Annotation of imach096d/doc/imach.htm, revision 1.5

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                      9: <title>Computing Health Expectancies using IMaCh</title>
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        !           365:        mso-level-number-position:left;
        !           366:        text-indent:-18.0pt;
        !           367:        mso-ansi-font-size:10.0pt;
        !           368:        font-family:Symbol;}
        !           369: @list l18
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        !           371:        mso-list-type:hybrid;
        !           372:        mso-list-template-ids:638092306 940881202 -784414886 1026841176 1011505968 -653358884 -269310374 2133217052 1173680566 -1995784172;}
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        !           382:        {margin-bottom:0cm;}
        !           383: ul
        !           384:        {margin-bottom:0cm;}
        !           385: -->
        !           386: </style>
        !           387: <!--[if gte mso 9]><xml>
        !           388:  <o:shapedefaults v:ext="edit" spidmax="1027"/>
        !           389: </xml><![endif]-->
        !           390: <!--[if gte mso 9]><xml>
        !           391:  <o:shapelayout v:ext="edit">
        !           392:   <o:idmap v:ext="edit" data="1"/>
        !           393:  </o:shapelayout></xml><![endif]-->
1.2       lievre    394: <!-- Changed by: Agnes Lievre, 12-Oct-2000 -->
                    395: </head>
                    396: 
1.5     ! lievre    397: <body bgcolor="#FFFFFF" link="#0000FF" vlink="#0000FF" lang="FR"
        !           398: style="tab-interval:35.4pt">
1.2       lievre    399: 
1.5     ! lievre    400: <hr size="3" noshade color="#EC5E5E">
1.2       lievre    401: 
1.5     ! lievre    402: <h1 align="center" style="text-align:center"><span lang="EN-GB" style="color:#00006A;
        !           403: mso-ansi-language:EN-GB">Computing Health
        !           404: Expectancies using IMaCh</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
        !           405: 
        !           406: <h1 align="center" style="text-align:center"><span lang="EN-GB" style="font-size:
        !           407: 18.0pt;color:#00006A;mso-ansi-language:EN-GB">(a Maximum
        !           408: Likelihood Computer Program using Interpolation of Markov Chains)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h1>
        !           409: 
        !           410: <p align="center" style="text-align:center"><span lang="EN-GB" style="mso-ansi-language:
        !           411: EN-GB">&nbsp;<o:p></o:p></span></p>
        !           412: 
        !           413: <p align="center" style="text-align:center"><a
        !           414: href="http://www.ined.fr/"><span style="text-decoration:none;text-underline:none"><img src="logo-ined.gif" border="0"
        !           415: width="151" height="76" id="_x0000_i1026"></span></a><img
        !           416: src="euroreves2.gif" width="151" height="75" id="_x0000_i1027"></p>
        !           417: 
        !           418: <h3 align="center" style="text-align:center"><a
        !           419: href="http://www.ined.fr/"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">INED</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a> and </span><a
        !           420: href="http://euroreves.ined.fr"><span lang="EN-GB" style="color:#00006A;
        !           421: mso-ansi-language:EN-GB">EUROREVES</span><span lang="EN-GB" style="mso-ansi-language:
        !           422: EN-GB"><o:p></o:p></span></a></h3>
        !           423: 
        !           424: <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="font-size:13.5pt;color:#00006A;mso-ansi-language:EN-GB">Version 0.7,
        !           425: February 2002</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
        !           426: 
        !           427: <hr size="3" noshade color="#EC5E5E">
        !           428: 
        !           429: <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Authors of
        !           430: the program: </span></strong><a href="http://sauvy.ined.fr/brouard"><strong><span lang="EN-GB" style="color:#00006A;
        !           431: mso-ansi-language:EN-GB">Nicolas
        !           432: Brouard</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></strong></a><strong>, senior researcher at the </span></strong><a
        !           433: href="http://www.ined.fr"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Institut National d'Etudes
        !           434: Démographiques</span><span lang="EN-GB" style="color:#00006A;
        !           435: mso-ansi-language:EN-GB"></strong></a><strong> (INED, Paris) in the
        !           436: &quot;Mortality, Health and Epidemiology&quot; Research Unit </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
        !           437: 
        !           438: <p align="center" style="text-align:center"><strong><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">and Agnès
        !           439: Lièvre</span></strong><b><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"><br clear="left"
        !           440: style="mso-special-character:line-break">
        !           441: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></b></p>
        !           442: 
        !           443: <h4><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Contribution to the mathematics: C. R. Heathcote </span><span lang="EN-GB" style="font-size:
        !           444: 10.0pt;color:#00006A;mso-ansi-language:EN-GB">(Australian
        !           445: National University, Canberra).</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
1.2       lievre    446: 
1.5     ! lievre    447: <h4><span style="color:#00006A">Contact: Agnès Lièvre (</span><a href="mailto:lievre@ined.fr"><i><span style="color:#00006A">lievre@ined.fr</span><span style="color:#00006A"></i></a>)
        !           448: </span></h4>
1.2       lievre    449: 
                    450: <hr>
1.5     ! lievre    451: <span style="font-size:12.0pt;font-family:&quot;Times New Roman&quot;;mso-fareast-font-family:
        !           452: &quot;Times New Roman&quot;;mso-ansi-language:FR;mso-fareast-language:FR;mso-bidi-language:
        !           453: AR-SA">
        !           454: <ul type="disc">
        !           455:     <li class="MsoNormal"
        !           456:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           457:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           458:         href="#intro"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Introduction</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !           459:     <li class="MsoNormal"
        !           460:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           461:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           462:         href="#data"><span lang="EN-GB" style="mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
        !           463:     <li class="MsoNormal"
        !           464:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           465:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           466:         href="#datafile"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The data file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !           467:     <li class="MsoNormal"
        !           468:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           469:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           470:         href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The parameter file</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !           471:     <li class="MsoNormal"
        !           472:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           473:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           474:         href="#running"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Running Imach</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !           475:     <li class="MsoNormal"
        !           476:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           477:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           478:         href="#output"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output files and graphs</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !           479:     <li class="MsoNormal"
        !           480:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           481:      mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a
        !           482:         href="#example">Exemple</a> </li>
1.2       lievre    483: </ul>
1.5     ! lievre    484: </span>
