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<title>Computing Health Expectancies using IMaCh</title>	<title>Computing Health Expectancies using IMaCh</title>
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<body bgcolor="#FFFFFF">	<body bgcolor="#FFFFFF">
Line 30 color="#00006A">INED</font></a><font col	Line 37 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
0.71a, March 2002</strong></font></p>	0.8, March 2002</strong></font></p>

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

Line 272 weights or covariates, you must fill the	Line 279 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 0.71a, March 2002,	<h2><a name="biaspar"></a>#Imach version 0.8, March 2002,
INED-EUROREVES </h2>	INED-EUROREVES </h2>

<p>This is a comment. Comments start with a '#'.</p>	<p>This is a comment. Comments start with a '#'.</p>
Line 304 INED-EUROREVES </h2>	Line 311 INED-EUROREVES </h2>
<h4><a name="biaspar-2"><font color="#FF0000">Second uncommented	<h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
line</font></a></h4>	line</font></a></h4>

<pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>	<pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>

<ul>	<ul>
<li><b>ftol=1e-8</b> Convergence tolerance on the function	<li><b>ftol=1e-8</b> Convergence tolerance on the function
Line 320 line</font></a></h4>	Line 327 line</font></a></h4>
<li>... </li>	<li>... </li>
</ul>	</ul>
</li>	</li>
<li><b>ncov=2</b> Number of covariates in the datafile. The	<li><b>ncovcol=2</b> Number of covariate columns in the datafile
intercept and the age parameter are counting for 2	which precede the date of birth. Here you can put variables that
covariates.</li>	won't necessary be used during the run. It is not the number of
	covariates that will be specified by the model. The 'model'
	syntax describe the covariates to take into account. </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 348 line</font></a></h4>	Line 357 line</font></a></h4>
<h4><font color="#FF0000">Covariates</font></h4>	<h4><font color="#FF0000">Covariates</font></h4>

<p>Intercept and age are systematically included in the model.	<p>Intercept and age are systematically included in the model.
Additional covariates (actually two) can be included with the command: </p>	Additional covariates can be included with the command: </p>

<pre>model=<em>list of covariates</em></pre>	<pre>model=<em>list of covariates</em></pre>

Line 368 Additional covariates (actually two) can	Line 377 Additional covariates (actually two) can
the product covariate*age</li>	the product covariate*age</li>
</ul>	</ul>

	<p>In this example, we have two covariates in the data file
	(fields 2 and 3). The number of covariates included in the data file
	between the id and the date of birth is ncovcol=2 (it was named ncov
	in version prior to 0.8). If you have 3 covariates in the datafile
	(fields 2, 3 and 4), you will set ncovcol=3. Then you can run the
	programme with a new parametrisation taking into account the
	third covariate. For example, <strong>model=V1+V3 </strong>estimates
	a model with the first and third covariates. More complicated
	models can be used, but it will takes more time to converge. With
	a simple model (no covariates), the programme estimates 8
	parameters. Adding covariates increases the number of parameters
	: 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
	</strong>and 20 for <strong>model=V1+V2+V3.</strong></p>

<h4><font color="#FF0000">Guess values for optimization</font><font	<h4><font color="#FF0000">Guess values for optimization</font><font
color="#00006A"> </font></h4>	color="#00006A"> </font></h4>

Line 376 optimization. The number of parameters,	Line 399 optimization. The number of parameters,
number of absorbing states and non-absorbing states and on the	number of absorbing states and non-absorbing states and on the
number of covariates. <br>	number of covariates. <br>
<em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +	<em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
<em>ndeath</em>-1)<em>nlstate</em><em>ncov</em> . <br>	<em>ndeath</em>-1)<em>nlstate</em><em>ncovmodel</em> . <br>
<br>	<br>
Thus in the simple case with 2 covariates (the model is log	Thus in the simple case with 2 covariates (the model is log
(pij/pii) = aij + bij * age where intercept and age are the two	(pij/pii) = aij + bij * age where intercept and age are the two
Line 397 aij bij</b> </p>	Line 420 aij bij</b> </p>
23 -6.234642 0.022315 </pre>	23 -6.234642 0.022315 </pre>
</blockquote>	</blockquote>

<p>or, to simplify (in most of cases it converges but there is no warranty!): </p>	<p>or, to simplify (in most of cases it converges but there is no
	warranty!): </p>

<blockquote>	<blockquote>
<pre>12 0.0 0.0	<pre>12 0.0 0.0
Line 406 aij bij</b> </p>	Line 430 aij bij</b> </p>
23 0.0 0.0</pre>	23 0.0 0.0</pre>
</blockquote>	</blockquote>

