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<title>Computing Health Expectancies using IMaCh</title>	<title>Computing Health Expectancies using IMaCh</title>
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Line 36 color="#00006A">INED</font></a><font col	Line 34 color="#00006A">INED</font></a><font col
href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>	href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>

<p align="center"><font color="#00006A" size="4"><strong>Version	<p align="center"><font color="#00006A" size="4"><strong>Version
0.8a, May 2002</strong></font></p>	0.97, June 2004</strong></font></p>

<hr size="3" color="#EC5E5E">	<hr size="3" color="#EC5E5E">

Line 102 population) is then decomposed into DFLE	Line 100 population) is then decomposed into DFLE
computing HE is usually called the Sullivan method (from the name	computing HE is usually called the Sullivan method (from the name
of the author who first described it).</p>	of the author who first described it).</p>

<p>Age-specific proportions of people disable are very difficult	<p>Age-specific proportions of people disabled (prevalence of
to forecast because each proportion corresponds to historical	disability) are dependent on the historical flows from entering
conditions of the cohort and it is the result of the historical	disability and recovering in the past until today. The age-specific
flows from entering disability and recovering in the past until	forces (or incidence rates), estimated over a recent period of time
today. The age-specific intensities (or incidence rates) of	(like for period forces of mortality), of entering disability or
entering disability or recovering a good health, are reflecting	recovering a good health, are reflecting current conditions and
actual conditions and therefore can be used at each age to	therefore can be used at each age to forecast the future of this
forecast the future of this cohort. For example if a country is	cohort<em>if nothing changes in the future</em>, i.e to forecast the
improving its technology of prosthesis, the incidence of	prevalence of disability of each cohort. Our finding (2) is that the period
recovering the ability to walk will be higher at each (old) age,	prevalence of disability (computed from period incidences) is lower
but the prevalence of disability will only slightly reflect an	than the cross-sectional prevalence. For example if a country is
improve because the prevalence is mostly affected by the history	improving its technology of prosthesis, the incidence of recovering
of the cohort and not by recent period effects. To measure the	the ability to walk will be higher at each (old) age, but the
period improvement we have to simulate the future of a cohort of	prevalence of disability will only slightly reflect an improve because
new-borns entering or leaving at each age the disability state or	the prevalence is mostly affected by the history of the cohort and not
dying according to the incidence rates measured today on	by recent period effects. To measure the period improvement we have to
different cohorts. The proportion of people disabled at each age	simulate the future of a cohort of new-borns entering or leaving at
in this simulated cohort will be much lower (using the exemple of	each age the disability state or dying according to the incidence
an improvement) that the proportions observed at each age in a	rates measured today on different cohorts. The proportion of people
cross-sectional survey. This new prevalence curve introduced in a	disabled at each age in this simulated cohort will be much lower that
life table will give a much more actual and realistic HE level	the proportions observed at each age in a cross-sectional survey. This
than the Sullivan method which mostly measured the History of	new prevalence curve introduced in a life table will give a more
health conditions in this country.</p>	realistic HE level than the Sullivan method which mostly measured the
	History of health conditions in this country.</p>

<p>Therefore, the main question is how to measure incidence rates	<p>Therefore, the main question is how to measure incidence rates
from cross-longitudinal surveys? This is the goal of the IMaCH	from cross-longitudinal surveys? This is the goal of the IMaCH
Line 196 Unix.<br>	Line 195 Unix.<br>
<p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New	<p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
Methods for Analyzing Active Life Expectancy". <i>Journal of	Methods for Analyzing Active Life Expectancy". <i>Journal of
Aging and Health</i>. Vol 10, No. 2. </p>	Aging and Health</i>. Vol 10, No. 2. </p>
	<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
	>Ličvre A., Brouard N. and Heathcote Ch. (2003) Estimating Health Expectancies
	from Cross-longitudinal surveys. <em>Mathematical Population Studies</em>.- 10(4), pp. 211-248</a>

<hr>	<hr>

Line 223 survival time after the last interview.<	Line 225 survival time after the last interview.<
<h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>	<h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>

<p>In this example, 8,000 people have been interviewed in a	<p>In this example, 8,000 people have been interviewed in a
cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).	cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). Some
Some people missed 1, 2 or 3 interviews. Health statuses are	people missed 1, 2 or 3 interviews. Health statuses are healthy (1)
healthy (1) and disable (2). The survey is not a real one. It is	and disable (2). The survey is not a real one. It is a simulation of
a simulation of the American Longitudinal Survey on Aging. The	the American Longitudinal Survey on Aging. The disability state is
disability state is defined if the individual missed one of four	defined if the individual missed one of four ADL (Activity of daily
ADL (Activity of daily living, like bathing, eating, walking).	living, like bathing, eating, walking). Therefore, even if the
Therefore, even is the individuals interviewed in the sample are	individuals interviewed in the sample are virtual, the information
virtual, the information brought with this sample is close to the	brought with this sample is close to the situation of the United
situation of the United States. Sex is not recorded is this	States. Sex is not recorded is this sample. The LSOA survey is biased
sample.</p>	in the sense that people living in an institution were not surveyed at
	first pass in 1984. Thus the prevalence of disability in 1984 is
	biased downwards at old ages. But when people left their household to
	an institution, they have been surveyed in their institution in 1986,
	1988 or 1990. Thus incidences are not biased. But cross-sectional
	prevalences of disability at old ages are thus artificially increasing
	in 1986, 1988 and 1990 because of a higher weight of people
	institutionalized in the sample. Our article shows the
	opposite: the period prevalence is lower at old ages than the
	adjusted cross-sectional prevalence proving important current progress
	against disability.</p>

<p>Each line of the data set (named <a href="data1.txt">data1.txt</a>	<p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
in this first example) is an individual record which fields are: </p>	in this first example) is an individual record. Fields are separated
	by blanks: </p>

<ul>	<ul>
<li><b>Index number</b>: positive number (field 1) </li>	<li><b>Index number</b>: positive number (field 1) </li>
Line 278 weights or covariates, you must fill the	Line 291 weights or covariates, you must fill the
<h2><font color="#00006A">Your first example parameter file</font><a	<h2><font color="#00006A">Your first example parameter file</font><a
href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>	href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>

<h2><a name="biaspar"></a>#Imach version 0.8a, May 2002,	<h2><a name="biaspar"></a>#Imach version 0.97b, June 2004,
INED-EUROREVES </h2>	INED-EUROREVES </h2>

<p>This is a comment. Comments start with a '#'.</p>	<p>This first line was a comment. Comments line start with a '#'.</p>

<h4><font color="#FF0000">First uncommented line</font></h4>	<h4><font color="#FF0000">First uncommented line</font></h4>