1.2       lievre    485: <hr>
                    486: 
1.5     ! lievre    487: <h2><a name="intro"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Introduction</span><span style="mso-bookmark:intro"></span><span lang="EN-GB" style="mso-ansi-language:
        !           488: EN-GB"><o:p></o:p></span></a></h2>
1.2       lievre    489: 
1.5     ! lievre    490: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This program computes <b>Healthy
        !           491: Life Expectancies</b> from <b>cross-longitudinal data</b> using
        !           492: the methodology pioneered by Laditka and Wolf (1). Within the
        !           493: family of Health Expectancies (HE), Disability-free life
        !           494: expectancy (DFLE) is probably the most important index to
1.2       lievre    495: monitor. In low mortality countries, there is a fear that when
                    496: mortality declines, the increase in DFLE is not proportionate to
                    497: the increase in total Life expectancy. This case is called the <em>Expansion
                    498: of morbidity</em>. Most of the data collected today, in
1.5     ! lievre    499: particular by the international </span><a href="http://euroreves/reves"><span lang="EN-GB" style="mso-ansi-language:EN-GB">REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
1.2       lievre    500: network on Health expectancy, and most HE indices based on these
                    501: data, are <em>cross-sectional</em>. It means that the information
                    502: collected comes from a single cross-sectional survey: people from
                    503: various ages (but mostly old people) are surveyed on their health
                    504: status at a single date. Proportion of people disabled at each
                    505: age, can then be measured at that date. This age-specific
                    506: prevalence curve is then used to distinguish, within the
                    507: stationary population (which, by definition, is the life table
                    508: estimated from the vital statistics on mortality at the same
                    509: date), the disable population from the disability-free
                    510: population. Life expectancy (LE) (or total population divided by
                    511: the yearly number of births or deaths of this stationary
                    512: population) is then decomposed into DFLE and DLE. This method of
                    513: computing HE is usually called the Sullivan method (from the name
1.5     ! lievre    514: of the author who first described it).<o:p></o:p></span></p>
1.2       lievre    515: 
1.5     ! lievre    516: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age-specific proportions of people
        !           517: disable are very difficult to forecast because each proportion
        !           518: corresponds to historical conditions of the cohort and it is the
        !           519: result of the historical flows from entering disability and
        !           520: recovering in the past until today. The age-specific intensities
        !           521: (or incidence rates) of entering disability or recovering a good
        !           522: health, are reflecting actual conditions and therefore can be
        !           523: used at each age to forecast the future of this cohort. For
        !           524: example if a country is improving its technology of prosthesis,
        !           525: the incidence of recovering the ability to walk will be higher at
        !           526: each (old) age, but the prevalence of disability will only
        !           527: slightly reflect an improve because the prevalence is mostly
        !           528: affected by the history of the cohort and not by recent period
        !           529: effects. To measure the period improvement we have to simulate
        !           530: the future of a cohort of new-borns entering or leaving at each
        !           531: age the disability state or dying according to the incidence
        !           532: rates measured today on different cohorts. The proportion of
        !           533: people disabled at each age in this simulated cohort will be much
        !           534: lower (using the example of an improvement) that the proportions
        !           535: observed at each age in a cross-sectional survey. This new
        !           536: prevalence curve introduced in a life table will give a much more
        !           537: actual and realistic HE level than the Sullivan method which
        !           538: mostly measured the History of health conditions in this country.<o:p></o:p></span></p>
        !           539: 
        !           540: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Therefore, the main question is how
        !           541: to measure incidence rates from cross-longitudinal surveys? This
        !           542: is the goal of the IMaCH program. From your data and using IMaCH
        !           543: you can estimate period HE and not only Sullivan's HE. Also the
        !           544: standard errors of the HE are computed.<o:p></o:p></span></p>
        !           545: 
        !           546: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">A cross-longitudinal survey
        !           547: consists in a first survey (&quot;cross&quot;) where individuals
        !           548: from different ages are interviewed on their health status or
        !           549: degree of disability. At least a second wave of interviews
        !           550: (&quot;longitudinal&quot;) should measure each new individual
        !           551: health status. Health expectancies are computed from the
        !           552: transitions observed between waves and are computed for each
        !           553: degree of severity of disability (number of life states). More
        !           554: degrees you consider, more time is necessary to reach the Maximum
        !           555: Likelihood of the parameters involved in the model. Considering
        !           556: only two states of disability (disable and healthy) is generally
        !           557: enough but the computer program works also with more health
        !           558: statuses.<span style="mso-spacerun:
        !           559: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><br>
1.2       lievre    560: <br>
                    561: The simplest model is the multinomial logistic model where <i>pij</i>
                    562: is the probability to be observed in state <i>j</i> at the second
                    563: wave conditional to be observed in state <em>i</em> at the first
                    564: wave. Therefore a simple model is: log<em>(pij/pii)= aij +
                    565: bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
                    566: is a covariate. The advantage that this computer program claims,
                    567: comes from that if the delay between waves is not identical for
                    568: each individual, or if some individual missed an interview, the
                    569: information is not rounded or lost, but taken into account using
                    570: an interpolation or extrapolation. <i>hPijx</i> is the
                    571: probability to be observed in state <i>i</i> at age <i>x+h</i>
                    572: conditional to the observed state <i>i</i> at age <i>x</i>. The
                    573: delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
                    574: of unobserved intermediate states. This elementary transition (by
                    575: month or quarter trimester, semester or year) is modeled as a
                    576: multinomial logistic. The <i>hPx</i> matrix is simply the matrix
                    577: product of <i>nh*stepm</i> elementary matrices and the
                    578: contribution of each individual to the likelihood is simply <i>hPijx</i>.
1.5     ! lievre    579: <o:p></o:p></span></p>
1.2       lievre    580: 
1.5     ! lievre    581: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The program presented in this
        !           582: manual is a quite general program named <strong>IMaCh</strong>
        !           583: (for <strong>I</strong>nterpolated <strong>MA</strong>rkov <strong>CH</strong>ain),
        !           584: designed to analyse transition data from longitudinal surveys.
        !           585: The first step is the parameters estimation of a transition
        !           586: probabilities model between an initial status and a final status.
