+<em>n stepm</em>) or positive if the interview occurs after <em>n\r
+stepm</em> (and before <em>(n+1)stepm</em>).\r
+<br>\r
+Then the final contribution to the total likelihood is a weighted\r
+average of these two exact likelihoods at <em>n stepm</em> (out) and\r
+at <em>(n-1)stepm</em>(savm). We did not want to compute the third\r
+likelihood at <em>(n+1)stepm</em> because it is too costly in time, so\r
+we used an extrapolation if <em>bh</em> is positive. <br> Formula of\r
+inter/extrapolation may vary according to the value of parameter mle:\r
+<pre>\r
+mle=1 lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */\r
+\r
+mle=2 lli= (savm[s1][s2]>(double)1.e-8 ? \\r
+ log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])): \\r
+ log((1.+bbh)*out[s1][s2])); /* linear interpolation */\r
+mle=3 lli= (savm[s1][s2]>1.e-8 ? \\r
+ (1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]): \\r
+ log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */\r
+\r
+mle=4 lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* No interpolation */\r
+ no need to save previous likelihood into memory.\r
+</pre>\r
+<p>\r
+If the death occurs between first and second pass, and for example\r
+more precisely between <em>n stepm</em> and <em>(n+1)stepm</em> the\r
+contribution of this people to the likelihood is simply the difference\r
+between the probability of dying before <em>n stepm</em> and the\r
+probability of dying before <em>(n+1)stepm</em>. There was a bug in\r
+version 0.8 and death was treated as any other state, i.e. as if it\r
+was an observed death at second pass. This was not precise but\r
+correct, but when information on the precise month of death came\r
+(death occuring prior to second pass) we did not change the likelihood\r
+accordingly. Thanks to Chris Jackson for correcting us. In earlier\r
+versions (fortunately before first publication) the total mortality\r
+was overestimated (people were dying too early) of about 10%. Version\r
+0.95 and higher are correct.\r
+\r
+<p> Our suggested choice is mle=1 . If stepm=1 there is no difference\r
+between various mle options (methods of interpolation). If stepm is\r
+big, like 12 or 24 or 48 and mle=4 (no interpolation) the bias may be\r
+very important if the mean duration between two waves is not a\r
+multiple of stepm. See the appendix in our main publication concerning\r
+the sine curve of biases.\r
+ \r
+\r
<h4><font color="#FF0000">Guess values for computing variances</font></h4>\r
\r
-<p>This is an output if <a href="#mle">mle</a>=1. But it can be\r
-used as an input to get the various output data files (Health\r
-expectancies, stationary prevalence etc.) and figures without\r
-rerunning the rather long maximisation phase (mle=0). </p>\r
+<p>These values are output by the maximisation of the likelihood <a\r
+href="#mle">mle</a>=1. These valuse can be used as an input of a\r
+second run in order to get the various output data files (Health\r
+expectancies, period prevalence etc.) and figures without rerunning\r
+the long maximisation phase (mle=0). </p>\r
\r
-<p>The scales are small values for the evaluation of numerical\r
-derivatives. These derivatives are used to compute the hessian\r
-matrix of the parameters, that is the inverse of the covariance\r
-matrix, and the variances of health expectancies. Each line\r
-consists in indices "ij" followed by the initial scales\r
-(zero to simplify) associated with aij and bij. </p>\r
+<p>These 'scales' are small values needed for the computing of\r
+numerical derivatives. These derivatives are used to compute the\r
+hessian matrix of the parameters, that is the inverse of the\r
+covariance matrix. They are often used for estimating variances and\r
+confidence intervals. Each line consists in indices "ij"\r
+followed by the initial scales (zero to simplify) associated with aij\r
+and bij. </p>\r
\r
<ul>\r
<li>If mle=1 you can enter zeros:</li>\r
23 0. 0. </pre>\r
</blockquote>\r
</li>\r
- <li>If mle=0 you must enter a covariance matrix (usually\r
+ <li>If mle=0 (no maximisation of Likelihood) you must enter a covariance matrix (usually\r
obtained from an earlier run).</li>\r
</ul>\r
\r
<h4><font color="#FF0000">Covariance matrix of parameters</font></h4>\r
\r
-<p>Th
is is an output if <a href="#mle">mle</a>=1. But it can be
\r-used as an input to get the various output data files (Health\r
-expectancies, stationary prevalence etc.) and figures without\r
-rerunning the rather long maximisation phase (mle=0). <br>\r
+<p>Th
e covariance matrix is output if <a href="#mle">mle</a>=1. But it can be
\r+also used as an input to get the various output data files (Health\r
+expectancies, period prevalence etc.) and figures without\r
+rerunning the maximisation phase (mle=0). <br>\r
Each line starts with indices "ijk" followed by the\r
covariances between aij and bij:<br>\r
</p>\r
\r
<pre>agemin=70 agemax=100 bage=50 fage=100</pre>\r
\r
-<pre>\r
+<p>\r
Once we obtained the estimated parameters, the program is able\r
-to calculated stationary prevalence, transitions probabilities\r
+to calculate period prevalence, transitions probabilities\r
and life expectancies at any age. Choice of age range is useful\r
-for extrapolation. In our data file, ages varies from age 70 to\r
-102. It is possible to get extrapolated stationary prevalence by\r
-age ranging from agemin to agemax.\r
-\r
-\r
-Setting bage=50 (begin age) and fage=100 (final age), makes\r
-the program computing life expectancy from age 'bage' to age\r
+for extrapolation. In this example, age of people interviewed varies\r
+from 69 to 102 and the model is estimated using their exact ages. But\r
+if you are interested in the age-specific period prevalence you can\r
+start the simulation at an exact age like 70 and stop at 100. Then the\r
+program will draw at least two curves describing the forecasted\r
+prevalences of two cohorts, one for healthy people at age 70 and the second\r
+for disabled people at the same initial age. And according to the\r
+mixing property (ergodicity) and because of recovery, both prevalences\r
+will tend to be identical at later ages. Thus if you want to compute\r
+the prevalence at age 70, you should enter a lower agemin value.\r
