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<head>	<head>
Line 28 src="euroreves2.gif" width="151" height=	Line 29 src="euroreves2.gif" width="151" height=
color="#00006A">INED</font></a><font color="#00006A"> and </font><a	color="#00006A">INED</font></a><font color="#00006A"> and </font><a
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>March	<p align="center"><font color="#00006A" size="4"><strong>Version
2000</strong></font></p>	0.71a, March 2002</strong></font></p>

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

Line 58 color="#00006A">) </font></h4>	Line 59 color="#00006A">) </font></h4>

<ul>	<ul>
<li><a href="#intro">Introduction</a> </li>	<li><a href="#intro">Introduction</a> </li>
<li>The detailed statistical model (<a href="docmath.pdf">PDF
version</a>),(<a href="docmath.ps">ps version</a>) </li>
<li><a href="#data">On what kind of data can it be used?</a></li>	<li><a href="#data">On what kind of data can it be used?</a></li>
<li><a href="#datafile">The data file</a> </li>	<li><a href="#datafile">The data file</a> </li>
<li><a href="#biaspar">The parameter file</a> </li>	<li><a href="#biaspar">The parameter file</a> </li>
Line 80 monitor. In low mortality countries, the	Line 79 monitor. In low mortality countries, the
mortality declines, the increase in DFLE is not proportionate to	mortality declines, the increase in DFLE is not proportionate to
the increase in total Life expectancy. This case is called the <em>Expansion	the increase in total Life expectancy. This case is called the <em>Expansion
of morbidity</em>. Most of the data collected today, in	of morbidity</em>. Most of the data collected today, in
particular by the international <a href="http://euroreves/reves">REVES</a>	particular by the international <a href="http://www.reves.org">REVES</a>
network on Health expectancy, and most HE indices based on these	network on Health expectancy, and most HE indices based on these
data, are <em>cross-sectional</em>. It means that the information	data, are <em>cross-sectional</em>. It means that the information
collected comes from a single cross-sectional survey: people from	collected comes from a single cross-sectional survey: people from
Line 181 according to parameters: selection of a	Line 180 according to parameters: selection of a
absorbing and non-absorbing states, number of waves taken in	absorbing and non-absorbing states, number of waves taken in
account (the user inputs the first and the last interview), a	account (the user inputs the first and the last interview), a
tolerance level for the maximization function, the periodicity of	tolerance level for the maximization function, the periodicity of
the transitions (we can compute annual, quaterly or monthly	the transitions (we can compute annual, quarterly or monthly
transitions), covariates in the model. It works on Windows or on	transitions), covariates in the model. It works on Windows or on
Unix.<br>	Unix.<br>
</p>	</p>
Line 273 weights or covariates, you must fill the	Line 272 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 0.63, February 2000,	<h2><a name="biaspar"></a>#Imach version 0.71a, 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 349 line</font></a></h4>	Line 348 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 can be included with the command </p>	Additional covariates (actually two) can be included with the command: </p>

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

Line 365 Additional covariates can be included wi	Line 364 Additional covariates can be included wi
<li>if <strong>model=V1*V2 </strong>the model includes the	<li>if <strong>model=V1*V2 </strong>the model includes the
product of the first and the second covariate (fields 2	product of the first and the second covariate (fields 2
and 3)</li>	and 3)</li>
	<li>if <strong>model=V1+V1*age</strong> the model includes
	the product covariate*age</li>
</ul>	</ul>

<h4><font color="#FF0000">Guess values for optimization</font><font	<h4><font color="#FF0000">Guess values for optimization</font><font
Line 385 initials values, a12, b12, a13, b13, a21	Line 386 initials values, a12, b12, a13, b13, a21
start with zeros as in this example, but if you have a more	start with zeros as in this example, but if you have a more
precise set (for example from an earlier run) you can enter it	precise set (for example from an earlier run) you can enter it
and it will speed up them<br>	and it will speed up them<br>
Each of the four lines starts with indices "ij": <br>	Each of the four lines starts with indices "ij": <b>ij
<br>	aij bij</b> </p>
<b>ij aij bij</b> </p>