        !           587: From there, the computer program produces some indicators such as
        !           588: observed and stationary prevalence, life expectancies and their
        !           589: variances and graphs. Our transition model consists in absorbing
        !           590: and non-absorbing states with the possibility of return across
        !           591: the non-absorbing states. The main advantage of this package,
1.2       lievre    592: compared to other programs for the analysis of transition data
1.5     ! lievre    593: (For example: Proc Catmod of SAS<sup>(r)</sup>) is that the whole
1.2       lievre    594: individual information is used even if an interview is missing, a
                    595: status or a date is unknown or when the delay between waves is
                    596: not identical for each individual. The program can be executed
                    597: according to parameters: selection of a sub-sample, number of
                    598: absorbing and non-absorbing states, number of waves taken in
                    599: account (the user inputs the first and the last interview), a
                    600: tolerance level for the maximization function, the periodicity of
1.5     ! lievre    601: the transitions (we can compute annual, quarterly or monthly
1.2       lievre    602: transitions), covariates in the model. It works on Windows or on
1.5     ! lievre    603: Unix.<o:p></o:p></span></p>
1.2       lievre    604: 
                    605: <hr>
                    606: 
1.5     ! lievre    607: <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), &quot;New
1.2       lievre    608: Methods for Analyzing Active Life Expectancy&quot;. <i>Journal of
1.5     ! lievre    609: Aging and Health</i>. </span>Vol 10, No. 2. </p>
1.2       lievre    610: 
                    611: <hr>
                    612: 
1.5     ! lievre    613: <h2><a name="data"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">On what kind of data can it be used?</span><span style="mso-bookmark:data"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
1.2       lievre    614: 
1.5     ! lievre    615: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The minimum data required for a
        !           616: transition model is the recording of a set of individuals
        !           617: interviewed at a first date and interviewed again at least one
        !           618: another time. From the observations of an individual, we obtain a
        !           619: follow-up over time of the occurrence of a specific event. In
        !           620: this documentation, the event is related to health status at
        !           621: older ages, but the program can be applied on a lot of
        !           622: longitudinal studies in different contexts. To build the data
        !           623: file explained into the next section, you must have the month and
        !           624: year of each interview and the corresponding health status. But
        !           625: in order to get age, date of birth (month and year) is required
        !           626: (missing values is allowed for month). Date of death (month and
        !           627: year) is an important information also required if the individual
        !           628: is dead. Shorter steps (i.e. a month) will more closely take into
        !           629: account the survival time after the last interview.<o:p></o:p></span></p>
1.2       lievre    630: 
                    631: <hr>
                    632: 
1.5     ! lievre    633: <h2><a name="datafile"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:
        !           634: EN-GB">The data file</span><span style="mso-bookmark:datafile"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
1.2       lievre    635: 
1.5     ! lievre    636: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, 8,000 people have
        !           637: been interviewed in a cross-longitudinal survey of 4 waves (1984,
        !           638: 1986, 1988, 1990). Some people missed 1, 2 or 3 interviews.
        !           639: Health statuses are healthy (1) and disable (2). The survey is
        !           640: not a real one. It is a simulation of the American Longitudinal
        !           641: Survey on Aging. The disability state is defined if the
        !           642: individual missed one of four ADL (Activity of daily living, like
        !           643: bathing, eating, walking). Therefore, even is the individuals
        !           644: interviewed in the sample are virtual, the information brought
        !           645: with this sample is close to the situation of the United States.
        !           646: Sex is not recorded is this sample.<o:p></o:p></span></p>
        !           647: 
        !           648: <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each line of the data set (named </span><a href="data1.txt"><span lang="EN-GB" style="mso-ansi-language:
        !           649: EN-GB">data1.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
        !           650: in this first example) is an individual record which fields are: <o:p></o:p></span></p>
        !           651: 
        !           652: <ul type="disc">
        !           653:     <li class="MsoNormal"
        !           654:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           655:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Index
        !           656:         number</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number (field 1) <o:p></o:p></span></li>
        !           657:     <li class="MsoNormal"
        !           658:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           659:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
        !           660:         covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 2) <o:p></o:p></span></li>
        !           661:     <li class="MsoNormal"
        !           662:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           663:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Second
        !           664:         covariate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> positive number (field 3) <o:p></o:p></span></li>
        !           665:     <li class="MsoNormal"
        !           666:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           667:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><a
        !           668:         name="Weight"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Weight</span><span style="mso-bookmark:Weight"></span><span lang="EN-GB" style="mso-ansi-language:
        !           669:      EN-GB"></b></a>: positive number (field
        !           670:         4) . In most surveys individuals are weighted according
        !           671:         to the stratification of the sample.<o:p></o:p></span></li>
        !           672:     <li class="MsoNormal"
        !           673:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           674:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           675:         of birth</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
        !           676:         as 99/9999 (field 5) <o:p></o:p></span></li>
        !           677:     <li class="MsoNormal"
        !           678:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           679:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           680:         of death</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates are coded
        !           681:         as 99/9999 (field 6) <o:p></o:p></span></li>
        !           682:     <li class="MsoNormal"
        !           683:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           684:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           685:         of first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
        !           686:         are coded as 99/9999 (field 7) <o:p></o:p></span></li>
        !           687:     <li class="MsoNormal"
        !           688:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           689:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
        !           690:         at first interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: positive number. Missing values
        !           691:         ar coded -1. (field 8) <o:p></o:p></span></li>
        !           692:     <li class="MsoNormal"
        !           693:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           694:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           695:         of second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
        !           696:         are coded as 99/9999 (field 9) <o:p></o:p></span></li>
        !           697:     <li class="MsoNormal"
        !           698:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           699:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
        !           700:         at second interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
        !           701:         values ar coded -1. (field 10) <o:p></o:p></span></li>
        !           702:     <li class="MsoNormal"
        !           703:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           704:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           705:         of third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
        !           706:         are coded as 99/9999 (field 11) <o:p></o:p></span></li>
        !           707:     <li class="MsoNormal"
        !           708:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           709:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
        !           710:         at third interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
        !           711:         values ar coded -1. (field 12) <o:p></o:p></span></li>
        !           712:     <li class="MsoNormal"
        !           713:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           714:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">Date
        !           715:         of fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>: coded as mm/yyyy. Missing dates
        !           716:         are coded as 99/9999 (field 13) <o:p></o:p></span></li>
        !           717:     <li class="MsoNormal"
        !           718:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           719:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Status
        !           720:         at fourth interview</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong> positive number. Missing
        !           721:         values are coded -1. (field 14) <o:p></o:p></span></li>
        !           722:     <li class="MsoNormal"
        !           723:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           724:      mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">etc<o:p></o:p></span></li>
1.2       lievre    725: </ul>
                    726: 
1.5     ! lievre    727: <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></p>
1.2       lievre    728: 
1.5     ! lievre    729: <p style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If your longitudinal survey do not
        !           730: include information about weights or covariates, you must fill
        !           731: the column with a number (e.g. 1) because a missing field is not
        !           732: allowed.<o:p></o:p></span></p>
1.2       lievre    733: 
                    734: <hr>
                    735: 
1.5     ! lievre    736: <h2><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Your first example parameter file</span><a
        !           737: href="http://euroreves.ined.fr/imach"></a><a name="uio"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h2>
1.2       lievre    738: 
1.5     ! lievre    739: <h2><a name="biaspar"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>#Imach version 0.7, February 2002,
        !           740: INED-EUROREVES <o:p></o:p></span></h2>
1.2       lievre    741: 
1.5     ! lievre    742: <p><span lang="EN-GB" style="mso-ansi-language:EN-GB">This is a comment. Comments start with a '#'.<o:p></o:p></span></p>
1.2       lievre    743: 
1.5     ! lievre    744: <h4><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">First uncommented line</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !           745: 
        !           746: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4<o:p></o:p></span></pre>
        !           747: 
        !           748: <ul type="disc">
        !           749:     <li class="MsoNormal"
        !           750:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           751:      text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">title=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           752:         1st_example is title of the run. <o:p></o:p></span></li>
        !           753:     <li class="MsoNormal"
        !           754:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           755:      text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">datafile=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>data1.txt
        !           756:         is the name of the data set. Our example is a six years
        !           757:         follow-up survey. It consists in a baseline followed by 3
        !           758:         reinterviews. <o:p></o:p></span></li>
        !           759:     <li class="MsoNormal"
        !           760:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           761:      text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">lastobs=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           762:         8600 the program is able to run on a subsample where the
        !           763:         last observation number is lastobs. It can be set a
        !           764:         bigger number than the real number of observations (e.g.