Line 326 line</font></a></h4>	Line 339 line</font></a></h4>
<li>... </li>	<li>... </li>
</ul>	</ul>
</li>	</li>
<li><b>ncovcol=2</b> Number of covariate columns in the	<li><b>ncovcol=2</b> Number of covariate columns included in the
datafile which precede the date of birth. Here you can	datafile before the column of the date of birth. You can have
put variables that won't necessary be used during the	covariates that won't necessary be used during the
run. It is not the number of covariates that will be	run. It is not the number of covariates that will be
specified by the model. The 'model' syntax describe the	specified by the model. The 'model' syntax describes the
covariates to take into account. </li>	covariates to be taken into account during the run. </li>
<li><b>nlstate=2</b> Number of non-absorbing (alive) states.	<li><b>nlstate=2</b> Number of non-absorbing (alive) states.
Here we have two alive states: disability-free is coded 1	Here we have two alive states: disability-free is coded 1
and disability is coded 2. </li>	and disability is coded 2. </li>
Line 343 line</font></a></h4>	Line 356 line</font></a></h4>
<li>If mle=1 the program does the maximisation and	<li>If mle=1 the program does the maximisation and
the calculation of health expectancies </li>	the calculation of health expectancies </li>
<li>If mle=0 the program only does the calculation of	<li>If mle=0 the program only does the calculation of
the health expectancies. </li>	the health expectancies and other indices and graphs
	but without the maximization.. </li>
	There also other possible values:
	<ul>
	<li>If mle=-1 you get a template which can be useful if
	your model is complex with many covariates.</li>
	<li> If mle=-3 IMaCh computes the mortality but without
	any health status (May 2004)</li> <li>If mle=2 IMach
	likelihood corresponds to a linear interpolation</li> <li>
	If mle=3 IMach likelihood corresponds to an exponential
	inter-extrapolation</li>
	<li> If mle=4 IMach likelihood
	corresponds to no inter-extrapolation, and thus biasing
	the results. </li>
	<li> If mle=5 IMach likelihood
	corresponds to no inter-extrapolation, and before the
	correction of the Jackson's bug (avoid this).</li>
	</ul>
</ul>	</ul>
</li>	</li>
<li><b>weight=0</b> Possibility to add weights. <ul>	<li><b>weight=0</b> Possibility to add weights. <ul>
Line 484 know if you will speed up the convergenc	Line 514 know if you will speed up the convergenc
-ln(12/6)=-ln(2)= -0.693	-ln(12/6)=-ln(2)= -0.693
</pre>	</pre>

	In version 0.9 and higher you can still have valuable results even if
	your stepm parameter is bigger than a month. The idea is to run with
	bigger stepm in order to have a quicker convergence at the price of a
	small bias. Once you know which model you want to fit, you can put
	stepm=1 and wait hours or days to get the convergence!

	To get unbiased results even with large stepm we introduce the idea of
	pseudo likelihood by interpolating two exact likelihoods. Let us
	detail this:
	<p>
	If the interval of <em>d</em> months between two waves is not a
	mutliple of 'stepm', but is comprised between <em>(n-1) stepm</em> and
	<em>n stepm</em> then both exact likelihoods are computed (the
	contribution to the likelihood at <em>n stepm</em> requires one matrix
	product more) (let us remember that we are modelling the probability
	to be observed in a particular state after <em>d</em> months being
	observed at a particular state at 0). The distance, (<em>bh</em> in
	the program), from the month of interview to the rounded date of <em>n
	stepm</em> is computed. It can be negative (interview occurs before
	<em>n stepm</em>) or positive if the interview occurs after <em>n
	stepm</em> (and before <em>(n+1)stepm</em>).
	<br>
	Then the final contribution to the total likelihood is a weighted
	average of these two exact likelihoods at <em>n stepm</em> (out) and
	at <em>(n-1)stepm</em>(savm). We did not want to compute the third
	likelihood at <em>(n+1)stepm</em> because it is too costly in time, so
	we used an extrapolation if <em>bh</em> is positive. <br> Formula of
	inter/extrapolation may vary according to the value of parameter mle:
	<pre>
	mle=1 lli= log((1.+bbh)out[s1][s2]- bbhsavm[s1][s2]); /* linear interpolation */

	mle=2 lli= (savm[s1][s2]>(double)1.e-8 ? \
	log((1.+bbh)out[s1][s2]- bbh(savm[s1][s2])): \
	log((1.+bbh)out[s1][s2])); / linear interpolation */
	mle=3 lli= (savm[s1][s2]>1.e-8 ? \
	(1.+bbh)log(out[s1][s2])- bbhlog(savm[s1][s2]): \
	log((1.+bbh)out[s1][s2])); / exponential inter-extrapolation */

	mle=4 lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* No interpolation */
	no need to save previous likelihood into memory.
	</pre>
	<p>
	If the death occurs between first and second pass, and for example
	more precisely between <em>n stepm</em> and <em>(n+1)stepm</em> the
	contribution of this people to the likelihood is simply the difference
	between the probability of dying before <em>n stepm</em> and the
	probability of dying before <em>(n+1)stepm</em>. There was a bug in
	version 0.8 and death was treated as any other state, i.e. as if it
	was an observed death at second pass. This was not precise but
	correct, but when information on the precise month of death came
	(death occuring prior to second pass) we did not change the likelihood
	accordingly. Thanks to Chris Jackson for correcting us. In earlier
	versions (fortunately before first publication) the total mortality
	was overestimated (people were dying too early) of about 10%. Version
	0.95 and higher are correct.

	<p> Our suggested choice is mle=1 . If stepm=1 there is no difference
	between various mle options (methods of interpolation). If stepm is
	big, like 12 or 24 or 48 and mle=4 (no interpolation) the bias may be
	very important if the mean duration between two waves is not a
	multiple of stepm. See the appendix in our main publication concerning
	the sine curve of biases.


<h4><font color="#FF0000">Guess values for computing variances</font></h4>	<h4><font color="#FF0000">Guess values for computing variances</font></h4>

<p>This is an output if <a href="#mle">mle</a>=1. But it can be	<p>These values are output by the maximisation of the likelihood <a
used as an input to get the various output data files (Health	href="#mle">mle</a>=1. These valuse can be used as an input of a
expectancies, stationary prevalence etc.) and figures without	second run in order to get the various output data files (Health
rerunning the rather long maximisation phase (mle=0). </p>	expectancies, period prevalence etc.) and figures without rerunning
	the long maximisation phase (mle=0). </p>
<p>The scales are small values for the evaluation of numerical
derivatives. These derivatives are used to compute the hessian	<p>These 'scales' are small values needed for the computing of
matrix of the parameters, that is the inverse of the covariance	numerical derivatives. These derivatives are used to compute the
matrix, and the variances of health expectancies. Each line	hessian matrix of the parameters, that is the inverse of the
consists in indices "ij" followed by the initial scales	covariance matrix. They are often used for estimating variances and
(zero to simplify) associated with aij and bij. </p>	confidence intervals. Each line consists in indices "ij"
	followed by the initial scales (zero to simplify) associated with aij
	and bij. </p>

<ul>	<ul>
<li>If mle=1 you can enter zeros:</li>	<li>If mle=1 you can enter zeros:</li>
Line 508 consists in indices "ij" follo	Line 604 consists in indices "ij" follo
23 0. 0. </pre>	23 0. 0. </pre>
</blockquote>	</blockquote>
</li>	</li>
<li>If mle=0 you must enter a covariance matrix (usually	<li>If mle=0 (no maximisation of Likelihood) you must enter a covariance matrix (usually
obtained from an earlier run).</li>	obtained from an earlier run).</li>
</ul>	</ul>

<h4><font color="#FF0000">Covariance matrix of parameters</font></h4>	<h4><font color="#FF0000">Covariance matrix of parameters</font></h4>

<p>This is an output if <a href="#mle">mle</a>=1. But it can be	<p>The covariance matrix is output if <a href="#mle">mle</a>=1. But it can be
used as an input to get the various output data files (Health	also used as an input to get the various output data files (Health
expectancies, stationary prevalence etc.) and figures without	expectancies, period prevalence etc.) and figures without
rerunning the rather long maximisation phase (mle=0). <br>	rerunning the maximisation phase (mle=0). <br>
Each line starts with indices "ijk" followed by the	Each line starts with indices "ijk" followed by the
covariances between aij and bij:<br>	covariances between aij and bij:<br>
</p>	</p>
Line 549 prevalences and health expectancies</fon	Line 645 prevalences and health expectancies</fon

<pre>agemin=70 agemax=100 bage=50 fage=100</pre>	<pre>agemin=70 agemax=100 bage=50 fage=100</pre>