<blockquote>	<blockquote>
<pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age	<pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
Line 397 Each of the four lines starts with indic	Line 397 Each of the four lines starts with indic
23 -6.234642 0.022315 </pre>	23 -6.234642 0.022315 </pre>
</blockquote>	</blockquote>

<p>or, to simplify: </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 409 Each of the four lines starts with indic	Line 409 Each of the four lines starts with indic
<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
used as an input to get the vairous 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). </p>

Line 440 consists in indices "ij" follo	Line 440 consists in indices "ij" follo
<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>This is an output if <a href="#mle">mle</a>=1. But it can be
used as an input to get the vairous output data files (Health	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). </p>

Line 475 covariances between aij and bij: </p>	Line 475 covariances between aij and bij: </p>
</li>	</li>
</ul>	</ul>

<h4><a name="biaspar-l"></a><font color="#FF0000">last	<h4><font color="#FF0000">Age range for calculation of stationary
uncommented line</font></h4>	prevalences and health expectancies</font></h4>

<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	<p>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 ranges 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. Setting bage=50 and fage=100, makes the program computing	102. It is possible to get extrapolated stationary
life expectancy from age bage to age fage. As we use a model, we	prevalence by age ranging from agemin to agemax. </p>
can compute life expectancy on a wider age range than the age
range from the data. But the model can be rather wrong on big
intervals.</p>

<p>Similarly, it is possible to get extrapolated stationary	<p>Setting bage=50 (begin age) and fage=100 (final age), makes the program computing
prevalence by age raning from agemin to agemax. </p>	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>

<ul>	<ul>
<li><b>agemin=</b> Minimum age for calculation of the	<li><b>agemin=</b> Minimum age for calculation of the
Line 500 prevalence by age raning from agemin to	Line 501 prevalence by age raning from agemin to
stationary prevalence </li>	stationary 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 ages for calculation of the health	<li><b>fage=</b> Maximum age for calculation of the health
expectancies </li>	expectancies </li>
</ul>	</ul>

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

	<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
	select the period in which we calculate the observed prevalences
	in each state. In this example, the prevalences are calculated on
	data survey collected between 1 january 1984 and 1 june 1988. </p>

	<ul>
	<li><strong>begin-prev-date= </strong>Starting date
	(day/month/year)</li>
	<li><strong>end-prev-date= </strong>Final date
	(day/month/year)</li>
	</ul>

	<h4><font color="#FF0000">Population- or status-based health
	expectancies</font></h4>

	<pre>pop_based=0</pre>

	<p>The program computes status-based health expectancies, i.e health
	expectancies which depends on your initial health state. If you are
	healthy your healthy life expectancy (e11) is higher than if you were
	disabled (e21, with e11 > e21).<br>
	To compute a healthy life expectancy independant of the initial status
	we have to weight e11 and e21 according to the probability to be in
	each state at initial age or, with other word, according to the
	proportion of people in each state.<br>

	We prefer computing a 'pure' period healthy life expectancy based only
	on the transtion forces. Then the weights are simply the stationnary
	prevalences or 'implied' prevalences at the initial age.<br>

	Some other people would like to use the cross-sectional prevalences
	(the "Sullivan prevalences") observed at the initial age during a
	period of time <a href="#Computing">defined just above</a>.

	<ul>
	<li><strong>popbased= 0 </strong> Health expectancies are computed
	at each age from stationary prevalences 'expected' at this initial age.</li>
	<li><strong>popbased= 1 </strong> Health expectancies are computed
	at each age from cross-sectional 'observed' 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>

	</p>

	<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>

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

	<ul>
	<li><strong>starting-proj-date</strong>= starting date
	(day/month/year) of forecasting</li>
	<li><strong>final-proj-date= </strong>final date
	(day/month/year) of forecasting</li>
	<li><strong>mov_average</strong>= smoothing with a five-age
	moving average centered at the mid-age of the five-age
	period. The command<strong> mov_average</strong> takes
	value 1 if the prevalences are smoothed and 0 otherwise.</li>
	</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.</p>

	<ul type="disc">
	<li class="MsoNormal"
	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
	popforecast=1, the programme does the forecasting<b>.</b></li>
	<li class="MsoNormal"
	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>
	<li class="MsoNormal"
	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>
	<li class="MsoNormal"
	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>
	</ul>