        !           765:         100000). In this example, maximisation will be done on
        !           766:         the 8600 first records. <o:p></o:p></span></li>
        !           767:     <li class="MsoNormal"
        !           768:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           769:      text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">firstpass=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           770:         , <b>lastpass=4 </b>In case of more than two interviews
        !           771:         in the survey, the program can be run on selected
        !           772:         transitions periods. firstpass=1 means the first
        !           773:         interview included in the calculation is the baseline
        !           774:         survey. lastpass=4 means that the information brought by
        !           775:         the 4th interview is taken into account.<o:p></o:p></span></li>
1.2       lievre    776: </ul>
                    777: 
1.5     ! lievre    778: <p
        !           779: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></p>
1.2       lievre    780: 
1.5     ! lievre    781: <h4
        !           782: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Second
        !           783: uncommented line</span><a name="biaspar-2"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h4>
        !           784: 
        !           785: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
        !           786: 
        !           787: <ul type="disc">
        !           788:     <li class="MsoNormal"
        !           789:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           790:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1e-8</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           791:         Convergence tolerance on the function value in the
        !           792:         maximisation of the likelihood. Choosing a correct value
        !           793:         for ftol is difficult. 1e-8 is a correct value for a 32
        !           794:         bits computer.<o:p></o:p></span></li>
        !           795:     <li class="MsoNormal"
        !           796:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           797:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">stepm=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           798:         Time unit in months for interpolation. Examples:<o:p></o:p></span></li>
        !           799:     <li><ul type="circle">
        !           800:             <li class="MsoNormal"
        !           801:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           802:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           803:                 stepm=1, the unit is a month <o:p></o:p></span></li>
        !           804:             <li class="MsoNormal"
        !           805:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           806:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           807:                 stepm=4, the unit is a trimester<o:p></o:p></span></li>
        !           808:             <li class="MsoNormal"
        !           809:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           810:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           811:                 stepm=12, the unit is a year <o:p></o:p></span></li>
        !           812:             <li class="MsoNormal"
        !           813:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           814:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           815:                 stepm=24, the unit is two years<o:p></o:p></span></li>
        !           816:             <li class="MsoNormal"
        !           817:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           818:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">...
        !           819: <o:p></o:p></span>            </li>
1.2       lievre    820:         </ul>
                    821:     </li>
1.5     ! lievre    822:     <li class="MsoNormal"
        !           823:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           824:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ncov=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           825:         Number of covariates in the datafile. The intercept and
        !           826:         the age parameter are counting for 2 covariates.<o:p></o:p></span></li>
        !           827:     <li class="MsoNormal"
        !           828:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           829:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">nlstate=2</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           830:         Number of non-absorbing (alive) states. Here we have two
        !           831:         alive states: disability-free is coded 1 and disability
        !           832:         is coded 2. <o:p></o:p></span></li>
        !           833:     <li class="MsoNormal"
        !           834:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           835:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">ndeath=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           836:         Number of absorbing states. The absorbing state death is
        !           837:         coded 3. <o:p></o:p></span></li>
        !           838:     <li class="MsoNormal"
        !           839:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           840:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">maxwav=4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           841:         Number of waves in the datafile.<o:p></o:p></span></li>
        !           842:     <li class="MsoNormal"
        !           843:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           844:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><a
        !           845:         name="mle"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b></a><b>=1</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for the
        !           846:         Maximisation Likelihood Estimation. <o:p></o:p></span></li>
        !           847:     <li><ul type="circle">
        !           848:             <li class="MsoNormal"
        !           849:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           850:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           851:                 mle=1 the program does the maximisation and the
        !           852:                 calculation of health expectancies <o:p></o:p></span></li>
        !           853:             <li class="MsoNormal"
        !           854:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           855:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           856:                 mle=0 the program only does the calculation of
        !           857:                 the health expectancies. <o:p></o:p></span></li>
1.2       lievre    858:         </ul>
                    859:     </li>
1.5     ! lievre    860:     <li class="MsoNormal"
        !           861:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           862:      text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">weight=0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !           863:         Possibility to add weights. <o:p></o:p></span></li>
        !           864:     <li><ul type="circle">
        !           865:             <li class="MsoNormal"
        !           866:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           867:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           868:                 weight=0 no weights are included <o:p></o:p></span></li>
        !           869:             <li class="MsoNormal"
        !           870:             style="mso-margin-top-alt:auto;mso-margin-bottom-alt:
        !           871:       auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !           872:                 weight=1 the maximisation integrates the weights
        !           873:                 which are in field </span><a href="#Weight"><span lang="EN-GB" style="mso-ansi-language:EN-GB">4</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></li>
1.2       lievre    874:         </ul>
                    875:     </li>
                    876: </ul>
                    877: 
1.5     ! lievre    878: <h4
        !           879: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariates</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
1.2       lievre    880: 
1.5     ! lievre    881: <p
        !           882: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Intercept
        !           883: and age are systematically included in the model. Additional
        !           884: covariates can be included with the command <o:p></o:p></span></p>
        !           885: 
        !           886: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">model=<em>list of covariates<o:p></o:p></span></em></pre>
        !           887: 
        !           888: <ul type="disc">
        !           889:     <li class="MsoNormal"
        !           890:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           891:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if<strong>
        !           892:         model=. </strong>then no covariates are included<o:p></o:p></span></li>
        !           893:     <li class="MsoNormal"
        !           894:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           895:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
        !           896:         <strong>model=V1</strong> the model includes the first
        !           897:         covariate (field 2)<o:p></o:p></span></li>
        !           898:     <li class="MsoNormal"
        !           899:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           900:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
        !           901:         <strong>model=V2 </strong>the model includes the second
        !           902:         covariate (field 3)<o:p></o:p></span></li>
        !           903:     <li class="MsoNormal"