+\r
+<p>\r
+Setting bage=50 (begin age) and fage=100 (final age), let\r
+the program compute life expectancy from age 'bage' to age\r
'fage'. As we use a model, we can interessingly compute life\r
expectancy on a wider age range than the age range from the data.\r
But the model can be rather wrong on much larger intervals.\r
\r
<ul>\r
<li><b>agemin=</b> Minimum age for calculation of the\r
- stationary prevalence </li>\r
+ period prevalence </li>\r
<li><b>agemax=</b> Maximum age for calculation of the\r
- stationary prevalence </li>\r
+ period prevalence </li>\r
<li><b>bage=</b> Minimum age for calculation of the health\r
expectancies </li>\r
<li><b>fage=</b> Maximum age for calculation of the health\r
</ul>\r
\r
<h4><a name="Computing"><font color="#FF0000">Computing</font></a><font\r
-color="#FF0000"> the observed prevalence</font></h4>\r
+color="#FF0000"> the cross-sectional prevalence</font></h4>\r
\r
<pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</pre>\r
\r
-<pre>\r
+<p>\r
Statements 'begin-prev-date' and 'end-prev-date' allow to\r
select the period in which we calculate the observed prevalences\r
in each state. In this example, the prevalences are calculated on\r
data survey collected between 1 january 1984 and 1 june 1988. \r
-</pre>\r
+</p>\r
\r
<ul>\r
<li><strong>begin-prev-date= </strong>Starting date\r
\r
<pre>pop_based=0</pre>\r
\r
-<p>The program computes status-based health expectancies, i.e\r
-health expectancies which depends on your initial health state.\r
-If you are healthy your healthy life expectancy (e11) is higher\r
-than if you were disabled (e21, with e11 > e21).<br>\r
-To compute a healthy life expectancy independant of the initial\r
-status we have to weight e11 and e21 according to the probability\r
-to be in each state at initial age or, with other word, according\r
-to the proportion of people in each state.<br>\r
-We prefer computing a 'pure' period healthy life expectancy based\r
-only on the transtion forces. Then the weights are simply the\r
-stationnary prevalences or 'implied' prevalences at the initial\r
-age.<br>\r
-Some other people would like to use the cross-sectional\r
-prevalences (the "Sullivan prevalences") observed at\r
-the initial age during a period of time <a href="#Computing">defined\r
-just above</a>. <br>\r
-</p>\r
+<p>The program computes status-based health expectancies, i.e health\r
+expectancies which depend on the initial health state. If you are\r
+healthy, your healthy life expectancy (e11) is higher than if you were\r
+disabled (e21, with e11 > e21).<br> To compute a healthy life\r
+expectancy 'independent' of the initial status we have to weight e11\r
+and e21 according to the probability to be in each state at initial\r
+age which are corresponding to the proportions of people in each health\r
+state (cross-sectional prevalences).<p> \r
+\r
+We could also compute e12 and e12 and get e.2 by weighting them\r
+according to the observed cross-sectional prevalences at initial age.\r
+<p> In a similar way we could compute the total life expectancy by\r
+summing e.1 and e.2 .\r
+<br>\r
+The main difference between 'population based' and 'implied' or\r
+'period' consists in the weights used. 'Usually', cross-sectional\r
+prevalences of disability are higher than period prevalences\r
+particularly at old ages. This is true if the country is improving its\r
+health system by teaching people how to prevent disability as by\r
+promoting better screening, for example of people needing cataracts\r
+surgeryand for many unknown reasons that this program may help to\r
+discover. Then the proportion of disabled people at age 90 will be\r
+lower than the current observed proportion.\r
+<p>\r
+Thus a better Health Expectancy and even a better Life Expectancy\r
+value is given by forecasting not only the current lower mortality at\r
+all ages but also a lower incidence of disability and higher recovery.\r
+<br> Using the period prevalences as weight instead of the\r
+cross-sectional prevalences we are computing indices which are more\r
+specific to the current situations and therefore more useful to\r
+predict improvements or regressions in the future as to compare\r
+different policies in various countries.\r
\r
<ul>\r
- <li><strong>popbased= 0 </strong>Health expectancies are\r
- computed at each age from stationary prevalences\r
- 'expected' at this initial age.</li>\r
+ <li><strong>popbased= 0 </strong>Health expectancies are computed\r
+ at each age from period prevalences 'expected' at this initial\r
+ age.</li> \r
<li><strong>popbased= 1 </strong>Health expectancies are\r
- computed at each age from cross-sectional 'observed'\r
- prevalence at this initial age. As all the population is\r
- not observed at the same exact date we define a short\r
- period were the observed prevalence is computed.</li>\r
+ computed at each age from cross-sectional 'observed' prevalence at\r
+ this initial age. As all the population is not observed at the\r
+ same exact date we define a short period were the observed\r
+ prevalence can be computed.<br>\r
+\r
+ We simply sum all people surveyed within these two exact dates\r
+ who belong to a particular age group (single year) at the date of\r
+ interview and being in a particular health state. Then it is easy to\r
+get the proportion of people of a particular health status among all\r
+people of the same age group.<br>\r
+\r
+If both dates are spaced and are covering two waves or more, people\r
+being interviewed twice or more are counted twice or more. The program\r
+takes into account the selection of individuals interviewed between\r
+firstpass and lastpass too (we don't know if it can be useful).\r
+</li>\r
</ul>\r
\r
-<h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>\r
+<h4><font color="#FF0000">Prevalence forecasting (Experimental)</font></h4>\r
\r
<pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>\r
\r
centered at the mid-age of the five-age period. <br>\r
</p>\r
\r
+<h4><font color="#FF0000">Population forecasting (Experimental)</font></h4>\r
+\r
<ul>\r
<li><strong>starting-proj-date</strong>= starting date\r
(day/month/year) of forecasting</li>\r