<hr>	<hr>

<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.txt">1st_example	<p>We assume that you entered 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>. To
run the program you should click on the imach.exe icon and enter	run the program you should 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
Line 533 and graphs</font> </a></h2>	Line 638 and graphs</font> </a></h2>

<p>Once the optimization is finished, some graphics can be made	<p>Once the optimization is finished, some graphics can be made
with a grapher. We use Gnuplot which is an interactive plotting	with a grapher. We use Gnuplot which is an interactive plotting
program copyrighted but freely distributed. Imach outputs the	program copyrighted but freely distributed. A gnuplot reference
source of a gnuplot file, named 'graph.gp', which can be directly	manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
input into gnuplot.<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>

Line 543 for plotting and output editing. </p>	Line 647 for plotting and output editing. </p>

<ul>	<ul>
<li>'c' to start again the program from the beginning.</li>	<li>'c' to start again the program from the beginning.</li>
<li>'g' to made graphics. The output graphs are in GIF format	<li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
and you have no control over which is produced. If you	file to edit the output files and graphs. </li>
want to modify the graphics or make another one, you
should modify the parameters in the file <b>graph.gp</b>
located in imach\bin. A gnuplot reference manual is
available <a
href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.
</li>
<li>'e' opens the <strong>index.htm</strong> file to edit the
output files and graphs. </li>
<li>'q' for exiting.</li>	<li>'q' for exiting.</li>
</ul>	</ul>

Line 578 The header of the file is </p>	Line 674 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>

<pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
70 0.95721 604 631 70 0.04279 27 631</pre>

<p>It means that at age 70, the prevalence in state 1 is 1.000	<p>It means that at age 70, 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
Line 592 covariance matrix</b></font><b>: </b><a	Line 685 covariance matrix</b></font><b>: </b><a

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

<pre> Number of iterations=47	<pre> -2 log likelihood= 21660.918613445392
-2 log likelihood=46553.005854373667	Estimated parameters: a12 = -12.290174 b12 = 0.092161
Estimated parameters: a12 = -12.691743 b12 = 0.095819	a13 = -9.155590 b13 = 0.046627
a13 = -7.815392 b13 = 0.031851	a21 = -2.629849 b21 = -0.022030
a21 = -1.809895 b21 = -0.030470	a23 = -7.958519 b23 = 0.042614
a23 = -7.838248 b23 = 0.039490	Covariance matrix: Var(a12) = 1.47453e-001
Covariance matrix: Var(a12) = 1.03611e-001	Var(b12) = 2.18676e-005
Var(b12) = 1.51173e-005	Var(a13) = 2.09715e-001
Var(a13) = 1.08952e-001	Var(b13) = 3.28937e-005
Var(b13) = 1.68520e-005	Var(a21) = 9.19832e-001
Var(a21) = 4.82801e-001	Var(b21) = 1.29229e-004
Var(b21) = 6.86392e-005	Var(a23) = 4.48405e-001
Var(a23) = 2.27587e-001	Var(b23) = 5.85631e-005
Var(b23) = 3.04465e-005
</pre>	</pre>

	<p>By substitution of these parameters in the regression model,
	we obtain the elementary transition probabilities:</p>

	<p><img src="pebiaspar1.gif" 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="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>

Line 617 is a multiple of 2 years. The first colu	Line 714 is a multiple of 2 years. The first colu
the transition probabilities p11, p12, p13, p21, p22, p23. For	the transition probabilities p11, p12, p13, p21, p22, p23. For
example, line 5 of the file is: </p>	example, line 5 of the file is: </p>

<pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>	<pre> 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>

<pre>p11(100,106)=0.03286	<pre>p11(100,106)=0.02655
p12(100,106)=0.23512	p12(100,106)=0.17622
p13(100,106)=0.73202	p13(100,106)=0.79722
p21(100,106)=0.02330	p21(100,106)=0.01809
p22(100,106)=0.19210	p22(100,106)=0.13678
p22(100,106)=0.78460 </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="Stationary prevalence in each state"><font color="#EC5E5E"
size="3"><b>Stationary prevalence in each state</b></font></a><b>:	size="3"><b>Stationary prevalence in each state</b></font></a><b>:
</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>	</b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>