        !           904:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           905:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
        !           906:         <strong>model=V1+V2 </strong>the model includes the first
        !           907:         and the second covariate (fields 2 and 3)<o:p></o:p></span></li>
        !           908:     <li class="MsoNormal"
        !           909:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           910:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
        !           911:         <strong>model=V1*V2 </strong>the model includes the
1.2       lievre    912:         product of the first and the second covariate (fields 2
1.5     ! lievre    913:         and 3)<o:p></o:p></span></li>
        !           914:     <li class="MsoNormal"
        !           915:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !           916:      text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">if
        !           917:         <strong>model=V1+V1*age</strong> the model includes the
        !           918:         product covariate*age<o:p></o:p></span></li>
1.2       lievre    919: </ul>
                    920: 
1.5     ! lievre    921: <h4
        !           922: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
        !           923: values for optimisation</span><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !           924: 
        !           925: <p
        !           926: style="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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">You
        !           927: must write the initial guess values of the parameters for
        !           928: optimisation. The number of parameters, <em>N</em> depends on the
1.2       lievre    929: number of absorbing states and non-absorbing states and on the
                    930: number of covariates. <br>
                    931: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
                    932: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>
                    933: <br>
                    934: Thus in the simple case with 2 covariates (the model is log
                    935: (pij/pii) = aij + bij * age where intercept and age are the two
                    936: covariates), and 2 health degrees (1 for disability-free and 2
                    937: for disability) and 1 absorbing state (3), you must enter 8
                    938: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
                    939: start with zeros as in this example, but if you have a more
                    940: precise set (for example from an earlier run) you can enter it
                    941: and it will speed up them<br>
1.4       lievre    942: Each of the four lines starts with indices &quot;ij&quot;: <b>ij
1.5     ! lievre    943: aij bij</b> <o:p></o:p></span></p>
1.2       lievre    944: 
1.5     ! lievre    945: <pre
        !           946: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
        !           947: 36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Guess values of aij and bij in log (pij/pii) = aij + bij * age<o:p></o:p></span></pre>
        !           948: 
        !           949: <pre
        !           950: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           951: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           952: EN-GB">12 -14.155633<span style="mso-spacerun: yes">&nbsp; </span>0.110794 <o:p></o:p></span></pre>
        !           953: 
        !           954: <pre
        !           955: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           956: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           957: EN-GB">13<span style="mso-spacerun: yes">&nbsp; </span>-7.925360<span style="mso-spacerun: yes">&nbsp; </span>0.032091 <o:p></o:p></span></pre>
        !           958: 
        !           959: <pre
        !           960: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           961: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           962: EN-GB">21<span style="mso-spacerun: yes">&nbsp; </span>-1.890135 -0.029473 <o:p></o:p></span></pre>
        !           963: 
        !           964: <pre
        !           965: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           966: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           967: EN-GB">23<span style="mso-spacerun: yes">&nbsp; </span>-6.234642<span style="mso-spacerun: yes">&nbsp; </span>0.022315 <o:p></o:p></span></pre>
        !           968: 
        !           969: <p
        !           970: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">or,
        !           971: to simplify: <o:p></o:p></span></p>
        !           972: 
        !           973: <pre
        !           974: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
        !           975: 36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12 0.0 0.0<o:p></o:p></span></pre>
        !           976: 
        !           977: <pre
        !           978: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           979: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           980: EN-GB">13 0.0 0.0<o:p></o:p></span></pre>
        !           981: 
        !           982: <pre
        !           983: style="margin-top:0cm;margin-right:
        !           984: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
        !           985: justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">21 0.0 0.0<o:p></o:p></span></pre>
        !           986: 
        !           987: <pre
        !           988: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !           989: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !           990: EN-GB">23 0.0 0.0<o:p></o:p></span></pre>
        !           991: 
        !           992: <h4
        !           993: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Guess
        !           994: values for computing variances</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !           995: 
        !           996: <p
        !           997: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !           998: is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
        !           999: an input to get the various output data files (Health
1.2       lievre   1000: expectancies, stationary prevalence etc.) and figures without
1.5     ! lievre   1001: rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
1.2       lievre   1002: 
1.5     ! lievre   1003: <p
        !          1004: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1005: scales are small values for the evaluation of numerical
1.2       lievre   1006: derivatives. These derivatives are used to compute the hessian
                   1007: matrix of the parameters, that is the inverse of the covariance
                   1008: matrix, and the variances of health expectancies. Each line
                   1009: consists in indices &quot;ij&quot; followed by the initial scales
1.5     ! lievre   1010: (zero to simplify) associated with aij and bij. <o:p></o:p></span></p>
1.2       lievre   1011: 
1.5     ! lievre   1012: <ul type="disc">
        !          1013:     <li class="MsoNormal"
        !          1014:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1015:      text-align:justify;mso-list:l16 level1 lfo18;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !          1016:         mle=1 you can enter zeros:<o:p></o:p></span></li>
1.2       lievre   1017: </ul>
                   1018: 
1.5     ! lievre   1019: <pre
        !          1020: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
        !          1021: 36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Scales (for hessian or gradient estimation)<o:p></o:p></span></pre>
        !          1022: 
        !          1023: <pre
        !          1024: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1025: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1026: EN-GB">12 0. 0. <o:p></o:p></span></pre>
        !          1027: 
        !          1028: <pre
        !          1029: style="margin-top:0cm;margin-right:
        !          1030: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
        !          1031: justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">13 0. 0. <o:p></o:p></span></pre>
        !          1032: 
        !          1033: <pre
        !          1034: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1035: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1036: EN-GB">21 0. 0. <o:p></o:p></span></pre>
        !          1037: 
        !          1038: <pre
        !          1039: style="margin-top:0cm;margin-right:
        !          1040: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
        !          1041: justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">23 0. 0. <o:p></o:p></span></pre>
        !          1042: 
        !          1043: <ul type="disc">
        !          1044:     <li class="MsoNormal"
        !          1045:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1046:      text-align:justify;mso-list:l11 level1 lfo21;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !          1047:         mle=0 you must enter a covariance matrix (usually
        !          1048:         obtained from an earlier run).<o:p></o:p></span></li>
1.2       lievre   1049: </ul>
                   1050: 
1.5     ! lievre   1051: <h4
        !          1052: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Covariance
        !          1053: matrix of parameters</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !          1054: 
        !          1055: <p
        !          1056: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1057: is an output if </span><a href="#mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>=1. But it can be used as
        !          1058: an input to get the various output data files (Health
        !          1059: expectancies, stationary prevalence etc.) and figures without
        !          1060: rerunning the rather long maximisation phase (mle=0). <o:p></o:p></span></p>
        !          1061: 
        !          1062: <p
        !          1063: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Each