value 1 if the prevalences are smoothed and 0 otherwise.</li>\r
</ul>\r
\r
-<h4><font color="#FF0000">Last uncommented line : Population\r
-forecasting </font></h4>\r
-\r
-<pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>\r
-\r
-<p>This command is available if the interpolation unit is a\r
-month, i.e. stepm=1 and if popforecast=1. From a data file\r
-including age and number of persons alive at the precise date\r
-‘popfiledate’, you can forecast the number of persons\r
-in each state until date ‘last-popfiledate’. In this\r
-example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>\r
-includes real data which are the Japanese population in 1989.<br>\r
-</p>\r
\r
<ul type="disc">\r
- <li class="MsoNormal"\r
- style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=\r
+ <li><b>popforecast=\r
0 </b>Option for population forecasting. If\r
popforecast=1, the programme does the forecasting<b>.</b></li>\r
- <li class="MsoNormal"\r
- style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=\r
+ <li><b>popfile=\r
</b>name of the population file</li>\r
- <li class="MsoNormal"\r
- style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>\r
+ <li><b>popfiledate=</b>\r
date of the population population</li>\r
- <li class="MsoNormal"\r
- style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=\r
+ <li><b>last-popfiledate</b>=\r
date of the last population projection </li>\r
</ul>\r
\r
<h2><a name="running"></a><font color="#00006A">Running Imach\r
with this example</font></h2>\r
\r
-<p
re>We assume that you typed in your <a href="biaspar.imach">1st_example
\r+<p
>We assume that you already typed your <a href="biaspar.imach">1st_example
\r parameter file</a> as explained <a href="#biaspar">above</a>. \r
\r
-To run the program you should either:\r
-</pre>\r
+To run the program under Windows you should either:\r
+</p>\r
\r
<ul>\r
- <li>click on the imach.exe icon and enter the name of the\r
- parameter file which is for example <a\r
- href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>\r
- </li>\r
- <li>You also can locate the biaspar.imach icon in <a\r
- href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your\r
- mouse and drag it with the mouse on the imach window). </li>\r
- <li>With latest version (0.7 and higher) if you setup windows\r
- in order to understand ".imach" extension you\r
- can right click the biaspar.imach icon and either edit\r
- with notepad the parameter file or execute it with imach\r
- or whatever. </li>\r
+ <li>click on the imach.exe icon and either:\r
+ <ul>\r
+ <li>enter the name of the\r
+ parameter file which is for example <tt>\r
+C:\home\myname\lsoa\biaspar.imach"</tt></li>\r
+ <li>or locate the biaspar.imach icon in your folder such as\r
+ <tt>C:\home\myname\lsoa</tt> \r
+ and drag it, with your mouse, on the already open imach window. </li>\r
+ </ul>\r
+\r
+ <li>With version (0.97b) if you ran setup at installation, Windows is\r
+ supposed to understand the ".imach" extension and you can\r
+ right click the biaspar.imach icon and either edit with wordpad\r
+ (better than notepad) the parameter file or execute it with\r
+ IMaCh. </li>\r
</ul>\r
\r
-<pre>The time to converge depends on the step unit that you used (1\r
-month is cpu consuming), on the number of cases, and on the\r
-number of variables.\r
+<p>The time to converge depends on the step unit that you used (1\r
+month is more precise but more cpu consuming), on the number of cases,\r
+and on the number of variables (covariates).\r
\r
+<p>\r
+The program outputs many files. Most of them are files which will be\r
+plotted for better understanding.\r
\r
-The program outputs many files. Most of them are files which\r
-will be plotted for better understanding.\r
-\r
-</pre>\r
-\r
+</p>\r
+To run under Linux it is mostly the same.\r
+<p>\r
+It is neither more difficult to run it under a MacIntosh.\r
<hr>\r
\r
<h2><a name="output"><font color="#00006A">Output of the program\r
and graphs</font> </a></h2>\r
\r
-<p>Once the optimization is finished, some graphics can be made\r
-with a grapher. We use Gnuplot which is an interactive plotting\r
-program copyrighted but freely distributed. A gnuplot reference\r
-manual is available <a href="http://www.gnuplot.info/">here</a>. <br>\r
-When the running is finished, the user should enter a caracter\r
-for plotting and output editing. <br>\r
-These caracters are:<br>\r
+<p>Once the optimization is finished (once the convergence is\r
+reached), many tables and graphics are produced.<p>\r
+The IMaCh program will create a subdirectory of the same name as your\r
+parameter file (here mypar) where all the tables and figures will be\r
+stored.<br>\r
+\r
+Important files like the log file and the output parameter file (which\r
+contains the estimates of the maximisation) are stored at the main\r
+level not in this subdirectory. File with extension .log and .txt can\r
+be edited with a standard editor like wordpad or notepad or even can be\r
+viewed with a browser like Internet Explorer or Mozilla.\r
+\r
+<p> The main html file is also named with the same name <a\r
+href="biaspar.htm">biaspar.htm</a>. You can click on it by holding\r
+your shift key in order to open it in another window (Windows).\r
+<p>\r
+ Our grapher is Gnuplot, it is an interactive plotting program (GPL) which\r
+ can also work in batch. A gnuplot reference manual is available <a\r
+ href="http://www.gnuplot.info/">here</a>. <br> When the run is\r
+ finished, and in order that the window doesn't disappear, the user\r
+ should enter a character like <tt>q</tt> for quitting. <br> These\r
+ characters are:<br>\r
</p>\r
-\r
<ul>\r
- <li>'c' to start again the program from the beginning.</li>\r
- <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>\r
- file to edit the output files and graphs. </li>\r
+ <li>'e' for opening the main result html file <a\r
+ href="biaspar.htm"><strong>biaspar.htm</strong></a> file to edit\r
+ the output files and graphs. </li> \r
<li>'g' to graph again</li>\r
+ <li>'c' to start again the program from the beginning.</li>\r
<li>'q' for exiting.</li>\r
</ul>\r
\r
+The main gnuplot file is named <tt>biaspar.gp</tt> and can be edited (right\r