<pre>	<p>
Once we obtained the estimated parameters, the program is able	Once we obtained the estimated parameters, the program is able
to calculated stationary prevalence, transitions probabilities	to calculate period prevalence, transitions probabilities
and life expectancies at any age. Choice of age range is useful	and life expectancies at any age. Choice of age range is useful
for extrapolation. In our data file, ages varies from age 70 to	for extrapolation. In this example, age of people interviewed varies
102. It is possible to get extrapolated stationary prevalence by	from 69 to 102 and the model is estimated using their exact ages. But
age ranging from agemin to agemax.	if you are interested in the age-specific period prevalence you can
	start the simulation at an exact age like 70 and stop at 100. Then the
	program will draw at least two curves describing the forecasted
Setting bage=50 (begin age) and fage=100 (final age), makes	prevalences of two cohorts, one for healthy people at age 70 and the second
the program computing life expectancy from age 'bage' to age	for disabled people at the same initial age. And according to the
	mixing property (ergodicity) and because of recovery, both prevalences
	will tend to be identical at later ages. Thus if you want to compute
	the prevalence at age 70, you should enter a lower agemin value.

	<p>
	Setting bage=50 (begin age) and fage=100 (final age), let
	the program compute life expectancy from age 'bage' to age
'fage'. As we use a model, we can interessingly compute life	'fage'. As we use a model, we can interessingly compute life
expectancy on a wider age range than the age range from the data.	expectancy on a wider age range than the age range from the data.
But the model can be rather wrong on much larger intervals.	But the model can be rather wrong on much larger intervals.
Line 568 Program is limited to around 120 for upp	Line 671 Program is limited to around 120 for upp

<ul>	<ul>
<li><b>agemin=</b> Minimum age for calculation of the	<li><b>agemin=</b> Minimum age for calculation of the
stationary prevalence </li>	period prevalence </li>
<li><b>agemax=</b> Maximum age for calculation of the	<li><b>agemax=</b> Maximum age for calculation of the
stationary prevalence </li>	period prevalence </li>
<li><b>bage=</b> Minimum age for calculation of the health	<li><b>bage=</b> Minimum age for calculation of the health
expectancies </li>	expectancies </li>
<li><b>fage=</b> Maximum age for calculation of the health	<li><b>fage=</b> Maximum age for calculation of the health
Line 578 Program is limited to around 120 for upp	Line 681 Program is limited to around 120 for upp
</ul>	</ul>

<h4><a name="Computing"><font color="#FF0000">Computing</font></a><font	<h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
color="#FF0000"> the observed prevalence</font></h4>	color="#FF0000"> the cross-sectional prevalence</font></h4>

<pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</pre>	<pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</pre>

<pre>	<p>
Statements 'begin-prev-date' and 'end-prev-date' allow to	Statements 'begin-prev-date' and 'end-prev-date' allow to
select the period in which we calculate the observed prevalences	select the period in which we calculate the observed prevalences
in each state. In this example, the prevalences are calculated on	in each state. In this example, the prevalences are calculated on
data survey collected between 1 january 1984 and 1 june 1988.	data survey collected between 1 january 1984 and 1 june 1988.
</pre>	</p>

<ul>	<ul>
<li><strong>begin-prev-date= </strong>Starting date	<li><strong>begin-prev-date= </strong>Starting date
Line 615 expectancies</font></h4>	Line 718 expectancies</font></h4>

<pre>pop_based=0</pre>	<pre>pop_based=0</pre>

<p>The program computes status-based health expectancies, i.e	<p>The program computes status-based health expectancies, i.e health
health expectancies which depends on your initial health state.	expectancies which depend on the initial health state. If you are
If you are healthy your healthy life expectancy (e11) is higher	healthy, your healthy life expectancy (e11) is higher than if you were
than if you were disabled (e21, with e11 > e21).<br>	disabled (e21, with e11 > e21).<br> To compute a healthy life
To compute a healthy life expectancy independant of the initial	expectancy 'independent' of the initial status we have to weight e11
status we have to weight e11 and e21 according to the probability	and e21 according to the probability to be in each state at initial
to be in each state at initial age or, with other word, according	age which are corresponding to the proportions of people in each health
to the proportion of people in each state.<br>	state (cross-sectional prevalences).<p>
We prefer computing a 'pure' period healthy life expectancy based
only on the transtion forces. Then the weights are simply the	We could also compute e12 and e12 and get e.2 by weighting them
stationnary prevalences or 'implied' prevalences at the initial	according to the observed cross-sectional prevalences at initial age.
age.<br>	<p> In a similar way we could compute the total life expectancy by
Some other people would like to use the cross-sectional	summing e.1 and e.2 .
prevalences (the "Sullivan prevalences") observed at	<br>
the initial age during a period of time <a href="#Computing">defined	The main difference between 'population based' and 'implied' or
just above</a>. <br>	'period' consists in the weights used. 'Usually', cross-sectional
</p>	prevalences of disability are higher than period prevalences
	particularly at old ages. This is true if the country is improving its
	health system by teaching people how to prevent disability as by
	promoting better screening, for example of people needing cataracts
	surgeryand for many unknown reasons that this program may help to
	discover. Then the proportion of disabled people at age 90 will be
	lower than the current observed proportion.
	<p>
	Thus a better Health Expectancy and even a better Life Expectancy
	value is given by forecasting not only the current lower mortality at
	all ages but also a lower incidence of disability and higher recovery.
	<br> Using the period prevalences as weight instead of the
	cross-sectional prevalences we are computing indices which are more
	specific to the current situations and therefore more useful to
	predict improvements or regressions in the future as to compare
	different policies in various countries.

<ul>	<ul>
<li><strong>popbased= 0 </strong>Health expectancies are	<li><strong>popbased= 0 </strong>Health expectancies are computed
computed at each age from stationary prevalences	at each age from period prevalences 'expected' at this initial
'expected' at this initial age.</li>	age.</li>
<li><strong>popbased= 1 </strong>Health expectancies are	<li><strong>popbased= 1 </strong>Health expectancies are
computed at each age from cross-sectional 'observed'	computed at each age from cross-sectional 'observed' prevalence at
prevalence at this initial age. As all the population is	this initial age. As all the population is not observed at the
not observed at the same exact date we define a short	same exact date we define a short period were the observed
period were the observed prevalence is computed.</li>	prevalence can be computed.<br>

	We simply sum all people surveyed within these two exact dates
	who belong to a particular age group (single year) at the date of
	interview and being in a particular health state. Then it is easy to
	get the proportion of people of a particular health status among all
	people of the same age group.<br>

	If both dates are spaced and are covering two waves or more, people
	being interviewed twice or more are counted twice or more. The program
	takes into account the selection of individuals interviewed between
	firstpass and lastpass too (we don't know if it can be useful).
	</li>
</ul>	</ul>

<h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>	<h4><font color="#FF0000">Prevalence forecasting (Experimental)</font></h4>

<pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>	<pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>

Line 659 smoothed forecasted prevalences with a f	Line 789 smoothed forecasted prevalences with a f
centered at the mid-age of the five-age period. <br>	centered at the mid-age of the five-age period. <br>
</p>	</p>

	<h4><font color="#FF0000">Population forecasting (Experimental)</font></h4>

<ul>	<ul>
<li><strong>starting-proj-date</strong>= starting date	<li><strong>starting-proj-date</strong>= starting date
(day/month/year) of forecasting</li>	(day/month/year) of forecasting</li>
Line 670 centered at the mid-age of the five-age	Line 802 centered at the mid-age of the five-age
value 1 if the prevalences are smoothed and 0 otherwise.</li>	value 1 if the prevalences are smoothed and 0 otherwise.</li>
</ul>	</ul>