        !          1064: line starts with indices &quot;ijk&quot; followed by the
        !          1065: covariances between aij and bij: <o:p></o:p></span></p>
        !          1066: 
        !          1067: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          1068: 
        !          1069: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span>121 Var(a12) <o:p></o:p></span></pre>
        !          1070: 
        !          1071: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;</span>122 Cov(b12,a12)<span style="mso-spacerun: yes">&nbsp; </span>Var(b12) <o:p></o:p></span></pre>
1.2       lievre   1072: 
1.5     ! lievre   1073: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>...<o:p></o:p></span></pre>
        !          1074: 
        !          1075: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span>232 Cov(b23,a12)<span style="mso-spacerun: yes">&nbsp; </span>Cov(b23,b12) ... Var (b23) <o:p></o:p></span></pre>
1.2       lievre   1076: 
1.5     ! lievre   1077: <ul type="disc">
        !          1078:     <li class="MsoNormal"
        !          1079:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1080:      text-align:justify;mso-list:l18 level1 lfo24;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !          1081:         mle=1 you can enter zeros. <o:p></o:p></span></li>
        !          1082: </ul>
1.2       lievre   1083: 
1.5     ! lievre   1084: <pre
        !          1085: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:
        !          1086: 36.0pt;margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Covariance matrix<o:p></o:p></span></pre>
        !          1087: 
        !          1088: <pre
        !          1089: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1090: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1091: EN-GB">121 0.<o:p></o:p></span></pre>
        !          1092: 
        !          1093: <pre
        !          1094: style="margin-top:0cm;margin-right:
        !          1095: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align:
        !          1096: justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">122 0. 0.<o:p></o:p></span></pre>
        !          1097: 
        !          1098: <pre
        !          1099: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1100: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1101: EN-GB">131 0. 0. 0. <o:p></o:p></span></pre>
        !          1102: 
        !          1103: <pre
        !          1104: style="margin-top:0cm;
        !          1105: margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
        !          1106: text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">132 0. 0. 0. 0. <o:p></o:p></span></pre>
        !          1107: 
        !          1108: <pre
        !          1109: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1110: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1111: EN-GB">211 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
        !          1112: 
        !          1113: <pre
        !          1114: style="margin-top:0cm;
        !          1115: margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;
        !          1116: text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">212 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
        !          1117: 
        !          1118: <pre
        !          1119: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;
        !          1120: margin-bottom:.0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:
        !          1121: EN-GB">231 0. 0. 0. 0. 0. 0. 0. <o:p></o:p></span></pre>
        !          1122: 
        !          1123: <pre
        !          1124: style="margin-top:
        !          1125: 0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:
        !          1126: .0001pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">232 0. 0. 0. 0. 0. 0. 0. 0.<o:p></o:p></span></pre>
        !          1127: 
        !          1128: <ul type="disc">
        !          1129:     <li class="MsoNormal"
        !          1130:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1131:      text-align:justify;mso-list:l7 level1 lfo27;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">If
        !          1132:         mle=0 you must enter a covariance matrix (usually
        !          1133:         obtained from an earlier run).<o:p></o:p></span></li>
        !          1134: </ul>
1.2       lievre   1135: 
1.5     ! lievre   1136: <h4
        !          1137: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Age
        !          1138: range for calculation of stationary prevalences and health
        !          1139: expectancies</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !          1140: 
        !          1141: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
        !          1142: 
        !          1143: <p
        !          1144: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
        !          1145: we obtained the estimated parameters, the program is able to
        !          1146: calculated stationary prevalence, transitions probabilities and
        !          1147: life expectancies at any age. Choice of age range is useful for
        !          1148: extrapolation. In our data file, ages varies from age 70 to 102.
        !          1149: Setting bage=50 and fage=100, makes the program computing life
        !          1150: expectancy from age bage to age fage. As we use a model, we can
        !          1151: compute life expectancy on a wider age range than the age range
        !          1152: from the data. But the model can be rather wrong on big
        !          1153: intervals.<o:p></o:p></span></p>
        !          1154: 
        !          1155: <p
        !          1156: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Similarly,
        !          1157: it is possible to get extrapolated stationary prevalence by age
        !          1158: ranging from agemin to agemax. <o:p></o:p></span></p>
        !          1159: 
        !          1160: <ul type="disc">
        !          1161:     <li class="MsoNormal"
        !          1162:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1163:      text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !          1164:         Minimum age for calculation of the stationary prevalence <o:p></o:p></span></li>
        !          1165:     <li class="MsoNormal"
        !          1166:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1167:      text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemax=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !          1168:         Maximum age for calculation of the stationary prevalence <o:p></o:p></span></li>
        !          1169:     <li class="MsoNormal"
        !          1170:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1171:      text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">bage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !          1172:         Minimum age for calculation of the health expectancies <o:p></o:p></span></li>
        !          1173:     <li class="MsoNormal"
        !          1174:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1175:      text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">fage=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !          1176:         Maximum age for calculation of the health expectancies <o:p></o:p></span></li>
1.2       lievre   1177: </ul>
                   1178: 
1.5     ! lievre   1179: <h4
        !          1180: 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"><a
        !          1181: name="Computing"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Computing</span><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB"></a> the observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !          1182: 
        !          1183: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=1/1/1984 end-prev-date=1/6/1988 <o:p></o:p></span></pre>
        !          1184: 
        !          1185: <p
        !          1186: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Statements
        !          1187: 'begin-prev-date' and 'end-prev-date' allow to select the period
        !          1188: in which we calculate the observed prevalences in each state. In
        !          1189: this example, the prevalences are calculated on data survey
        !          1190: collected between 1 January 1984 and 1 June 1988. <o:p></o:p></span></p>
        !          1191: 
        !          1192: <ul type="disc">
        !          1193:     <li class="MsoNormal"
        !          1194:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1195:      text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">begin-prev-date=
        !          1196: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>Starting date (day/month/year)<o:p></o:p></span></li>
        !          1197:     <li class="MsoNormal"
        !          1198:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1199:      text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">end-prev-date=
        !          1200: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>Final date (day/month/year)<o:p></o:p></span></li>
1.2       lievre   1201: </ul>
                   1202: 
1.5     ! lievre   1203: <h4
        !          1204: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Population-
        !          1205: or status-based health expectancies</span><span lang="EN-GB" style="mso-ansi-language:
        !          1206: EN-GB"><o:p></o:p></span></h4>
        !          1207: 
        !          1208: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pop_based=0<o:p></o:p></span></pre>
        !          1209: 
        !          1210: <p
        !          1211: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1212: user has the possibility to choose between population-based or
        !          1213: status-based health expectancies. If pop_based=0 then
        !          1214: status-based health expectancies are computed and if pop_based=1,
        !          1215: the programme computes population-based health expectancies.
