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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 29 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
0.7, February 2002</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 66 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 86 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 273 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 0.7, February 2002,	<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 321 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>ncov=2</b> Number of covariates in the datafile. </li>
intercept and the age parameter are counting for 2
covariates.</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 349 line</font></a></h4>	Line 353 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 can be included with the command: </p>

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

Line 369 Additional covariates can be included wi	Line 373 Additional covariates can be included wi
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 is defined with
	statement ncov=2. If now you have 3 covariates in the datafile
	(fields 2, 3 and 4), you have to set ncov=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 398 aij bij</b> </p>	Line 415 aij bij</b> </p>
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 407 aij bij</b> </p>	Line 425 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(n stepm) = aij(stepm) +ln(n)
	</pre> and
	<pre>bij(n stepm) = bij(stepm) .</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 485 prevalences and health expectancies</fon	Line 511 prevalences and health expectancies</fon
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. Setting bage=50 and fage=100, makes the program computing	102. It is possible to get extrapolated stationary prevalence by
life expectancy from age bage to age fage. As we use a model, we	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
prevalence by age ranging from agemin to agemax. </p>	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>

<ul>	<ul>
<li><b>agemin=</b> Minimum age for calculation of the	<li><b>agemin=</b> Minimum age for calculation of the
Line 527 expectancies</font></h4>	Line 554 expectancies</font></h4>

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

<p>The user has the possibility to choose between	<p>The program computes status-based health expectancies, i.e
population-based or status-based health expectancies. If	health expectancies which depends on your initial health state.
pop_based=0 then status-based health expectancies are computed	If you are healthy your healthy life expectancy (e11) is higher
and if pop_based=1, the programme computes population-based	than if you were disabled (e21, with e11 > e21).<br>
health expectancies. Health expectancies are weighted averages of	To compute a healthy life expectancy independant of the initial
health expectancies respective of the initial state. For a	status we have to weight e11 and e21 according to the probability
status-based index, the weights are the cross-sectional	to be in each state at initial age or, with other word, according
prevalences observed between two dates, as <a href="#Computing">previously	to the proportion of people in each state.<br>
explained</a>, whereas for a population-based index, the weights	We prefer computing a 'pure' period healthy life expectancy based
are the stationary prevalences.</p>	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>. </p>

	<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>

<h4><font color="#FF0000">Prevalence forecasting </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	<p>Prevalence and population projections are only available if
the interpolation unit is a month, i.e. stepm=1. The programme	the interpolation unit is a month, i.e. stepm=1 and if there are
estimates the prevalence in each state at a precise date	no covariate. The programme estimates the prevalence in each
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	programme computes one forecasted prevalence a year from a
1989 in this example) to a final date (1 january 1992). The	starting date (1 january of 1989 in this example) to a final date
statement mov_average allows to compute smoothed forecasted	(1 january 1992). The statement mov_average allows to compute
prevalences with a five-age moving average centered at the	smoothed forecasted prevalences with a five-age moving average
mid-age of the five-age period. </p>	centered at the mid-age of the five-age period. </p>

<ul>	<ul>
<li><strong>starting-proj-date</strong>= starting date	<li><strong>starting-proj-date</strong>= starting date
Line 569 forecasting </font></h4>	Line 613 forecasting </font></h4>
<pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>	<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	<p>This command is available if the interpolation unit is a
month, i.e. stepm=1 and if popforecast=1. From a data file </p>	month, i.e. stepm=1 and if popforecast=1. From a data file
	including age and number of persons alive at the precise date
<p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>	popfiledate, you can forecast the number of persons
: </b>age numbers</p>	in each state until date last-popfiledate. In this
	example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
<p> </p>	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>

Line 775 href="erbiaspar.txt"><b>erbiaspar.txt</b	Line 835 href="erbiaspar.txt"><b>erbiaspar.txt</b
72 9.9667 3.0502 4.8663 6.1025	72 9.9667 3.0502 4.8663 6.1025
73 9.5077 3.0524 4.5044 6.0401 </pre>	73 9.5077 3.0524 4.5044 6.0401 </pre>

<pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:	<pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>	e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>

<pre><img src="expbiaspar21.gif" width="400" height="300"><img	<pre><img src="expbiaspar21.gif" width="400" height="300"><img
src="expbiaspar11.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 10.92 in the healthy state and 3.04 in the disability state	is 10.42 in the healthy state and 3.04 in the disability state
(=13.96 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, 5.64 in the healthy state and 6.21 in the	will be shorter, 5.64 in the healthy state and 5.71 in the
disability state (=11.85 years). The total life expectancy is a	disability state (=11.35 years). The total life expectancy is a
weighted mean of both, 13.96 and 11.85; 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 813 href="trbiaspar.txt"><font face="Courier	Line 873 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 13.76 (0.22) 10.40 (0.20) 3.35 (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..=13.76years is	<p>Thus, at age 70 the total life expectancy, e..=13.26 years is
the weighted mean of e1.=13.96 and e2.=11.85 by the stationary	the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
prevalence at age 70 which are 0.90134 in state 1 and 0.09866 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=10.40 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=3.35 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
Line 921 program while saving the old output file	Line 981 program while saving the old output file
<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="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>

<p>On a d'abord estim� la date moyenne des interviaew. ie	<p
13/9/1995. This file contains </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
<p>Example, at date 1/1/1989 : </p>	1/6/1988. The mean date of interview (weighed average of the
	interviews performed between1/1/1984 and 1/6/1988) is estimated
<p>73 0.807 0.078 0.115 </p>	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>This means that at age 73, the probability for a person age 70
at 13/9/1989 to be in state 1 is 0.807, in state 2 is 0.078 and	<p
to die is 0.115 at 1/1/1989.</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>:	<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="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
Line 946 to die is 0.115 at 1/1/1989.</p>	Line 1020 to die is 0.115 at 1/1/1989.</p>
75 487781.02 91367.97 121915.51	75 487781.02 91367.97 121915.51
74 512892.07 85003.47 117282.76 </pre>	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></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
Line 965 question:'<strong>Enter the parameter fi	Line 1044 question:'<strong>Enter the parameter fi

<table border="1">	<table border="1">
<tr>	<tr>
<td width="100%"><strong>IMACH, Version 0.7</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 1138 simple justification (name, email, insti	Line 1217 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 (0.7 of February 2002) 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://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
</p>	</p>
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