	<p> In order to speed up the convergence you can make a first run with
	a large stepm i.e stepm=12 or 24 and then decrease the stepm until
	stepm=1 month. If newstepm is the new shorter stepm and stepm can be
	expressed as a multiple of newstepm, like newstepm=n stepm, then the
	following approximation holds:
	<pre>aij(stepm) = aij(n . stepm) - ln(n)
	</pre> and
	<pre>bij(stepm) = bij(n . stepm) .</pre>

	<p> For example if you already ran for a 6 months interval and
	got:<br>
	<pre># Parameters
	12 -13.390179 0.126133
	13 -7.493460 0.048069
	21 0.575975 -0.041322
	23 -4.748678 0.030626
	</pre>
	If you now want to get the monthly estimates, you can guess the aij by
	substracting ln(6)= 1,7917<br> and running<br>
	<pre>12 -15.18193847 0.126133
	13 -9.285219469 0.048069
	21 -1.215784469 -0.041322
	23 -6.540437469 0.030626
	</pre>
	and get<br>
	<pre>12 -15.029768 0.124347
	13 -8.472981 0.036599
	21 -1.472527 -0.038394
	23 -6.553602 0.029856
	</br>
	which is closer to the results. The approximation is probably useful
	only for very small intervals and we don't have enough experience to
	know if you will speed up the convergence or not.
	<pre> -ln(12)= -2.484
	-ln(6/1)=-ln(6)= -1.791
	-ln(3/1)=-ln(3)= -1.0986
	-ln(12/6)=-ln(2)= -0.693
	</pre>

<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>This is an output if <a href="#mle">mle</a>=1. But it can be
Line 419 matrix of the parameters, that is the in	Line 482 matrix of the parameters, that is the in
matrix, and the variances of health expectancies. Each line	matrix, and the variances of health expectancies. Each line
consists in indices "ij" followed by the initial scales	consists in indices "ij" followed by the initial scales
(zero to simplify) associated with aij and bij. </p>	(zero to simplify) associated with aij and bij. </p>
	<ul> <li>If mle=1 you can enter zeros:</li>
<ul>	<blockquote><pre># Scales (for hessian or gradient estimation)
<li>If mle=1 you can enter zeros:</li>
</ul>

<blockquote>
<pre># Scales (for hessian or gradient estimation)
12 0. 0.	12 0. 0.
13 0. 0.	13 0. 0.
21 0. 0.	21 0. 0.
23 0. 0. </pre>	23 0. 0. </pre>
</blockquote>	</blockquote>

<ul>
<li>If mle=0 you must enter a covariance matrix (usually	<li>If mle=0 you must enter a covariance matrix (usually
obtained from an earlier run).</li>	obtained from an earlier run).</li>
</ul>	</ul>
Line 442 consists in indices "ij" follo	Line 498 consists in indices "ij" follo
<p>This is an output if <a href="#mle">mle</a>=1. But it can be	<p>This is an output if <a href="#mle">mle</a>=1. But it can be
used as an input to get the various output data files (Health	used as an input to get the various output data files (Health
expectancies, stationary prevalence etc.) and figures without	expectancies, stationary prevalence etc.) and figures without
rerunning the rather long maximisation phase (mle=0). </p>	rerunning the rather long maximisation phase (mle=0). <br>
	Each line starts with indices "ijk" followed by the
<p>Each line starts with indices "ijk" followed by the	covariances between aij and bij:<br>
covariances between aij and bij: </p>

<pre>	<pre>
121 Var(a12)	121 Var(a12)
122 Cov(b12,a12) Var(b12)	122 Cov(b12,a12) Var(b12)
...	...
232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>	232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>

<ul>	<ul>
<li>If mle=1 you can enter zeros. </li>	<li>If mle=1 you can enter zeros. </li>
</ul>

<blockquote>
<pre># Covariance matrix	<pre># Covariance matrix
121 0.	121 0.
122 0. 0.	122 0. 0.
Line 467 covariances between aij and bij: </p>	Line 517 covariances between aij and bij: </p>
212 0. 0. 0. 0. 0. 0.	212 0. 0. 0. 0. 0. 0.
231 0. 0. 0. 0. 0. 0. 0.	231 0. 0. 0. 0. 0. 0. 0.
232 0. 0. 0. 0. 0. 0. 0. 0.</pre>	232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
</blockquote>

<ul>
<li>If mle=0 you must enter a covariance matrix (usually	<li>If mle=0 you must enter a covariance matrix (usually
obtained from an earlier run).<br>	obtained from an earlier run). </li>
</li>
</ul>	</ul>

<h4><font color="#FF0000">Age range for calculation of stationary	<h4><font color="#FF0000">Age range for calculation of stationary
Line 480 prevalences and health expectancies</fon	Line 526 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>

<p>Once we obtained the estimated parameters, the program is able	<br>Once we obtained the estimated parameters, the program is able
to calculated stationary prevalence, transitions probabilities	to calculated stationary 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 our data file, ages varies from age 70 to
102. It is possible to get extrapolated stationary	102. It is possible to get extrapolated stationary prevalence by
prevalence by age ranging from agemin to agemax. </p>	age ranging from agemin to agemax.