        !          1216: Health expectancies are weighted averages of health expectancies
        !          1217: respective of the initial state. For a status-based index, the
        !          1218: weights are the cross-sectional prevalences observed between two
        !          1219: dates, as </span><a href="#Computing"><span lang="EN-GB" style="mso-ansi-language:EN-GB">previously explained</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, whereas
        !          1220: for a population-based index, the weights are the stationary
        !          1221: prevalences.<o:p></o:p></span></p>
        !          1222: 
        !          1223: <h4
        !          1224: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Prevalence
        !          1225: forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !          1226: 
        !          1227: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 <o:p></o:p></span></pre>
        !          1228: 
        !          1229: <p
        !          1230: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Prevalence
        !          1231: and population projections are available only if the
        !          1232: interpolation unit is a month, i.e. stepm=1. The programme
        !          1233: estimates the prevalence in each state at a precise date
        !          1234: expressed in day/month/year. The programme computes one
        !          1235: forecasted prevalence a year from a starting date (1 January of
        !          1236: 1989 in this example) to a final date (1 January 1992). The
        !          1237: statement mov_average allows to compute smoothed forecasted
        !          1238: prevalences with a five-age moving average centred at the mid-age
        !          1239: of the five-age period. <o:p></o:p></span></p>
1.2       lievre   1240: 
1.5     ! lievre   1241: <ul type="disc">
        !          1242:     <li class="MsoNormal"
        !          1243:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1244:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">starting-proj-date</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
        !          1245:         starting date (day/month/year) of forecasting<o:p></o:p></span></li>
        !          1246:     <li class="MsoNormal"
        !          1247:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1248:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">final-proj-date=
        !          1249: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </strong>final date (day/month/year) of forecasting<o:p></o:p></span></li>
        !          1250:     <li class="MsoNormal"
        !          1251:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1252:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">mov_average</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>=
        !          1253:         smoothing with a five-age moving average centred at the
        !          1254:         mid-age of the five-age period. The command<strong>
        !          1255:         mov_average</strong> takes value 1 if the prevalences are
        !          1256:         smoothed and 0 otherwise.<o:p></o:p></span></li>
        !          1257: </ul>
1.2       lievre   1258: 
1.5     ! lievre   1259: <h4
        !          1260: 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"><span lang="EN-GB" style="color:red;mso-ansi-language:EN-GB">Last
        !          1261: uncommented line : Population forecasting </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h4>
        !          1262: 
        !          1263: <pre><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992<o:p></o:p></span></pre>
        !          1264: 
        !          1265: <p
        !          1266: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1267: command is available if the interpolation unit is a month, i.e.
        !          1268: stepm=1 and if popforecast=1. From a data file including age and
        !          1269: number of persons alive at the precise date &#145;</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:&quot;Courier New&quot;;
        !          1270: mso-ansi-language:EN-GB">popfiledate&#146;,
        !          1271: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">you can forecast the number of persons in each state until date</span><span lang="EN-GB" style="font-size:10.0pt;mso-bidi-font-size:
        !          1272: 12.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">
        !          1273: &#145;last-popfiledate&#146;. </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">In this example, the popfile </span><a
        !          1274: href="pyram.txt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">pyram.txt</span><span style="mso-ansi-language:EN-GB"></b></a><b> </span><span lang="EN-GB" style="mso-ansi-language:
        !          1275: EN-GB"><span style="mso-spacerun: yes"></b>&nbsp;</span>includes real
        !          1276: data which are the Japanese population in 1989.<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></p>
        !          1277: 
        !          1278: <ul type="disc">
        !          1279:     <li class="MsoNormal"
        !          1280:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1281:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popforecast=
        !          1282:         0</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b> Option for population forecasting. If
        !          1283:         popforecast=1, the programme does the forecasting<b>.<o:p></o:p></span></b></li>
        !          1284:     <li class="MsoNormal"
        !          1285:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1286:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfile=
        !          1287: </span><span lang="EN-GB" style="mso-ansi-language:EN-GB">        </b>name of the population file<o:p></o:p></span></li>
        !          1288:     <li class="MsoNormal"
        !          1289:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1290:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">popfiledate=</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>
        !          1291:         date of the population population<o:p></o:p></span></li>
        !          1292:     <li class="MsoNormal"
        !          1293:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1294:      text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt"><b><span lang="EN-GB" style="mso-ansi-language:EN-GB">last-popfiledate</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></b>=
        !          1295:         date of the last population projection&nbsp;<o:p></o:p></span></li>
1.2       lievre   1296: </ul>
                   1297: 
1.5     ! lievre   1298: <hr>
1.4       lievre   1299: 
1.5     ! lievre   1300: <h2
        !          1301: 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"><a
        !          1302: name="running"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Running Imach with this example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
        !          1303: 
        !          1304: <p
        !          1305: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">We
        !          1306: assume that you entered your </span><a href="biaspar.imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">1st_example
        !          1307: parameter file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> as explained </span><a href="#biaspar"><span lang="EN-GB" style="mso-ansi-language:
        !          1308: EN-GB">above</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. To
        !          1309: run the program you should click on the imach.exe icon and enter
        !          1310: the name of the parameter file which is for example </span><a
        !          1311: href="..\mle\biaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle\biaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> (you
        !          1312: also can click on the biaspar.txt icon located in </span><a
        !          1313: href="..\mle"><span lang="EN-GB" style="mso-ansi-language:EN-GB">C:\usr\imach\mle</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and put it with the mouse on
        !          1314: the imach window).<o:p></o:p></span></p>
        !          1315: 
        !          1316: <p
        !          1317: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1318: time to converge depends on the step unit that you used (1 month
        !          1319: is cpu consuming), on the number of cases, and on the number of
        !          1320: variables.<o:p></o:p></span></p>
        !          1321: 
        !          1322: <p
        !          1323: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1324: program outputs many files. Most of them are files which will be
        !          1325: plotted for better understanding.<o:p></o:p></span></p>
        !          1326: 
        !          1327: <hr>
1.4       lievre   1328: 
1.5     ! lievre   1329: <h2
        !          1330: 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"><a
        !          1331: name="output"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB">Output of the program and graphs</span><span style="mso-bookmark:output"><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
        !          1332: 
        !          1333: <p
        !          1334: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
        !          1335: the optimization is finished, some graphics can be made with a
        !          1336: grapher. We use Gnuplot which is an interactive plotting program
        !          1337: copyrighted but freely distributed. A gnuplot reference manual is
        !          1338: available </span><a href="http://www.gnuplot.info/"><span lang="EN-GB" style="mso-ansi-language:EN-GB">here</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>. <br>