<h4><font color="#FF0000">Last uncommented line : Population
forecasting </font></h4>

<pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>

<p>This command is available if the interpolation unit is a
month, i.e. stepm=1 and if popforecast=1. From a data file
including age and number of persons alive at the precise date
popfiledate, you can forecast the number of persons
in each state until date last-popfiledate. In this
example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
includes real data which are the Japanese population in 1989.<br>
</p>

<ul type="disc">	<ul type="disc">
<li class="MsoNormal"	<li><b>popforecast=
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
0 </b>Option for population forecasting. If	0 </b>Option for population forecasting. If
popforecast=1, the programme does the forecasting<b>.</b></li>	popforecast=1, the programme does the forecasting<b>.</b></li>
<li class="MsoNormal"	<li><b>popfile=
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
</b>name of the population file</li>	</b>name of the population file</li>
<li class="MsoNormal"	<li><b>popfiledate=</b>
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
date of the population population</li>	date of the population population</li>
<li class="MsoNormal"	<li><b>last-popfiledate</b>=
style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
date of the last population projection </li>	date of the last population projection </li>
</ul>	</ul>

Line 705 includes real data which are the Japanes	Line 820 includes real data which are the Japanes
<h2><a name="running"></a><font color="#00006A">Running Imach	<h2><a name="running"></a><font color="#00006A">Running Imach
with this example</font></h2>	with this example</font></h2>

<pre>We assume that you typed in your <a href="biaspar.imach">1st_example	<p>We assume that you already typed your <a href="biaspar.imach">1st_example
parameter file</a> as explained <a href="#biaspar">above</a>.	parameter file</a> as explained <a href="#biaspar">above</a>.

To run the program you should either:	To run the program under Windows you should either:
</pre>	</p>

<ul>	<ul>
<li>click on the imach.exe icon and enter the name of the	<li>click on the imach.exe icon and either:
parameter file which is for example <a	<ul>
href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>	<li>enter the name of the
</li>	parameter file which is for example <tt>
<li>You also can locate the biaspar.imach icon in <a	C:\home\myname\lsoa\biaspar.imach"</tt></li>
href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your	<li>or locate the biaspar.imach icon in your folder such as
mouse and drag it with the mouse on the imach window). </li>	<tt>C:\home\myname\lsoa</tt>
<li>With latest version (0.7 and higher) if you setup windows	and drag it, with your mouse, on the already open imach window. </li>
in order to understand ".imach" extension you	</ul>
can right click the biaspar.imach icon and either edit
with notepad the parameter file or execute it with imach	<li>With version (0.97b) if you ran setup at installation, Windows is
or whatever. </li>	supposed to understand the ".imach" extension and you can
	right click the biaspar.imach icon and either edit with wordpad
	(better than notepad) the parameter file or execute it with
	IMaCh. </li>
</ul>	</ul>

<pre>The time to converge depends on the step unit that you used (1	<p>The time to converge depends on the step unit that you used (1
month is cpu consuming), on the number of cases, and on the	month is more precise but more cpu consuming), on the number of cases,
number of variables.	and on the number of variables (covariates).

	<p>
The program outputs many files. Most of them are files which	The program outputs many files. Most of them are files which will be
will be plotted for better understanding.	plotted for better understanding.

</pre>

	</p>
	To run under Linux it is mostly the same.
	<p>
	It is neither more difficult to run it under a MacIntosh.
<hr>	<hr>

<h2><a name="output"><font color="#00006A">Output of the program	<h2><a name="output"><font color="#00006A">Output of the program
and graphs</font> </a></h2>	and graphs</font> </a></h2>

<p>Once the optimization is finished, some graphics can be made	<p>Once the optimization is finished (once the convergence is
with a grapher. We use Gnuplot which is an interactive plotting	reached), many tables and graphics are produced.<p>
program copyrighted but freely distributed. A gnuplot reference	The IMaCh program will create a subdirectory of the same name as your
manual is available <a href="http://www.gnuplot.info/">here</a>. <br>	parameter file (here mypar) where all the tables and figures will be
When the running is finished, the user should enter a caracter	stored.<br>
for plotting and output editing. <br>
These caracters are:<br>	Important files like the log file and the output parameter file (which
	contains the estimates of the maximisation) are stored at the main
	level not in this subdirectory. File with extension .log and .txt can
	be edited with a standard editor like wordpad or notepad or even can be
	viewed with a browser like Internet Explorer or Mozilla.

	<p> The main html file is also named with the same name <a
	href="biaspar.htm">biaspar.htm</a>. You can click on it by holding
	your shift key in order to open it in another window (Windows).
	<p>
	Our grapher is Gnuplot, it is an interactive plotting program (GPL) which
	can also work in batch. A gnuplot reference manual is available <a
	href="http://www.gnuplot.info/">here</a>. <br> When the run is
	finished, and in order that the window doesn't disappear, the user
	should enter a character like <tt>q</tt> for quitting. <br> These
	characters are:<br>
</p>	</p>

<ul>	<ul>
<li>'c' to start again the program from the beginning.</li>	<li>'e' for opening the main result html file <a
<li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>	href="biaspar.htm"><strong>biaspar.htm</strong></a> file to edit
file to edit the output files and graphs. </li>	the output files and graphs. </li>
<li>'g' to graph again</li>	<li>'g' to graph again</li>
	<li>'c' to start again the program from the beginning.</li>
<li>'q' for exiting.</li>	<li>'q' for exiting.</li>
</ul>	</ul>

	The main gnuplot file is named <tt>biaspar.gp</tt> and can be edited (right
	click) and run again.
	<p>Gnuplot is easy and you can use it to make more complex
	graphs. Just click on gnuplot and type plot sin(x) to see how easy it
	is.


<h5><font size="4"><strong>Results files </strong></font><br>	<h5><font size="4"><strong>Results files </strong></font><br>
<br>	<br>
<font color="#EC5E5E" size="3"><strong>- </strong></font><a	<font color="#EC5E5E" size="3"><strong>- </strong></font><a
name="Observed prevalence in each state"><font color="#EC5E5E"	name="cross-sectional prevalence in each state"><font color="#EC5E5E"
size="3"><strong>Observed prevalence in each state</strong></font></a><font	size="3"><strong>cross-sectional prevalence in each state</strong></font></a><font
color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:	color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
</b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>	</b><a href="biaspar/prbiaspar.txt"><b>biaspar/prbiaspar.txt</b></a><br>
</h5>	</h5>

<p>The first line is the title and displays each field of the	<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	file. First column corresponds to age. Fields 2 and 6 are the
proportion of individuals in states 1 and 2 respectively as	proportion of individuals in states 1 and 2 respectively as
observed during the first exam. Others fields are the numbers of	observed at first exam. Others fields are the numbers of
people in states 1, 2 or more. The number of columns increases if	people in states 1, 2 or more. The number of columns increases if
the number of states is higher than 2.<br>	the number of states is higher than 2.<br>
The header of the file is </p>	The header of the file is </p>
Line 780 The header of the file is </p>	Line 922 The header of the file is </p>
71 0.99681 625 627 71 0.00319 2 627	71 0.99681 625 627 71 0.00319 2 627
72 0.97125 1115 1148 72 0.02875 33 1148 </pre>	72 0.97125 1115 1148 72 0.02875 33 1148 </pre>