+click) and run again.\r
+<p>Gnuplot is easy and you can use it to make more complex\r
+graphs. Just click on gnuplot and type plot sin(x) to see how easy it\r
+is.\r
+\r
+\r
<h5><font size="4"><strong>Results files </strong></font><br>\r
<br>\r
<font color="#EC5E5E" size="3"><strong>- </strong></font><a\r
-name="Observed prevalence in each state"><font color="#EC5E5E"\r
-size="3"><strong>Observed prevalence in each state</strong></font></a><font\r
+name="cross-sectional prevalence in each state"><font color="#EC5E5E"\r
+size="3"><strong>cross-sectional prevalence in each state</strong></font></a><font\r
color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:\r
-</b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>\r
+</b><a href="biaspar/prbiaspar.txt"><b>biaspar/prbiaspar.txt</b></a><br>\r
</h5>\r
\r
<p>The first line is the title and displays each field of the\r
-file. The first column is age. The fields 2 and 6 are the\r
+file. First column corresponds to age. Fields 2 and 6 are the\r
proportion of individuals in states 1 and 2 respectively as\r
-observed during the first exam. Others fields are the numbers of\r
+observed at first exam. Others fields are the numbers of\r
people in states 1, 2 or more. The number of columns increases if\r
the number of states is higher than 2.<br>\r
The header of the file is </p>\r
71 0.99681 625 627 71 0.00319 2 627 \r
72 0.97125 1115 1148 72 0.02875 33 1148 </pre>\r
\r
-<p>It means that at age 70, the prevalence in state 1 is 1.000\r
+<p>It means that at age 70 (between 70 and 71), the prevalence in state 1 is 1.000\r
and in state 2 is 0.00 . At age 71 the number of individuals in\r
state 1 is 625 and in state 2 is 2, hence the total number of\r
people aged 71 is 625+2=627. <br>\r
<p>By substitution of these parameters in the regression model,\r
we obtain the elementary transition probabilities:</p>\r
\r
-<p><img src="pebiaspar1.gif" width="400" height="300"></p>\r
+<p><img src="biaspar/pebiaspar11.png" width="400" height="300"></p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:\r
-</b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>\r
+</b><a href="biaspar/pijrbiaspar.txt"><b>biaspar/pijrbiaspar.txt</b></a></h5>\r
\r
-<p>Here are the transitions probabilities Pij(x, x+nh) where nh\r
-is a multiple of 2 years. The first column is the starting age x\r
-(from age 50 to 100), the second is age (x+nh) and the others are\r
-the transition probabilities p11, p12, p13, p21, p22, p23. For\r
-example, line 5 of the file is: </p>\r
+<p>Here are the transitions probabilities Pij(x, x+nh). The second\r
+column is the starting age x (from age 95 to 65), the third is age\r
+(x+nh) and the others are the transition probabilities p11, p12, p13,\r
+p21, p22, p23. The first column indicates the value of the covariate\r
+(without any other variable than age it is equal to 1) For example, line 5 of the file\r
+is: </p>\r
\r
-<pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>\r
+<pre>1 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>\r
\r
<p>and this means: </p>\r
\r
p22(100,106)=0.84513 </pre>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- </b></font><a\r
-name="Stationary prevalence in each state"><font color="#EC5E5E"\r
-size="3"><b>Stationary prevalence in each state</b></font></a><b>:\r
-</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>\r
+name="Period prevalence in each state"><font color="#EC5E5E"\r
+size="3"><b>Period prevalence in each state</b></font></a><b>:\r
+</b><a href="biaspar/plrbiaspar.txt"><b>biaspar/plrbiaspar.txt</b></a></h5>\r
\r
<pre>#Prevalence\r
#Age 1-1 2-2\r
72 0.88139 0.11861 \r
73 0.87015 0.12985 </pre>\r
\r
-<p>At age 70 the stationary prevalence is 0.90134 in state 1 and\r
-0.09866 in state 2. This stationary prevalence differs from\r
-observed prevalence. Here is the point. The observed prevalence\r
-at age 70 results from the incidence of disability, incidence of\r
-recovery and mortality which occurred in the past of the cohort.\r
-Stationary prevalence results from a simulation with actual\r
-incidences and mortality (estimated from this cross-longitudinal\r
-survey). It is the best predictive value of the prevalence in the\r
-future if "nothing changes in the future". This is\r
-exactly what demographers do with a Life table. Life expectancy\r
-is the expected mean time to survive if observed mortality rates\r
-(incidence of mortality) "remains constant" in the\r
-future. </p>\r
+<p>At age 70 the period prevalence is 0.90134 in state 1 and 0.09866\r
+in state 2. This period prevalence differs from the cross-sectional\r
+prevalence. Here is the point. The cross-sectional prevalence at age\r
+70 results from the incidence of disability, incidence of recovery and\r
+mortality which occurred in the past of the cohort. Period prevalence\r
+results from a simulation with current incidences of disability,\r
+recovery and mortality estimated from this cross-longitudinal\r
+survey. It is a good predictin of the prevalence in the\r
+future if "nothing changes in the future". This is exactly\r
+what demographers do with a period life table. Life expectancy is the\r
+expected mean survival time if current mortality rates (age-specific incidences\r
+of mortality) "remain constant" in the future. </p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Standard deviation of\r
-stationary prevalence</b></font><b>: </b><a\r
-href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>\r
-\r
-<p>The stationary prevalence has to be compared with the observed\r
-prevalence by age. But both are statistical estimates and\r
-subjected to stochastic errors due to the size of the sample, the\r
-design of the survey, and, for the stationary prevalence to the\r
-model used and fitted. It is possible to compute the standard\r
-deviation of the stationary prevalence at each age.</p>\r
-\r
-<h5><font color="#EC5E5E" size="3">-Observed and stationary\r
+period prevalence</b></font><b>: </b><a\r
+href="biaspar/vplrbiaspar.txt"><b>biaspar/vplrbiaspar.txt</b></a></h5>\r
+\r
+<p>The period prevalence has to be compared with the cross-sectional\r
+prevalence. But both are statistical estimates and therefore\r