<pre>#Age 1-1 2-2	<pre>#Prevalence
70 0.92274 0.07726	#Age 1-1 2-2
71 0.91420 0.08580
72 0.90481 0.09519	#************
73 0.89453 0.10547</pre>	70 0.90134 0.09866
	71 0.89177 0.10823
	72 0.88139 0.11861
	73 0.87015 0.12985 </pre>

<p>At age 70 the stationary prevalence is 0.92274 in state 1 and	<p>At age 70 the stationary prevalence is 0.90134 in state 1 and
0.07726 in state 2. This stationary prevalence differs from	0.09866 in state 2. This stationary prevalence differs from
observed prevalence. Here is the point. The observed prevalence	observed prevalence. Here is the point. The observed prevalence
at age 70 results from the incidence of disability, incidence of	at age 70 results from the incidence of disability, incidence of
recovery and mortality which occurred in the past of the cohort.	recovery and mortality which occurred in the past of the cohort.
Line 664 design of the survey, and, for the stati	Line 764 design of the survey, and, for the stati
model used and fitted. It is possible to compute the standard	model used and fitted. It is possible to compute the standard
deviation of the stationary prevalence at each age.</p>	deviation of the stationary prevalence at each age.</p>

<h6><font color="#EC5E5E" size="3">Observed and stationary	<h5><font color="#EC5E5E" size="3">-Observed and stationary
prevalence in state (2=disable) with the confident interval</font>:<b>	prevalence in state (2=disable) with the confident interval</font>:<b>
vbiaspar2.gif</b></h6>	</b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>

<p><br>	<p>This graph exhibits the stationary prevalence in state (2)
This graph exhibits the stationary prevalence in state (2) with	with the confidence interval in red. The green curve is the
the confidence interval in red. The green curve is the observed	observed prevalence (or proportion of individuals in state (2)).
prevalence (or proportion of individuals in state (2)). Without	Without discussing the results (it is not the purpose here), we
discussing the results (it is not the purpose here), we observe	observe that the green curve is rather below the stationary
that the green curve is rather below the stationary prevalence.	prevalence. It suggests an increase of the disability prevalence
It suggests an increase of the disability prevalence in the	in the future.</p>
future.</p>
	<p><img src="vbiaspar21.gif" width="400" height="300"></p>
<p><img src="vbiaspar2.gif" width="400" height="300"></p>
	<h5><font color="#EC5E5E" size="3"><b>-Convergence to the
<h6><font color="#EC5E5E" size="3"><b>Convergence to the	stationary prevalence of disability</b></font><b>: </b><a
stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>	href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
<img src="pbiaspar1.gif" width="400" height="300"> </h6>	<img src="pbiaspar11.gif" 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 703 href="erbiaspar.txt"><b>erbiaspar.txt</b	Line 803 href="erbiaspar.txt"><b>erbiaspar.txt</b

<pre># Health expectancies	<pre># Health expectancies
# Age 1-1 1-2 2-1 2-2	# Age 1-1 1-2 2-1 2-2
70 10.7297 2.7809 6.3440 5.9813	70 10.9226 3.0401 5.6488 6.2122
71 10.3078 2.8233 5.9295 5.9959	71 10.4384 3.0461 5.2477 6.1599
72 9.8927 2.8643 5.5305 6.0033	72 9.9667 3.0502 4.8663 6.1025
73 9.4848 2.9036 5.1474 6.0035 </pre>	73 9.5077 3.0524 4.5044 6.0401 </pre>

<pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:	<pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>	e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>

<pre><img src="exbiaspar1.gif" width="400" height="300"><img	<pre><img src="expbiaspar21.gif" width="400" height="300"><img
src="exbiaspar2.gif" width="400" height="300"></pre>	src="expbiaspar11.gif" 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 10.73 in the healthy state and 2.78 in the disability state	is 10.42 in the healthy state and 3.04 in the disability state
(=13.51 years). If he was disable at age 70, his life expectancy	(=13.46 years). If he was disable at age 70, his life expectancy
will be shorter, 6.34 in the healthy state and 5.98 in the	will be shorter, 5.64 in the healthy state and 5.71 in the
disability state (=12.32 years). The total life expectancy is a	disability state (=11.35 years). The total life expectancy is a
weighted mean of both, 13.51 and 12.32; weight is the proportion	weighted mean of both, 13.46 and 11.35; 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 pure 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="#Stationary prevalence in each state">computed or
Line 736 href="vrbiaspar.txt"><b>vrbiaspar.txt</b	Line 836 href="vrbiaspar.txt"><b>vrbiaspar.txt</b
<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>