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

	<br>Setting bage=50 (begin age) and fage=100 (final age), makes
	the program computing life expectancy from age 'bage' to age
	'fage'. As we use a model, we can interessingly compute life
	expectancy on a wider age range than the age range from the data.
	But the model can be rather wrong on much larger intervals.
	Program is limited to around 120 for upper age!
<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>	stationary prevalence </li>
Line 510 color="#FF0000"> the observed prevalence	Line 555 color="#FF0000"> the observed prevalence

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

<p>Statements 'begin-prev-date' and 'end-prev-date' allow to	<br>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. </p>	data survey collected between 1 january 1984 and 1 june 1988.

<ul>	<ul>
<li><strong>begin-prev-date= </strong>Starting date	<li><strong>begin-prev-date= </strong>Starting date
(day/month/year)</li>	(day/month/year)</li>
Line 527 expectancies</font></h4>	Line 571 expectancies</font></h4>

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

<p>The program computes status-based health expectancies, i.e health	<p>The program computes status-based health expectancies, i.e
expectancies which depends on your initial health state. If you are	health expectancies which depends on your initial health state.
healthy your healthy life expectancy (e11) is higher than if you were	If you are healthy your healthy life expectancy (e11) is higher
disabled (e21, with e11 > e21).<br>	than if you were disabled (e21, with e11 > e21).<br>
To compute a healthy life expectancy independant of the initial status	To compute a healthy life expectancy independant of the initial
we have to weight e11 and e21 according to the probability to be in	status we have to weight e11 and e21 according to the probability
each state at initial age or, with other word, according to the	to be in each state at initial age or, with other word, according
proportion of people in each state.<br>	to the proportion of people in each state.<br>
	We prefer computing a 'pure' period healthy life expectancy based
We prefer computing a 'pure' period healthy life expectancy based only	only on the transtion forces. Then the weights are simply the
on the transtion forces. Then the weights are simply the stationnary	stationnary prevalences or 'implied' prevalences at the initial
prevalences or 'implied' prevalences at the initial age.<br>	age.<br>
	Some other people would like to use the cross-sectional
Some other people would like to use the cross-sectional prevalences	prevalences (the "Sullivan prevalences") observed at
(the "Sullivan prevalences") observed at the initial age during a	the initial age during a period of time <a href="#Computing">defined
period of time <a href="#Computing">defined just above</a>.	just above</a>. <br>

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

</p>

<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>

<p>Prevalence and population projections are only available if the	<p>Prevalence and population projections are only available if
interpolation unit is a month, i.e. stepm=1 and if there are no	the interpolation unit is a month, i.e. stepm=1 and if there are
covariate. The programme estimates the prevalence in each state at a	no covariate. The programme estimates the prevalence in each
precise date expressed in day/month/year. The programme computes one	state at a precise date expressed in day/month/year. The
forecasted prevalence a year from a starting date (1 january of 1989	programme computes one forecasted prevalence a year from a
in this example) to a final date (1 january 1992). The statement	starting date (1 january of 1989 in this example) to a final date
mov_average allows to compute smoothed forecasted prevalences with a	(1 january 1992). The statement mov_average allows to compute
five-age moving average centered at the mid-age of the five-age	smoothed forecasted prevalences with a five-age moving average
period. </p>	centered at the mid-age of the five-age period. <br>

<ul>	<ul>
<li><strong>starting-proj-date</strong>= starting date	<li><strong>starting-proj-date</strong>= starting date
Line 591 including age and number of persons aliv	Line 635 including age and number of persons aliv
popfiledate, you can forecast the number of persons	popfiledate, you can forecast the number of persons
in each state until date last-popfiledate. In this	in each state until date last-popfiledate. In this
example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>	example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
includes real data which are the Japanese population in 1989.</p>	includes real data which are the Japanese population in 1989.<br>

<ul type="disc">	<ul type="disc">
<li class="MsoNormal"	<li class="MsoNormal"
Line 614 includes real data which are the Japanes	Line 658 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>

<p>We assume that you entered your <a href="biaspar.imach">1st_example	We assume that you typed in your <a href="biaspar.imach">1st_example
parameter file</a> as explained <a href="#biaspar">above</a>. To	parameter file</a> as explained <a href="#biaspar">above</a>.
run the program you should click on the imach.exe icon and enter	<br>To run the program you should either:
	<ul> <li> click on the imach.exe icon and enter
the name of the parameter file which is for example <a	the name of the parameter file which is for example <a
href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>	href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
(you also can click on the biaspar.txt icon located in <br>	<li> You also can locate the biaspar.imach icon in
<a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with	<a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with
the mouse on the imach window).<br>	the mouse on the imach window).
</p>	<li> With latest version (0.7 and higher) if you setup windows in order to
	understand ".imach" extension you can right click the
	biaspar.imach icon and either edit with notepad the parameter file or
	execute it with imach or whatever.
	</ul>

<p>The time to converge depends on the step unit that you used (1	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 cpu consuming), on the number of cases, and on the
number of variables.</p>	number of variables.