+have confidence intervals.\r
+<b>For the cross-sectional prevalence we generally need information on\r
+the design of the surveys. It is usually not enough to consider the\r
+number of people surveyed at a particular age and to estimate a\r
+Bernouilli confidence interval based on the prevalence at that\r
+age. But you can do it to have an idea of the randomness. At least you\r
+can get a visual appreciation of the randomness by looking at the\r
+fluctuation over ages.\r
+\r
+<p> For the period prevalence it is possible to estimate the\r
+confidence interval from the Hessian matrix (see the publication for\r
+details). We are supposing that the design of the survey will only\r
+alter the weight of each individual. IMaCh is scaling the weights of\r
+individuals-waves contributing to the likelihood by making the sum of\r
+the weights equal to the sum of individuals-waves contributing: a\r
+weighted survey doesn't increase or decrease the size of the survey,\r
+it only give more weights to some individuals and thus less to the\r
+others.\r
+\r
+<h5><font color="#EC5E5E" size="3">-cross-sectional and period\r
prevalence in state (2=disable) with confidence interval</font>:<b>\r
-</b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>\r
+</b><a href="biaspar/vbiaspar21.htm"><b>biaspar/vbiaspar21.png</b></a></h5>\r
\r
-<p>This graph exhibits the stationary prevalence in state (2)\r
-with the confidence interval in red. The green curve is the\r
-observed prevalence (or proportion of individuals in state (2)).\r
-Without discussing the results (it is not the purpose here), we\r
-observe that the green curve is rather below the stationary\r
-prevalence. It suggests an increase of the disability prevalence\r
-in the future.</p>\r
+<p>This graph exhibits the period prevalence in state (2) with the\r
+confidence interval in red. The green curve is the observed prevalence\r
+(or proportion of individuals in state (2)). Without discussing the\r
+results (it is not the purpose here), we observe that the green curve\r
+is rather below the period prevalence. It the data where not biased by\r
+the non inclusion of people living in institutions we would have\r
+concluded that the prevalence of disability will increase in the\r
+future (see the main publication if you are interested in real data\r
+and results which are opposite).</p>\r
\r
-<p><img src="vbiaspar21.gif" width="400" height="300"></p>\r
+<p><img src="biaspar/vbiaspar21.png" width="400" height="300"></p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>-Convergence to the\r
-
stationary prevalence of disability</b></font><b>: </b><a
\r-href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>\r
-<img src="pbiaspar11.gif" width="400" height="300"> </h5>\r
+
period prevalence of disability</b></font><b>: </b><a
\r+href="biaspar/pbiaspar11.png"><b>biaspar/pbiaspar11.png</b></a><br>\r
+<img src="biaspar/pbiaspar11.png" width="400" height="300"> </h5>\r
\r
<p>This graph plots the conditional transition probabilities from\r
an initial state (1=healthy in red at the bottom, or 2=disable in\r
age <em>x+h. </em>Conditional means at the condition to be alive\r
at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The\r
curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>\r
-+ <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary\r
-prevalence of disability</em>. In order to get the stationary\r
++ <em>hP22x) </em>converge with <em>h, </em>to the <em>period\r
+prevalence of disability</em>. In order to get the period\r
prevalence at age 70 we should start the process at an earlier\r
age, i.e.50. If the disability state is defined by severe\r
disability criteria with only a few chance to recover, then the\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age\r
and initial health status with standard deviation</b></font><b>: </b><a\r
-href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>\r
+href="biaspar/erbiaspar.txt"><b>biaspar/erbiaspar.txt</b></a></h5>\r
\r
<pre># Health expectancies \r
# Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)\r
-70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366)\r
-71 9.9325 (0.1409) 3.0495 (0.4234) 5.2627 (0.1107) 5.6384 (0.3129)\r
-72 9.4603 (0.1319) 3.0540 (0.3770) 4.8810 (0.1099) 5.5811 (0.2907)\r
-73 9.0009 (0.1246) 3.0565 (0.3345) 4.5188 (0.1098) 5.5187 (0.2702)\r
+ 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)\r
+ 71 10.4786 (0.1184) 3.2093 (0.3212) 4.3384 (0.0875) 4.4820 (0.2076)\r
+ 72 9.9551 (0.1103) 3.2236 (0.2827) 4.0426 (0.0885) 4.4827 (0.1966)\r
+ 73 9.4476 (0.1035) 3.2379 (0.2478) 3.7621 (0.0899) 4.4825 (0.1858)\r
+ 74 8.9564 (0.0980) 3.2522 (0.2165) 3.4966 (0.0920) 4.4815 (0.1754)\r
+ 75 8.4815 (0.0937) 3.2665 (0.1887) 3.2457 (0.0946) 4.4798 (0.1656)\r
+ 76 8.0230 (0.0905) 3.2806 (0.1645) 3.0090 (0.0979) 4.4772 (0.1565)\r
+ 77 7.5810 (0.0884) 3.2946 (0.1438) 2.7860 (0.1017) 4.4738 (0.1484)\r
+ 78 7.1554 (0.0871) 3.3084 (0.1264) 2.5763 (0.1062) 4.4696 (0.1416)\r
+ 79 6.7464 (0.0867) 3.3220 (0.1124) 2.3794 (0.1112) 4.4646 (0.1364)\r
+ 80 6.3538 (0.0868) 3.3354 (0.1014) 2.1949 (0.1168) 4.4587 (0.1331)\r
+ 81 5.9775 (0.0873) 3.3484 (0.0933) 2.0222 (0.1230) 4.4520 (0.1320)\r
</pre>\r
\r
-<pre>For example 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366) means:\r
-e11=10.4171 e12=3.0433 e21=5.6641 e22=5.6907 </pre>\r
+<pre>For example 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)\r
+means\r
+e11=11.0180 e12=3.1950 e21=4.6500 e22=4.4807 </pre>\r
\r
-<pre><img src="
expbiaspar21.gif" width="400" height="300"><img
\r-src="expbiaspar11.gif" width="400" height="300"></pre>\r
+<pre><img src="
biaspar/expbiaspar21.png" width="400" height="300"><img
\r+src="biaspar/expbiaspar11.png" width="400" height="300"></pre>\r
\r
<p>For example, life expectancy of a healthy individual at age 70\r
-is 10.42 in the healthy state and 3.04 in the disability state\r
-(=13.46 years). If he was disable at age 70, his life expectancy\r
-will be shorter, 5.66 in the healthy state and 5.69 in the\r
-disability state (=11.35 years). The total life expectancy is a\r
-weighted mean of both, 13.46 and 11.35; weight is the proportion\r
-of people disabled at age 70. In order to get a pure period index\r