<pre> Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183</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>- </b></font><a	<h5><font color="#EC5E5E" size="3"><b>- </b></font><a
name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health	name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
Line 746 href="trbiaspar.txt"><font face="Courier	Line 846 href="trbiaspar.txt"><font face="Courier

<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 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09) </pre>	<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..=13.42 years is	<p>Thus, at age 70 the total life expectancy, e..=13.26 years is
the weighted mean of e1.=13.51 and e2.=12.32 by the stationary	the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in	prevalence 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=10.39 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=3.03 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>

<h6><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>:
ebiaspar.gif</b></h6>	</b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</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 the confident interval in dashed curve. </p>

<pre> <img src="ebiaspar.gif" width="400" height="300"></pre>	<pre> <img src="ebiaspar1.gif" 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 826 estimated by month on 8,000 people may t	Line 926 estimated by month on 8,000 people may t
Also, the program is not yet a statistical package, which permits	Also, the program is not yet a statistical package, which permits
a simple writing of the variables and the model to take into	a simple writing of the variables and the model to take into
account in the maximisation. The actual program allows only to	account in the maximisation. The actual program allows only to
add simple variables without covariations, like age+sex but	add simple variables like age+sex or age+sex+ age*sex but will
without age+sex+ age*sex . This can be done from the source code
(you have to change three lines in the source code) but will
never be general enough. But what is to remember, is that	never be general enough. But what is to remember, is that
incidences or probability of change from one state to another is	incidences or probability of change from one state to another is
affected by the variables specified into the model.</p>	affected by the variables specified into the model.</p>
Line 853 file</b></font><b>: </b><a href="orbiasp	Line 951 file</b></font><b>: </b><a href="orbiasp
<p>This copy of the parameter file can be useful to re-run the	<p>This copy of the parameter file can be useful to re-run the
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>:
	</b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>

	<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,
	we have estimated the observed prevalence between 1/1/1984 and
	1/6/1988. The mean date of interview (weighed average of the
	interviews performed between1/1/1984 and 1/6/1988) is estimated
	to be 13/9/1985, as written on the top on the file. Then we
	forecast the probability to be in each state. </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,
	at date 1/1/1989 : </p>

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

	<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
	age is 73. This means that at age a person aged 70 at 13/9/1989
	has a 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
	probability to die is 0.115. Then, on the 1/1/1989, the
	prevalence of disability at age 73 is estimated to be 0.088.</p>

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

	<pre># Age P.1 P.2 P.3 [Population]
	# Forecasting at date 1/1/1989
	75 572685.22 83798.08
	74 621296.51 79767.99
	73 645857.70 69320.60 </pre>

	<pre># Forecasting at date 1/1/19909
	76 442986.68 92721.14 120775.48
	75 487781.02 91367.97 121915.51
	74 512892.07 85003.47 117282.76 </pre>

	<p>From the population file, we estimate the number of people in
	each state. At age 73, 645857 persons are in state 1 and 69320
	are in state 2. One year latter, 512892 are still in state 1,
	85003 are in state 2 and 117282 died before 1/1/1990.</p>

<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></a></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="file://../mytry/imachpar.txt">imachpar.txt</a> which is a	href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
copy of <font size="2" face="Courier New">mypar.txt</font>	size="2" face="Courier New">mypar.txt</font> included in the
included in the subdirectory of imach, <font size="2"	subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
face="Courier New">mytry</font>. Edit it to change the name of	Edit it to change the name of the data file to <font size="2"
the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>	face="Courier New">..\data\mydata.txt</font> if you don't want to
if you don't want to copy it on the same directory. The file <font	copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
face="Courier New">mydata.txt</font> is a smaller file of 3,000	is a smaller file of 3,000 people but still with 4 waves. </p>
people but still with 4 waves. </p>