<p>It means that at age 70, the prevalence in state 1 is 1.000	<p>It means that at age 70 (between 70 and 71), the prevalence in state 1 is 1.000
and in state 2 is 0.00 . At age 71 the number of individuals in	and in state 2 is 0.00 . At age 71 the number of individuals in
state 1 is 625 and in state 2 is 2, hence the total number of	state 1 is 625 and in state 2 is 2, hence the total number of
people aged 71 is 625+2=627. <br>	people aged 71 is 625+2=627. <br>
Line 809 covariance matrix</b></font><b>: </b><a	Line 951 covariance matrix</b></font><b>: </b><a
<p>By substitution of these parameters in the regression model,	<p>By substitution of these parameters in the regression model,
we obtain the elementary transition probabilities:</p>	we obtain the elementary transition probabilities:</p>

<p><img src="pebiaspar1.gif" width="400" height="300"></p>	<p><img src="biaspar/pebiaspar11.png" width="400" height="300"></p>

<h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:	<h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
</b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>	</b><a href="biaspar/pijrbiaspar.txt"><b>biaspar/pijrbiaspar.txt</b></a></h5>

<p>Here are the transitions probabilities Pij(x, x+nh) where nh	<p>Here are the transitions probabilities Pij(x, x+nh). The second
is a multiple of 2 years. The first column is the starting age x	column is the starting age x (from age 95 to 65), the third is age
(from age 50 to 100), the second is age (x+nh) and the others are	(x+nh) and the others are the transition probabilities p11, p12, p13,
the transition probabilities p11, p12, p13, p21, p22, p23. For	p21, p22, p23. The first column indicates the value of the covariate
example, line 5 of the file is: </p>	(without any other variable than age it is equal to 1) For example, line 5 of the file
	is: </p>

<pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>	<pre>1 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>

<p>and this means: </p>	<p>and this means: </p>

Line 832 p22(100,106)=0.13678	Line 975 p22(100,106)=0.13678
p22(100,106)=0.84513 </pre>	p22(100,106)=0.84513 </pre>

<h5><font color="#EC5E5E" size="3"><b>- </b></font><a	<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
name="Stationary prevalence in each state"><font color="#EC5E5E"	name="Period prevalence in each state"><font color="#EC5E5E"
size="3"><b>Stationary prevalence in each state</b></font></a><b>:	size="3"><b>Period prevalence in each state</b></font></a><b>:
</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>	</b><a href="biaspar/plrbiaspar.txt"><b>biaspar/plrbiaspar.txt</b></a></h5>

<pre>#Prevalence	<pre>#Prevalence
#Age 1-1 2-2	#Age 1-1 2-2
Line 845 size="3"><b>Stationary prevalence in eac	Line 988 size="3"><b>Stationary prevalence in eac
72 0.88139 0.11861	72 0.88139 0.11861
73 0.87015 0.12985 </pre>	73 0.87015 0.12985 </pre>

<p>At age 70 the stationary prevalence is 0.90134 in state 1 and	<p>At age 70 the period prevalence is 0.90134 in state 1 and 0.09866
0.09866 in state 2. This stationary prevalence differs from	in state 2. This period prevalence differs from the cross-sectional
observed prevalence. Here is the point. The observed prevalence	prevalence. Here is the point. The cross-sectional prevalence at age
at age 70 results from the incidence of disability, incidence of	70 results from the incidence of disability, incidence of recovery and
recovery and mortality which occurred in the past of the cohort.	mortality which occurred in the past of the cohort. Period prevalence
Stationary prevalence results from a simulation with actual	results from a simulation with current incidences of disability,
incidences and mortality (estimated from this cross-longitudinal	recovery and mortality estimated from this cross-longitudinal
survey). It is the best predictive value of the prevalence in the	survey. It is a good predictin of the prevalence in the
future if "nothing changes in the future". This is	future if "nothing changes in the future". This is exactly
exactly what demographers do with a Life table. Life expectancy	what demographers do with a period life table. Life expectancy is the
is the expected mean time to survive if observed mortality rates	expected mean survival time if current mortality rates (age-specific incidences
(incidence of mortality) "remains constant" in the	of mortality) "remain constant" in the future. </p>
future. </p>

<h5><font color="#EC5E5E" size="3"><b>- Standard deviation of	<h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
stationary prevalence</b></font><b>: </b><a	period prevalence</b></font><b>: </b><a
href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>	href="biaspar/vplrbiaspar.txt"><b>biaspar/vplrbiaspar.txt</b></a></h5>

<p>The stationary prevalence has to be compared with the observed	<p>The period prevalence has to be compared with the cross-sectional
prevalence by age. But both are statistical estimates and	prevalence. But both are statistical estimates and therefore
subjected to stochastic errors due to the size of the sample, the	have confidence intervals.
design of the survey, and, for the stationary prevalence to the	<b>For the cross-sectional prevalence we generally need information on
model used and fitted. It is possible to compute the standard	the design of the surveys. It is usually not enough to consider the
deviation of the stationary prevalence at each age.</p>	number of people surveyed at a particular age and to estimate a
	Bernouilli confidence interval based on the prevalence at that
	age. But you can do it to have an idea of the randomness. At least you
	can get a visual appreciation of the randomness by looking at the
	fluctuation over ages.

	<p> For the period prevalence it is possible to estimate the
	confidence interval from the Hessian matrix (see the publication for
	details). We are supposing that the design of the survey will only
	alter the weight of each individual. IMaCh is scaling the weights of
	individuals-waves contributing to the likelihood by making the sum of
	the weights equal to the sum of individuals-waves contributing: a
	weighted survey doesn't increase or decrease the size of the survey,
	it only give more weights to some individuals and thus less to the
	others.

<h5><font color="#EC5E5E" size="3">-Observed and stationary	<h5><font color="#EC5E5E" size="3">-cross-sectional and period
prevalence in state (2=disable) with confidence interval</font>:<b>	prevalence in state (2=disable) with confidence interval</font>:<b>
</b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>	</b><a href="biaspar/vbiaspar21.htm"><b>biaspar/vbiaspar21.png</b></a></h5>

<p>This graph exhibits the stationary prevalence in state (2)	<p>This graph exhibits the period prevalence in state (2) with the
with the confidence interval in red. The green curve is the	confidence interval in red. The green curve is the observed prevalence
observed prevalence (or proportion of individuals in state (2)).	(or proportion of individuals in state (2)). Without discussing the
Without discussing the results (it is not the purpose here), we	results (it is not the purpose here), we observe that the green curve
observe that the green curve is rather below the stationary	is rather below the period prevalence. It the data where not biased by
prevalence. It suggests an increase of the disability prevalence	the non inclusion of people living in institutions we would have
in the future.</p>	concluded that the prevalence of disability will increase in the
	future (see the main publication if you are interested in real data
	and results which are opposite).</p>

<p><img src="vbiaspar21.gif" width="400" height="300"></p>	<p><img src="biaspar/vbiaspar21.png" width="400" height="300"></p>

<h5><font color="#EC5E5E" size="3"><b>-Convergence to the	<h5><font color="#EC5E5E" size="3"><b>-Convergence to the
stationary prevalence of disability</b></font><b>: </b><a	period prevalence of disability</b></font><b>: </b><a
href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>	href="biaspar/pbiaspar11.png"><b>biaspar/pbiaspar11.png</b></a><br>
<img src="pbiaspar11.gif" width="400" height="300"> </h5>	<img src="biaspar/pbiaspar11.png" width="400" height="300"> </h5>