+is 11.0 in the healthy state and 3.2 in the disability state\r
+(total of 14.2 years). If he was disable at age 70, his life expectancy\r
+will be shorter, 4.65 years in the healthy state and 4.5 in the\r
+disability state (=9.15 years). The total life expectancy is a\r
+weighted mean of both, 14.2 and 9.15. The weight is the proportion\r
+of people disabled at age 70. In order to get a period index\r
(i.e. based only on incidences) we use the <a\r
-href="#Stationary prevalence in each state">computed or\r
-stationary prevalence</a> at age 70 (i.e. computed from\r
+href="#Period prevalence in each state">stable or\r
+period prevalence</a> at age 70 (i.e. computed from\r
incidences at earlier ages) instead of the <a\r
-href="#Observed prevalence in each state">observed prevalence</a>\r
-(
for example at first exam) (<a href="#Health expectancies">see
\r+href="#cross-sectional prevalence in each state">cross-sectional prevalence</a>\r
+(
observed for example at first medical exam) (<a href="#Health expectancies">see
\r below</a>).</p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Variances of life\r
expectancies by age and initial health status</b></font><b>: </b><a\r
-href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>\r
+href="biaspar/vrbiaspar.txt"><b>biaspar/vrbiaspar.txt</b></a></h5>\r
\r
<p>For example, the covariances of life expectancies Cov(ei,ej)\r
at age 50 are (line 3) </p>\r
<pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>\r
\r
<h5><font color="#EC5E5E" size="3"><b>-Variances of one-step\r
-probabilities </b></font><b>: </b><a href="probrbiaspar.txt"><b>probrbiaspar.txt</b></a></h5>\r
+probabilities </b></font><b>: </b><a href="biaspar/probrbiaspar.txt"><b>biaspar/probrbiaspar.txt</b></a></h5>\r
\r
<p>For example, at age 65</p>\r
\r
name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health\r
expectancies</b></font></a><font color="#EC5E5E" size="3"><b>\r
with standard errors in parentheses</b></font><b>: </b><a\r
-href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>\r
+href="biaspar/trbiaspar.txt"><font face="Courier New"><b>biaspar/trbiaspar.txt</b></font></a></h5>\r
\r
<pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>\r
\r
<pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>\r
\r
<p>Thus, at age 70 the total life expectancy, e..=13.26 years is\r
-the weighted mean of e1.=13.46 and e2.=11.35 by the stationary\r
-prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in\r
-state 2, respectively (the sum is equal to one). e.1=9.95 is the\r
+the weighted mean of e1.=13.46 and e2.=11.35 by the period\r
+prevalences at age 70 which are 0.90134 in state 1 and 0.09866 in\r
+state 2 respectively (the sum is equal to one). e.1=9.95 is the\r
Disability-free life expectancy at age 70 (it is again a weighted\r
mean of e11 and e21). e.2=3.30 is also the life expectancy at age\r
70 to be spent in the disability state.</p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by\r
age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:\r
-</b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>\r
+</b><a href="biaspar/ebiaspar1.png"><b>biaspar/ebiaspar1.png</b></a></h5>\r
\r
<p>This figure represents the health expectancies and the total\r
-life expectancy with the confident interval in dashed curve. </p>\r
+life expectancy with a confidence interval (dashed line). </p>\r
\r
-<pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>\r
+<pre> <img src="biaspar/ebiaspar1.png" width="400" height="300"></pre>\r
\r
<p>Standard deviations (obtained from the information matrix of\r
the model) of these quantities are very useful.\r
\r
<p>Our health expectancies estimates vary according to the sample\r
size (and the standard deviations give confidence intervals of\r
-the estimate) but also according to the model fitted. Let us\r
+the estimates) but also according to the model fitted. Let us\r
explain it in more details.</p>\r
\r
-<p>Choosing a model means ar least two kind of choices. First we\r
-have to decide the number of disability states. Second we have to\r
-design, within the logit model family, the model: variables,\r
-covariables, confonding factors etc. to be included.</p>\r
+<p>Choosing a model means at least two kind of choices. At first we\r
+have to decide the number of disability states. And at second we have to\r
+design, within the logit model family, the model itself: variables,\r
+covariables, confounding factors etc. to be included.</p>\r
\r
<p>More disability states we have, better is our demographical\r
approach of the disability process, but smaller are the number of\r
heterogeneity in the risk of dying. The total mortality at each\r
age is the weighted mean of the mortality in each state by the\r
prevalence in each state. Therefore if the proportion of people\r
-at each age and in each state is different from the stationary\r
+at each age and in each state is different from the period\r
equilibrium, there is no reason to find the same total mortality\r
at a particular age. Life expectancy, even if it is a very useful\r
tool, has a very strong hypothesis of homogeneity of the\r
latter. But the differential in mortality complexifies the\r
measurement.</p>\r
\r
-<p>Incidences of disability or recovery are not affected by the\r
-number of states if these states are independant. But incidences\r
-estimates are dependant on the specification of the model. More\r
-covariates we added in the logit model better is the model, but\r
-some covariates are not well measured, some are confounding\r
-factors like in any statistical model. The procedure to "fit\r
-the best model' is similar to logistic regression which itself is\r
-similar to regression analysis. We haven't yet been sofar because\r
-we also have a severe limitation which is the speed of the\r
-convergence. On a Pentium III, 500 MHz, even the simplest model,\r
-estimated by month on 8,000 people may take 4 hours to converge.\r
-Also, the program is not yet a statistical package, which permits\r
-a simple writing of the variables and the model to take into\r
-account in the maximisation. The actual program allows only to\r
-add simple variables like age+sex or age+sex+ age*sex but will\r