<p>Click on the imach.exe icon to open a window. Answer to the	<p>Click on the imach.exe icon to open a window. Answer to the
question:'<strong>Enter the parameter file name:'</strong></p>	question:'<strong>Enter the parameter file name:'</strong></p>

<table border="1">	<table border="1">
<tr>	<tr>
<td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter	<td width="100%"><strong>IMACH, Version 0.71</strong><p><strong>Enter
the parameter file name: ..\mytry\imachpar.txt</strong></p>	the parameter file name: ..\mytry\imachpar.txt</strong></p>
</td>	</td>
</tr>	</tr>
Line 983 requires a caracter:</font></p>	Line 1127 requires a caracter:</font></p>

<table border="1">	<table border="1">
<tr>	<tr>
<td width="100%"><strong>Type g for plotting (available	<td width="100%"><strong>Type e to edit output files, c
if mle=1), e to edit output files, c to start again,</strong><p><strong>and	to start again, and q for exiting:</strong></td>
q for exiting:</strong></p>
</td>
</tr>	</tr>
</table>	</table>

<p><font size="3">First you should enter <strong>g</strong> to	<p><font size="3">First you should enter <strong>e </strong>to
make the figures and then you can edit all the results by typing <strong>e</strong>.	edit the master file mypar.htm. </font></p>
</font></p>

<ul>	<ul>
<li><u>Outputs files</u> <br>	<li><u>Outputs files</u> <br>
- index.htm, this file is the master file on which you	<br>
should click first.<br>
- Observed prevalence in each state: <a	- Observed prevalence in each state: <a
href="..\mytry\prmypar.txt">mypar.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.txt</a> <br>
- Stationary prevalence in each state: <a	- Stationary prevalence in each state: <a
Line 1016 make the figures and then you can edit a	Line 1156 make the figures and then you can edit a
- Health expectancies with their variances: <a	- Health expectancies with their variances: <a
href="..\mytry\trmypar.txt">trmypar.txt</a> <br>	href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
- Standard deviation of stationary prevalence: <a	- Standard deviation of stationary prevalence: <a
href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>	href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
	- Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
<br>	<br>
	- Population forecasting (if popforecast=1): <a
	href="poprmypar.txt">poprmypar.txt</a> <br>
</li>	</li>
<li><u>Graphs</u> <br>	<li><u>Graphs</u> <br>
<br>	<br>
-<a href="..\mytry\vmypar1.gif">Observed and stationary	-<a href="../mytry/pemypar1.gif">One-step transition
	probabilities</a><br>
	-<a href="../mytry/pmypar11.gif">Convergence to the
	stationary prevalence</a><br>
	-<a href="..\mytry\vmypar11.gif">Observed and stationary
prevalence in state (1) with the confident interval</a> <br>	prevalence in state (1) with the confident interval</a> <br>
-<a href="..\mytry\vmypar2.gif">Observed and stationary	-<a href="..\mytry\vmypar21.gif">Observed and stationary
prevalence in state (2) with the confident interval</a> <br>	prevalence in state (2) with the confident interval</a> <br>
-<a href="..\mytry\exmypar1.gif">Health life expectancies	-<a href="..\mytry\expmypar11.gif">Health life
by age and initial health state (1)</a> <br>	expectancies by age and initial health state (1)</a> <br>
-<a href="..\mytry\exmypar2.gif">Health life expectancies	-<a href="..\mytry\expmypar21.gif">Health life
by age and initial health state (2)</a> <br>	expectancies by age and initial health state (2)</a> <br>
-<a href="..\mytry\emypar.gif">Total life expectancy by	-<a href="..\mytry\emypar1.gif">Total life expectancy by
age and health expectancies in states (1) and (2).</a> </li>	age and health expectancies in states (1) and (2).</a> </li>
</ul>	</ul>

Line 1043 simple justification (name, email, insti	Line 1190 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 (0.63 of 16 march 2000) can be accessed at <a	<p>Latest version (0.71a of March 2002) can be accessed at <a
href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>	href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
</p>	</p>
</body>	</body>

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