<p>This graph plots the conditional transition probabilities from	<p>This graph plots the conditional transition probabilities from
an initial state (1=healthy in red at the bottom, or 2=disable in	an initial state (1=healthy in red at the bottom, or 2=disable in
Line 895 green on top) at age <em>x </em>to the f	Line 1053 green on top) at age <em>x </em>to the f
age <em>x+h. </em>Conditional means at the condition to be alive	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	at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>	curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
+ <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary	+ <em>hP22x) </em>converge with <em>h, </em>to the <em>period
prevalence of disability</em>. In order to get the stationary	prevalence of disability</em>. In order to get the period
prevalence at age 70 we should start the process at an earlier	prevalence at age 70 we should start the process at an earlier
age, i.e.50. If the disability state is defined by severe	age, i.e.50. If the disability state is defined by severe
disability criteria with only a few chance to recover, then the	disability criteria with only a few chance to recover, then the
Line 905 probably longer. But we don't have exper	Line 1063 probably longer. But we don't have exper

<h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age	<h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
and initial health status with standard deviation</b></font><b>: </b><a	and initial health status with standard deviation</b></font><b>: </b><a
href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>	href="biaspar/erbiaspar.txt"><b>biaspar/erbiaspar.txt</b></a></h5>

<pre># Health expectancies	<pre># Health expectancies
# Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)	# Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)
70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366)	70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
71 9.9325 (0.1409) 3.0495 (0.4234) 5.2627 (0.1107) 5.6384 (0.3129)	71 10.4786 (0.1184) 3.2093 (0.3212) 4.3384 (0.0875) 4.4820 (0.2076)
72 9.4603 (0.1319) 3.0540 (0.3770) 4.8810 (0.1099) 5.5811 (0.2907)	72 9.9551 (0.1103) 3.2236 (0.2827) 4.0426 (0.0885) 4.4827 (0.1966)
73 9.0009 (0.1246) 3.0565 (0.3345) 4.5188 (0.1098) 5.5187 (0.2702)	73 9.4476 (0.1035) 3.2379 (0.2478) 3.7621 (0.0899) 4.4825 (0.1858)
	74 8.9564 (0.0980) 3.2522 (0.2165) 3.4966 (0.0920) 4.4815 (0.1754)
	75 8.4815 (0.0937) 3.2665 (0.1887) 3.2457 (0.0946) 4.4798 (0.1656)
	76 8.0230 (0.0905) 3.2806 (0.1645) 3.0090 (0.0979) 4.4772 (0.1565)
	77 7.5810 (0.0884) 3.2946 (0.1438) 2.7860 (0.1017) 4.4738 (0.1484)
	78 7.1554 (0.0871) 3.3084 (0.1264) 2.5763 (0.1062) 4.4696 (0.1416)
	79 6.7464 (0.0867) 3.3220 (0.1124) 2.3794 (0.1112) 4.4646 (0.1364)
	80 6.3538 (0.0868) 3.3354 (0.1014) 2.1949 (0.1168) 4.4587 (0.1331)
	81 5.9775 (0.0873) 3.3484 (0.0933) 2.0222 (0.1230) 4.4520 (0.1320)
</pre>	</pre>

<pre>For example 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366) means:	<pre>For example 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
e11=10.4171 e12=3.0433 e21=5.6641 e22=5.6907 </pre>	means
	e11=11.0180 e12=3.1950 e21=4.6500 e22=4.4807 </pre>

<pre><img src="expbiaspar21.gif" width="400" height="300"><img	<pre><img src="biaspar/expbiaspar21.png" width="400" height="300"><img
src="expbiaspar11.gif" width="400" height="300"></pre>	src="biaspar/expbiaspar11.png" width="400" height="300"></pre>

<p>For example, life expectancy of a healthy individual at age 70	<p>For example, life expectancy of a healthy individual at age 70
is 10.42 in the healthy state and 3.04 in the disability state	is 11.0 in the healthy state and 3.2 in the disability state
(=13.46 years). If he was disable at age 70, his life expectancy	(total of 14.2 years). If he was disable at age 70, his life expectancy
will be shorter, 5.66 in the healthy state and 5.69 in the	will be shorter, 4.65 years in the healthy state and 4.5 in the
disability state (=11.35 years). The total life expectancy is a	disability state (=9.15 years). The total life expectancy is a
weighted mean of both, 13.46 and 11.35; weight is the proportion	weighted mean of both, 14.2 and 9.15. The weight is the proportion
of people disabled at age 70. In order to get a pure period index	of people disabled at age 70. In order to get a period index
(i.e. based only on incidences) we use the <a	(i.e. based only on incidences) we use the <a
href="#Stationary prevalence in each state">computed or	href="#Period prevalence in each state">stable or
stationary prevalence</a> at age 70 (i.e. computed from	period prevalence</a> at age 70 (i.e. computed from
incidences at earlier ages) instead of the <a	incidences at earlier ages) instead of the <a
href="#Observed prevalence in each state">observed prevalence</a>	href="#cross-sectional prevalence in each state">cross-sectional prevalence</a>
(for example at first exam) (<a href="#Health expectancies">see	(observed for example at first medical exam) (<a href="#Health expectancies">see
below</a>).</p>	below</a>).</p>

<h5><font color="#EC5E5E" size="3"><b>- Variances of life	<h5><font color="#EC5E5E" size="3"><b>- Variances of life
expectancies by age and initial health status</b></font><b>: </b><a	expectancies by age and initial health status</b></font><b>: </b><a
href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>	href="biaspar/vrbiaspar.txt"><b>biaspar/vrbiaspar.txt</b></a></h5>

<p>For example, the covariances of life expectancies Cov(ei,ej)	<p>For example, the covariances of life expectancies Cov(ei,ej)
at age 50 are (line 3) </p>	at age 50 are (line 3) </p>
Line 946 at age 50 are (line 3) </p>	Line 1113 at age 50 are (line 3) </p>
<pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>	<pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>

<h5><font color="#EC5E5E" size="3"><b>-Variances of one-step	<h5><font color="#EC5E5E" size="3"><b>-Variances of one-step
probabilities </b></font><b>: </b><a href="probrbiaspar.txt"><b>probrbiaspar.txt</b></a></h5>	probabilities </b></font><b>: </b><a href="biaspar/probrbiaspar.txt"><b>biaspar/probrbiaspar.txt</b></a></h5>

<p>For example, at age 65</p>	<p>For example, at age 65</p>

Line 956 probabilities </b></font><b>: </b><a hre	Line 1123 probabilities </b></font><b>: </b><a hre
name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health	name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
expectancies</b></font></a><font color="#EC5E5E" size="3"><b>	expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
with standard errors in parentheses</b></font><b>: </b><a	with standard errors in parentheses</b></font><b>: </b><a
href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>	href="biaspar/trbiaspar.txt"><font face="Courier New"><b>biaspar/trbiaspar.txt</b></font></a></h5>

<pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>	<pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>

<pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>	<pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>

<p>Thus, at age 70 the total life expectancy, e..=13.26 years is	<p>Thus, at age 70 the total life expectancy, e..=13.26 years is
the weighted mean of e1.=13.46 and e2.=11.35 by the stationary	the weighted mean of e1.=13.46 and e2.=11.35 by the period
prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in	prevalences at age 70 which are 0.90134 in state 1 and 0.09866 in
state 2, respectively (the sum is equal to one). e.1=9.95 is the	state 2 respectively (the sum is equal to one). e.1=9.95 is the
Disability-free life expectancy at age 70 (it is again a weighted	Disability-free life expectancy at age 70 (it is again a weighted
mean of e11 and e21). e.2=3.30 is also the life expectancy at age	mean of e11 and e21). e.2=3.30 is also the life expectancy at age
70 to be spent in the disability state.</p>	70 to be spent in the disability state.</p>

<h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by	<h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:	age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
</b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>	</b><a href="biaspar/ebiaspar1.png"><b>biaspar/ebiaspar1.png</b></a></h5>