-never be general enough. But what is to remember, is that\r
-incidences or probability of change from one state to another is\r
-affected by the variables specified into the model.</p>\r
-\r
-<p>Also, the age range of the people interviewed has a link with\r
+<p>Incidences of disability or recovery are not affected by the number\r
+of states if these states are independent. But incidences estimates\r
+are dependent on the specification of the model. More covariates we\r
+added in the logit model better is the model, but some covariates are\r
+not well measured, some are confounding factors like in any\r
+statistical model. The procedure to "fit the best model' is\r
+similar to logistic regression which itself is similar to regression\r
+analysis. We haven't yet been sofar because we also have a severe\r
+limitation which is the speed of the convergence. On a Pentium III,\r
+500 MHz, even the simplest model, estimated by month on 8,000 people\r
+may take 4 hours to converge. Also, the IMaCh program is not a\r
+statistical package, and does not allow sophisticated design\r
+variables. If you need sophisticated design variable you have to them\r
+your self and and add them as ordinary variables. IMaCX allows up to 8\r
+variables. The current version of this program allows only to add\r
+simple variables like age+sex or age+sex+ age*sex but will never be\r
+general enough. But what is to remember, is that incidences or\r
+probability of change from one state to another is affected by the\r
+variables specified into the model.</p>\r
+\r
+<p>Also, the age range of the people interviewed is linked \r
the age range of the life expectancy which can be estimated by\r
extrapolation. If your sample ranges from age 70 to 95, you can\r
clearly estimate a life expectancy at age 70 and trust your\r
-confidence interval which is mostly based on your sample size,\r
+confidence interval because it is mostly based on your sample size,\r
but if you want to estimate the life expectancy at age 50, you\r
-should rely in your model, but fitting a logistic model on a age\r
-range of 70-95 and estimating probabilties of transition out of\r
-this age range, say at age 50 is very dangerous. At least you\r
+should rely in the design of your model. Fitting a logistic model on a age\r
+range of 70 to 95 and estimating probabilties of transition out of\r
+this age range, say at age 50, is very dangerous. At least you\r
should remember that the confidence interval given by the\r
standard deviation of the health expectancies, are under the\r
strong assumption that your model is the 'true model', which is\r
-probably not the case.</p>\r
+probably not the case outside the age range of your sample.</p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter\r
file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>\r
program while saving the old output files. </p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:\r
-</b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>\r
+</b><a href="biaspar/frbiaspar.txt"><b>biaspar/frbiaspar.txt</b></a></h5>\r
\r
-<p\r
-style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,\r
+<p>\r
+\r
+First,\r
we have estimated the observed prevalence between 1/1/1984 and\r
-1/6/1988. The mean date of interview (weighed average of the\r
-interviews performed between1/1/1984 and 1/6/1988) is estimated\r
+1/6/1988 (June, European syntax of dates). The mean date of all interviews (weighted average of the\r
+interviews performed between 1/1/1984 and 1/6/1988) is estimated\r
to be 13/9/1985, as written on the top on the file. Then we\r
forecast the probability to be in each state. </p>\r
\r
-<p\r
-style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,\r
-at date 1/1/1989 : </p>\r
+<p>\r
+For example on 1/1/1989 : </p>\r
\r
<pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3\r
# Forecasting at date 1/1/1989\r
73 0.807 0.078 0.115</pre>\r
\r
-<p\r
-style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Since\r
-the minimum age is 70 on the 13/9/1985, the youngest forecasted\r
-age is 73. This means that at age a person aged 70 at 13/9/1989\r
-has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.\r
+<p>\r
+\r
+Since the minimum age is 70 on the 13/9/1985, the youngest forecasted\r
+age is 73. This means that at age a person aged 70 at 13/9/1989 has a\r
+probability to enter state1 of 0.807 at age 73 on 1/1/1989.\r
Similarly, the probability to be in state 2 is 0.078 and the\r
-probability to die is 0.115. Then, on the 1/1/1989, the\r
-prevalence of disability at age 73 is estimated to be 0.088.</p>\r
+probability to die is 0.115. Then, on the 1/1/1989, the prevalence of\r
+disability at age 73 is estimated to be 0.088.</p>\r
\r
<h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:\r
-</b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>\r
+</b><a href="biaspar/poprbiaspar.txt"><b>biaspar/poprbiaspar.txt</b></a></h5>\r
\r
<pre># Age P.1 P.2 P.3 [Population]\r
# Forecasting at date 1/1/1989 \r
\r
<p>Since you know how to run the program, it is time to test it\r
on your own computer. Try for example on a parameter file named <a\r
-href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy\r
+href="imachpar.imach">imachpar.imach</a> which is a copy\r
of <font size="2" face="Courier New">mypar.imach</font> included\r
in the subdirectory of imach, <font size="2" face="Courier New">mytry</font>.\r
-Edit it to change the name of the data file to <font size="2"\r
-face="Courier New">..\data\mydata.txt</font> if you don't want to\r
+Edit it and change the name of the data file to <font size="2"\r
+face="Courier New">mydata.txt</font> if you don't want to\r
copy it on the same directory. The file <font face="Courier New">mydata.txt</font>\r
is a smaller file of 3,000 people but still with 4 waves. </p>\r
\r
-<p>Click on the imach.exe icon to open a window. Answer to the\r
-question:'<strong>Enter the parameter file name:'</strong></p>\r
+<p>Right click on the .imach file and a window will popup with the\r
+string '<strong>Enter the parameter file name:'</strong></p>\r
\r
<table border="1">\r
<tr>\r
- <td width="100%"><strong>IMACH, Version 0.