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

<hr>	<hr>

Line 641 with a grapher. We use Gnuplot which is	Line 690 with a grapher. We use Gnuplot which is
program copyrighted but freely distributed. A gnuplot reference	program copyrighted but freely distributed. A gnuplot reference
manual is available <a href="http://www.gnuplot.info/">here</a>. <br>	manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
When the running is finished, the user should enter a caracter	When the running is finished, the user should enter a caracter
for plotting and output editing. </p>	for plotting and output editing.

<p>These caracters are:</p>	<br>These caracters are:<br>

<ul>	<ul>
<li>'c' to start again the program from the beginning.</li>	<li>'c' to start again the program from the beginning.</li>
Line 681 people aged 71 is 625+2=627. <br>	Line 730 people aged 71 is 625+2=627. <br>
</p>	</p>

<h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and	<h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>	covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>

<p>This file contains all the maximisation results: </p>	<p>This file contains all the maximisation results: </p>

Line 1000 are in state 2. One year latter, 512892	Line 1049 are in state 2. One year latter, 512892

<hr>	<hr>

<h2><a name="example"> </a><font color="#00006A">Trying an example</font></a></h2>	<h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>

<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.txt">imachpar.txt</a> which is a copy of <font	href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of <font
size="2" face="Courier New">mypar.txt</font> included in the	size="2" face="Courier New">mypar.imach</font> included in the
subdirectory of imach, <font size="2" face="Courier New">mytry</font>.	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 to 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">..\data\mydata.txt</font> if you don't want to
Line 1017 question:'<strong>Enter the parameter fi	Line 1066 question:'<strong>Enter the parameter fi

<table border="1">	<table border="1">
<tr>	<tr>
<td width="100%"><strong>IMACH, Version 0.71</strong><p><strong>Enter	<td width="100%"><strong>IMACH, Version 0.8</strong><p><strong>Enter
the parameter file name: ..\mytry\imachpar.txt</strong></p>	the parameter file name: ..\mytry\imachpar.imach</strong></p>
</td>	</td>
</tr>	</tr>
</table>	</table>
Line 1036 href="imachrun.LOG">this Log file</a>	Line 1085 href="imachrun.LOG">this Log file</a>
#	#

title=MLE datafile=..\data\mydata.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 ncov=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 1141 edit the master file mypar.htm. </font><	Line 1190 edit the master file mypar.htm. </font><
- Observed prevalence in each state: <a	- Observed prevalence in each state: <a
href="..\mytry\prmypar.txt">pmypar.txt</a> <br>	href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
- Estimated parameters and the covariance matrix: <a	- Estimated parameters and the covariance matrix: <a
href="..\mytry\rmypar.txt">rmypar.txt</a> <br>	href="..\mytry\rmypar.txt">rmypar.imach</a> <br>
- Stationary prevalence in each state: <a	- Stationary prevalence in each state: <a
href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>	href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
- Transition probabilities: <a	- Transition probabilities: <a
Line 1164 edit the master file mypar.htm. </font><	Line 1213 edit the master file mypar.htm. </font><
</li>	</li>
<li><u>Graphs</u> <br>	<li><u>Graphs</u> <br>
<br>	<br>
-<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 stationary prevalence</a><br>
-<a href="../mytry/pmypar11.gif">Convergence to the	-<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> <br>
stationary prevalence</a><br>	-<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> <br>
-<a href="..\mytry\vmypar11.gif">Observed and stationary	-<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> <br>
prevalence in state (1) with the confident interval</a> <br>	-<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> <br>
-<a href="..\mytry\vmypar21.gif">Observed and stationary	-<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li>
prevalence in state (2) with the confident interval</a> <br>
-<a href="..\mytry\expmypar11.gif">Health life
expectancies by age and initial health state (1)</a> <br>
-<a href="..\mytry\expmypar21.gif">Health life
expectancies by age and initial health state (2)</a> <br>
-<a href="..\mytry\emypar1.gif">Total life expectancy by
age and health expectancies in states (1) and (2).</a> </li>
</ul>	</ul>

<p>This software have been partly granted by <a	<p>This software have been partly granted by <a
Line 1190 simple justification (name, email, insti	Line 1232 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 (0.71a of March 2002) can be accessed at <a	<p>Latest version (0.8 of March 2002) can be accessed at <a
href="http://euroeves.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>
</html>	</html>

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>

Removed from v.1.7
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	Added in v.1.12