<p>This figure represents the health expectancies and the total	<p>This figure represents the health expectancies and the total
life expectancy with the confident interval in dashed curve. </p>	life expectancy with a confidence interval (dashed line). </p>

<pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>	<pre> <img src="biaspar/ebiaspar1.png" width="400" height="300"></pre>

<p>Standard deviations (obtained from the information matrix of	<p>Standard deviations (obtained from the information matrix of
the model) of these quantities are very useful.	the model) of these quantities are very useful.
Line 992 but the standard deviation of the estima	Line 1159 but the standard deviation of the estima

<p>Our health expectancies estimates vary according to the sample	<p>Our health expectancies estimates vary according to the sample
size (and the standard deviations give confidence intervals of	size (and the standard deviations give confidence intervals of
the estimate) but also according to the model fitted. Let us	the estimates) but also according to the model fitted. Let us
explain it in more details.</p>	explain it in more details.</p>

<p>Choosing a model means ar least two kind of choices. First we	<p>Choosing a model means at least two kind of choices. At first we
have to decide the number of disability states. Second we have to	have to decide the number of disability states. And at second we have to
design, within the logit model family, the model: variables,	design, within the logit model family, the model itself: variables,
covariables, confonding factors etc. to be included.</p>	covariables, confounding factors etc. to be included.</p>

<p>More disability states we have, better is our demographical	<p>More disability states we have, better is our demographical
approach of the disability process, but smaller are the number of	approach of the disability process, but smaller are the number of
Line 1016 than the mortality from the healthy stat	Line 1183 than the mortality from the healthy stat
heterogeneity in the risk of dying. The total mortality at each	heterogeneity in the risk of dying. The total mortality at each
age is the weighted mean of the mortality in each state by the	age is the weighted mean of the mortality in each state by the
prevalence in each state. Therefore if the proportion of people	prevalence in each state. Therefore if the proportion of people
at each age and in each state is different from the stationary	at each age and in each state is different from the period
equilibrium, there is no reason to find the same total mortality	equilibrium, there is no reason to find the same total mortality
at a particular age. Life expectancy, even if it is a very useful	at a particular age. Life expectancy, even if it is a very useful
tool, has a very strong hypothesis of homogeneity of the	tool, has a very strong hypothesis of homogeneity of the
Line 1026 disability state in order to maximise th	Line 1193 disability state in order to maximise th
latter. But the differential in mortality complexifies the	latter. But the differential in mortality complexifies the
measurement.</p>	measurement.</p>

<p>Incidences of disability or recovery are not affected by the	<p>Incidences of disability or recovery are not affected by the number
number of states if these states are independant. But incidences	of states if these states are independent. But incidences estimates
estimates are dependant on the specification of the model. More	are dependent on the specification of the model. More covariates we
covariates we added in the logit model better is the model, but	added in the logit model better is the model, but some covariates are
some covariates are not well measured, some are confounding	not well measured, some are confounding factors like in any
factors like in any statistical model. The procedure to "fit	statistical model. The procedure to "fit the best model' is
the best model' is similar to logistic regression which itself is	similar to logistic regression which itself is similar to regression
similar to regression analysis. We haven't yet been sofar because	analysis. We haven't yet been sofar because we also have a severe
we also have a severe limitation which is the speed of the	limitation which is the speed of the convergence. On a Pentium III,
convergence. On a Pentium III, 500 MHz, even the simplest model,	500 MHz, even the simplest model, estimated by month on 8,000 people
estimated by month on 8,000 people may take 4 hours to converge.	may take 4 hours to converge. Also, the IMaCh program is not a
Also, the program is not yet a statistical package, which permits	statistical package, and does not allow sophisticated design
a simple writing of the variables and the model to take into	variables. If you need sophisticated design variable you have to them
account in the maximisation. The actual program allows only to	your self and and add them as ordinary variables. IMaCX allows up to 8
add simple variables like age+sex or age+sex+ age*sex but will	variables. The current version of this program allows only to add
never be general enough. But what is to remember, is that	simple variables like age+sex or age+sex+ age*sex but will never be
incidences or probability of change from one state to another is	general enough. But what is to remember, is that incidences or
affected by the variables specified into the model.</p>	probability of change from one state to another is affected by the
	variables specified into the model.</p>

<p>Also, the age range of the people interviewed has a link with	<p>Also, the age range of the people interviewed is linked
the age range of the life expectancy which can be estimated by	the age range of the life expectancy which can be estimated by
extrapolation. If your sample ranges from age 70 to 95, you can	extrapolation. If your sample ranges from age 70 to 95, you can
clearly estimate a life expectancy at age 70 and trust your	clearly estimate a life expectancy at age 70 and trust your
confidence interval which is mostly based on your sample size,	confidence interval because it is mostly based on your sample size,
but if you want to estimate the life expectancy at age 50, you	but if you want to estimate the life expectancy at age 50, you
should rely in your model, but fitting a logistic model on a age	should rely in the design of your model. Fitting a logistic model on a age
range of 70-95 and estimating probabilties of transition out of	range of 70 to 95 and estimating probabilties of transition out of
this age range, say at age 50 is very dangerous. At least you	this age range, say at age 50, is very dangerous. At least you
should remember that the confidence interval given by the	should remember that the confidence interval given by the
standard deviation of the health expectancies, are under the	standard deviation of the health expectancies, are under the
strong assumption that your model is the 'true model', which is	strong assumption that your model is the 'true model', which is
probably not the case.</p>	probably not the case outside the age range of your sample.</p>

<h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter	<h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>	file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
Line 1066 file</b></font><b>: </b><a href="orbiasp	Line 1234 file</b></font><b>: </b><a href="orbiasp
program while saving the old output files. </p>	program while saving the old output files. </p>

<h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:	<h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
</b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>	</b><a href="biaspar/frbiaspar.txt"><b>biaspar/frbiaspar.txt</b></a></h5>

<p	<p>
style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,
	First,
we have estimated the observed prevalence between 1/1/1984 and	we have estimated the observed prevalence between 1/1/1984 and
1/6/1988. The mean date of interview (weighed average of the	1/6/1988 (June, European syntax of dates). The mean date of all interviews (weighted average of the
interviews performed between1/1/1984 and 1/6/1988) is estimated	interviews performed between 1/1/1984 and 1/6/1988) is estimated
to be 13/9/1985, as written on the top on the file. Then we	to be 13/9/1985, as written on the top on the file. Then we
forecast the probability to be in each state. </p>	forecast the probability to be in each state. </p>

<p	<p>
style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,	For example on 1/1/1989 : </p>
at date 1/1/1989 : </p>

<pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3	<pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
# Forecasting at date 1/1/1989	# Forecasting at date 1/1/1989
73 0.807 0.078 0.115</pre>	73 0.807 0.078 0.115</pre>

<p	<p>
style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Since
the minimum age is 70 on the 13/9/1985, the youngest forecasted	Since the minimum age is 70 on the 13/9/1985, the youngest forecasted
age is 73. This means that at age a person aged 70 at 13/9/1989	age is 73. This means that at age a person aged 70 at 13/9/1989 has a
has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.	probability to enter state1 of 0.807 at age 73 on 1/1/1989.
Similarly, the probability to be in state 2 is 0.078 and the	Similarly, the probability to be in state 2 is 0.078 and the
probability to die is 0.115. Then, on the 1/1/1989, the	probability to die is 0.115. Then, on the 1/1/1989, the prevalence of
prevalence of disability at age 73 is estimated to be 0.088.</p>	disability at age 73 is estimated to be 0.088.</p>

<h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:	<h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
</b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>	</b><a href="biaspar/poprbiaspar.txt"><b>biaspar/poprbiaspar.txt</b></a></h5>