8a</strong><p><strong>Enter
\r- the parameter file name: ..\mytry\imachpar.imach</strong></p>\r
+ <td width="100%"><strong>IMACH, Version 0.
97b</strong><p><strong>Enter
\r+ the parameter file name: imachpar.imach</strong></p>\r
</td>\r
</tr>\r
</table>\r
\r
<ul>\r
<li><pre><u>Output on the screen</u> The output screen looks like <a\r
-href="imachrun.LOG">this Log file</a>\r
+href="biaspar.log">biaspar.log</a>\r
#\r
-\r
-title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3\r
+title=MLE datafile=mydaiata.txt lastobs=3000 firstpass=1 lastpass=3\r
ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>\r
</li>\r
<li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92\r
Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>\r
</li>\r
</ul>\r
+It includes some warnings or errors which are very important for\r
+you. Be careful with such warnings because your results may be biased\r
+if, for example, you have people who accepted to be interviewed at\r
+first pass but never after. Or if you don't have the exact month of\r
+death. In such cases IMaCh doesn't take any initiative, it does only\r
+warn you. It is up to you to decide what to do with these\r
+people. Excluding them is usually a wrong decision. It is better to\r
+decide that the month of death is at the mid-interval between the last\r
+two waves for example.<p>\r
+\r
+If you survey suffers from severe attrition, you have to analyse the\r
+characteristics of the lost people and overweight people with same\r
+characteristics for example.\r
+<p>\r
+By default, IMaCH warns and excludes these problematic people, but you\r
+have to be careful with such results.\r
\r
<p> </p>\r
\r
</ul>\r
\r
<p><font size="3">Once the running is finished, the program\r
-requires a caracter:</font></p>\r
+requires a character:</font></p>\r
\r
<table border="1">\r
<tr>\r
</tr>\r
</table>\r
\r
+In order to have an idea of the time needed to reach convergence,\r
+IMaCh gives an estimation if the convergence needs 10, 20 or 30\r
+iterations. It might be useful.\r
+\r
<p><font size="3">First you should enter <strong>e </strong>to\r
edit the master file mypar.htm. </font></p>\r
\r
<br>\r
- Copy of the parameter file: <a href="ormypar.txt">ormypar.txt</a><br>\r
- Gnuplot file name: <a href="mypar.gp.txt">mypar.gp.txt</a><br>\r
- -
Observed prevalence in each state: <a
\r+ -
Cross-sectional prevalence in each state: <a
\r href="prmypar.txt">prmypar.txt</a> <br>\r
- -
Stationary prevalence in each state: <a
\r+ -
Period prevalence in each state: <a
\r href="plrmypar.txt">plrmypar.txt</a> <br>\r
- Transition probabilities: <a href="pijrmypar.txt">pijrmypar.txt</a><br>\r
- Life expectancies by age and initial health status\r
health status (estepm=24 months): <a href="vrmypar.txt">vrmypar.txt</a><br>\r
- Health expectancies with their variances: <a\r
href="trmypar.txt">trmypar.txt</a> <br>\r
- - Standard deviation of
stationary prevalences: <a
\r+ - Standard deviation of
period prevalences: <a
\r href="vplrmypar.txt">vplrmypar.txt</a> <br>\r
No population forecast: popforecast = 0 (instead of 1) or\r
stepm = 24 (instead of 1) or model=. (instead of .)<br>\r
-<a href="../mytry/pemypar1.gif">One-step transition\r
probabilities</a><br>\r
-<a href="../mytry/pmypar11.gif">Convergence to the\r
- stationary prevalence</a><br>\r
- -<a href="..\mytry\vmypar11.gif">Observed and stationary\r
+ period prevalence</a><br>\r
+ -<a href="..\mytry\vmypar11.gif">Cross-sectional and period\r
prevalence in state (1) with the confident interval</a> <br>\r
- -<a href="..\mytry\vmypar21.gif">Observed and stationary\r
+ -<a href="..\mytry\vmypar21.gif">Cross-sectional and period\r
prevalence in state (2) with the confident interval</a> <br>\r
-<a href="..\mytry\expmypar11.gif">Health life\r
expectancies by age and initial health state (1)</a> <br>\r
href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a\r
href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>\r
\r
-<p>Latest version (0.
8a of May 2002) can be accessed at <a
\r+<p>Latest version (0.
97b of June 2004) can be accessed at <a
\r href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>\r
</p>\r
</body>\r
git://henry.ined.fr / .git / commitdiff