<pre># Age P.1 P.2 P.3 [Population]	<pre># Age P.1 P.2 P.3 [Population]
# Forecasting at date 1/1/1989	# Forecasting at date 1/1/1989
Line 1118 are in state 2. One year latter, 512892	Line 1286 are in state 2. One year latter, 512892

<p>Since you know how to run the program, it is time to test it	<p>Since you know how to run the program, it is time to test it
on your own computer. Try for example on a parameter file named <a	on your own computer. Try for example on a parameter file named <a
href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy	href="imachpar.imach">imachpar.imach</a> which is a copy
of <font size="2" face="Courier New">mypar.imach</font> included	of <font size="2" face="Courier New">mypar.imach</font> included
in the subdirectory of imach, <font size="2" face="Courier New">mytry</font>.	in the subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
Edit it to change the name of the data file to <font size="2"	Edit it and change the name of the data file to <font size="2"
face="Courier New">..\data\mydata.txt</font> if you don't want to	face="Courier New">mydata.txt</font> if you don't want to
copy it on the same directory. The file <font face="Courier New">mydata.txt</font>	copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
is a smaller file of 3,000 people but still with 4 waves. </p>	is a smaller file of 3,000 people but still with 4 waves. </p>

<p>Click on the imach.exe icon to open a window. Answer to the	<p>Right click on the .imach file and a window will popup with the
question:'<strong>Enter the parameter file name:'</strong></p>	string '<strong>Enter the parameter file name:'</strong></p>

<table border="1">	<table border="1">
<tr>	<tr>
<td width="100%"><strong>IMACH, Version 0.8a</strong><p><strong>Enter	<td width="100%"><strong>IMACH, Version 0.97b</strong><p><strong>Enter
the parameter file name: ..\mytry\imachpar.imach</strong></p>	the parameter file name: imachpar.imach</strong></p>
</td>	</td>
</tr>	</tr>
</table>	</table>
Line 1146 size="2" face="Courier New">mytry</font>	Line 1314 size="2" face="Courier New">mytry</font>

<ul>	<ul>
<li><pre><u>Output on the screen</u> The output screen looks like <a	<li><pre><u>Output on the screen</u> The output screen looks like <a
href="imachrun.LOG">this Log file</a>	href="biaspar.log">biaspar.log</a>
#	#
	title=MLE datafile=mydaiata.txt lastobs=3000 firstpass=1 lastpass=3
title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>	ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
</li>	</li>
<li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92	<li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
Line 1163 Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]	Line 1330 Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]
Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>	Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
</li>	</li>
</ul>	</ul>
	It includes some warnings or errors which are very important for
	you. Be careful with such warnings because your results may be biased
	if, for example, you have people who accepted to be interviewed at
	first pass but never after. Or if you don't have the exact month of
	death. In such cases IMaCh doesn't take any initiative, it does only
	warn you. It is up to you to decide what to do with these
	people. Excluding them is usually a wrong decision. It is better to
	decide that the month of death is at the mid-interval between the last
	two waves for example.<p>

	If you survey suffers from severe attrition, you have to analyse the
	characteristics of the lost people and overweight people with same
	characteristics for example.
	<p>
	By default, IMaCH warns and excludes these problematic people, but you
	have to be careful with such results.

<p> </p>	<p> </p>

Line 1237 End of Imach	Line 1420 End of Imach
</ul>	</ul>

<p><font size="3">Once the running is finished, the program	<p><font size="3">Once the running is finished, the program
requires a caracter:</font></p>	requires a character:</font></p>

<table border="1">	<table border="1">
<tr>	<tr>
Line 1246 requires a caracter:</font></p>	Line 1429 requires a caracter:</font></p>
</tr>	</tr>
</table>	</table>

	In order to have an idea of the time needed to reach convergence,
	IMaCh gives an estimation if the convergence needs 10, 20 or 30
	iterations. It might be useful.

<p><font size="3">First you should enter <strong>e </strong>to	<p><font size="3">First you should enter <strong>e </strong>to
edit the master file mypar.htm. </font></p>	edit the master file mypar.htm. </font></p>

Line 1254 edit the master file mypar.htm. </font><	Line 1441 edit the master file mypar.htm. </font><
<br>	<br>
- Copy of the parameter file: <a href="ormypar.txt">ormypar.txt</a><br>	- Copy of the parameter file: <a href="ormypar.txt">ormypar.txt</a><br>
- Gnuplot file name: <a href="mypar.gp.txt">mypar.gp.txt</a><br>	- Gnuplot file name: <a href="mypar.gp.txt">mypar.gp.txt</a><br>
- Observed prevalence in each state: <a	- Cross-sectional prevalence in each state: <a
href="prmypar.txt">prmypar.txt</a> <br>	href="prmypar.txt">prmypar.txt</a> <br>
- Stationary prevalence in each state: <a	- Period prevalence in each state: <a
href="plrmypar.txt">plrmypar.txt</a> <br>	href="plrmypar.txt">plrmypar.txt</a> <br>
- Transition probabilities: <a href="pijrmypar.txt">pijrmypar.txt</a><br>	- Transition probabilities: <a href="pijrmypar.txt">pijrmypar.txt</a><br>
- Life expectancies by age and initial health status	- Life expectancies by age and initial health status
Line 1270 edit the master file mypar.htm. </font><	Line 1457 edit the master file mypar.htm. </font><
health status (estepm=24 months): <a href="vrmypar.txt">vrmypar.txt</a><br>	health status (estepm=24 months): <a href="vrmypar.txt">vrmypar.txt</a><br>
- Health expectancies with their variances: <a	- Health expectancies with their variances: <a
href="trmypar.txt">trmypar.txt</a> <br>	href="trmypar.txt">trmypar.txt</a> <br>
- Standard deviation of stationary prevalences: <a	- Standard deviation of period prevalences: <a
href="vplrmypar.txt">vplrmypar.txt</a> <br>	href="vplrmypar.txt">vplrmypar.txt</a> <br>
No population forecast: popforecast = 0 (instead of 1) or	No population forecast: popforecast = 0 (instead of 1) or
stepm = 24 (instead of 1) or model=. (instead of .)<br>	stepm = 24 (instead of 1) or model=. (instead of .)<br>
Line 1281 edit the master file mypar.htm. </font><	Line 1468 edit the master file mypar.htm. </font><
-<a href="../mytry/pemypar1.gif">One-step transition	-<a href="../mytry/pemypar1.gif">One-step transition
probabilities</a><br>	probabilities</a><br>
-<a href="../mytry/pmypar11.gif">Convergence to the	-<a href="../mytry/pmypar11.gif">Convergence to the
stationary prevalence</a><br>	period prevalence</a><br>
-<a href="..\mytry\vmypar11.gif">Observed and stationary	-<a href="..\mytry\vmypar11.gif">Cross-sectional and period
prevalence in state (1) with the confident interval</a> <br>	prevalence in state (1) with the confident interval</a> <br>
-<a href="..\mytry\vmypar21.gif">Observed and stationary	-<a href="..\mytry\vmypar21.gif">Cross-sectional and period
prevalence in state (2) with the confident interval</a> <br>	prevalence in state (2) with the confident interval</a> <br>
-<a href="..\mytry\expmypar11.gif">Health life	-<a href="..\mytry\expmypar11.gif">Health life
expectancies by age and initial health state (1)</a> <br>	expectancies by age and initial health state (1)</a> <br>
Line 1304 simple justification (name, email, insti	Line 1491 simple justification (name, email, insti
href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a	href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>	href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>

<p>Latest version (0.8a of May 2002) can be accessed at <a	<p>Latest version (0.97b of June 2004) can be accessed at <a
href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>	href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
</p>	</p>
</body>	</body>

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