        !          1339: When the running is finished, the user should enter a character
        !          1340: for plotting and output editing. <o:p></o:p></span></p>
        !          1341: 
        !          1342: <p
        !          1343: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">These
        !          1344: characters are:<o:p></o:p></span></p>
        !          1345: 
        !          1346: <ul type="disc">
        !          1347:     <li class="MsoNormal"
        !          1348:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1349:      text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'c'
        !          1350:         to start again the program from the beginning.<o:p></o:p></span></li>
        !          1351:     <li class="MsoNormal"
        !          1352:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1353:      text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'e'
        !          1354:         opens the </span><a href="biaspar.htm"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">biaspar.htm</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong></a>
        !          1355:         file to edit the output files and graphs. <o:p></o:p></span></li>
        !          1356:     <li class="MsoNormal"
        !          1357:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1358:      text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">'q'
        !          1359:         for exiting.<o:p></o:p></span></li>
1.4       lievre   1360: </ul>
                   1361: 
1.5     ! lievre   1362: <h5
        !          1363: style="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"><span lang="EN-GB" style="font-size:18.0pt;mso-bidi-font-size:10.0pt;color:#00006A;
        !          1364: mso-ansi-language:EN-GB">Results
        !          1365: files</span><strong><span lang="EN-GB" style="font-size:13.5pt;mso-ansi-language:EN-GB"> </span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong><br>
        !          1366: <br>
        !          1367: </span><strong><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;
        !          1368: mso-ansi-language:EN-GB">- </strong><a name="Observed_prevalence_in_each_state"><strong>Observed
        !          1369: prevalence in each state</strong></a><strong> (and at first pass)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></strong>:
        !          1370: </span><a href="prbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">prbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1371: 
        !          1372: <p
        !          1373: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1374: first line is the title and displays each field of the file. The
        !          1375: first column is age. The fields 2 and 6 are the proportion of
        !          1376: individuals in states 1 and 2 respectively as observed during the
        !          1377: first exam. Others fields are the numbers of people in states 1,
        !          1378: 2 or more. The number of columns increases if the number of
        !          1379: states is higher than 2.<br>
        !          1380: The header of the file is <o:p></o:p></span></p>
        !          1381: 
        !          1382: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age Prev(1) N(1) N Age Prev(2) N(2) N<o:p></o:p></span></pre>
        !          1383: 
        !          1384: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 1.00000 631 631 70 0.00000 0 631<o:p></o:p></span></pre>
        !          1385: 
        !          1386: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.99681 625 627 71 0.00319 2 627 <o:p></o:p></span></pre>
        !          1387: 
        !          1388: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.97125 1115 1148 72 0.02875 33 1148 <o:p></o:p></span></pre>
        !          1389: 
        !          1390: <p
        !          1391: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">It
        !          1392: means that at age 70, the prevalence in state 1 is 1.000 and in
        !          1393: state 2 is 0.00 . At age 71 the number of individuals in state 1
        !          1394: is 625 and in state 2 is 2, hence the total number of people aged
        !          1395: 71 is 625+2=627. <o:p></o:p></span></p>
        !          1396: 
        !          1397: <h5
        !          1398: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1399: Estimated parameters and covariance matrix</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
        !          1400: href="rbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1401: 
        !          1402: <p
        !          1403: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1404: file contains all the maximisation results: <o:p></o:p></span></p>
        !          1405: 
        !          1406: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>-2 log likelihood= 21660.918613445392<o:p></o:p></span></pre>
        !          1407: 
        !          1408: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> Estimated parameters: a12 = -12.290174 b12 = 0.092161 <o:p></o:p></span></pre>
        !          1409: 
        !          1410: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span style="mso-spacerun: yes">&nbsp;</span>a13 = -9.155590<span style="mso-spacerun: yes">&nbsp; </span>b13 = 0.046627 <o:p></o:p></span></pre>
        !          1411: 
        !          1412: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>a21 = -2.629849<span style="mso-spacerun: yes">&nbsp; </span>b21 = -0.022030 <o:p></o:p></span></pre>
        !          1413: 
        !          1414: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>a23 = -7.958519<span style="mso-spacerun: yes">&nbsp; </span>b23 = 0.042614<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></pre>
        !          1415: 
        !          1416: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>Covariance matrix: Var(a12) = 1.47453e-001<o:p></o:p></span></pre>
        !          1417: 
        !          1418: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b12) = 2.18676e-005<o:p></o:p></span></pre>
        !          1419: 
        !          1420: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(a13) = 2.09715e-001<o:p></o:p></span></pre>
        !          1421: 
        !          1422: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b13) = 3.28937e-005<span style="mso-spacerun: yes">&nbsp; </span><o:p></o:p></span></pre>
        !          1423: 
        !          1424: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>Var(a21) = 9.19832e-001<o:p></o:p></span></pre>
        !          1425: 
        !          1426: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b21) = 1.29229e-004<o:p></o:p></span></pre>
1.4       lievre   1427: 
1.5     ! lievre   1428: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="DE" style="mso-ansi-language:DE">Var(a23) = 4.48405e-001<o:p></o:p></span></pre>
1.4       lievre   1429: 
1.5     ! lievre   1430: <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Var(b23) = 5.85631e-005 <o:p></o:p></span></pre>
1.4       lievre   1431: 
1.5     ! lievre   1432: <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE"><span style="mso-spacerun: yes">&nbsp;</span><o:p></o:p></span></pre>
1.4       lievre   1433: 
1.5     ! lievre   1434: <p
        !          1435: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">By
        !          1436: substitution of these parameters in the regression model, we
        !          1437: obtain the elementary transition probabilities:<o:p></o:p></span></p>
1.4       lievre   1438: 
1.5     ! lievre   1439: <p
        !          1440: style="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"><img
        !          1441: src="pebiaspar1.gif" width="400" height="300" id="_x0000_i1037"></p>
        !          1442: 
        !          1443: <h5
        !          1444: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1445: Transition probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="pijrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          1446: EN-GB">pijrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          1447: EN-GB"><o:p></o:p></span></a></h5>
        !          1448: 
        !          1449: <p
        !          1450: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Here
        !          1451: are the transitions probabilities Pij(x, x+nh) where nh is a
        !          1452: multiple of 2 years. The first column is the starting age x (from
        !          1453: age 50 to 100), the second is age (x+nh) and the others are the
        !          1454: transition probabilities p11, p12, p13, p21, p22, p23. For
        !          1455: example, line 5 of the file is: <o:p></o:p></span></p>
        !          1456: 
        !          1457: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;</span>100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 <o:p></o:p></span></pre>
        !          1458: 
        !          1459: <p
        !          1460: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">and
        !          1461: this means: <o:p></o:p></span></p>
        !          1462: 
        !          1463: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p11(100,106)=0.02655<o:p></o:p></span></pre>
1.4       lievre   1464: 
1.5     ! lievre   1465: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p12(100,106)=0.17622<o:p></o:p></span></pre>
1.4       lievre   1466: 
1.5     ! lievre   1467: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p13(100,106)=0.79722<o:p></o:p></span></pre>
1.4       lievre   1468: 
1.5     ! lievre   1469: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p21(100,106)=0.01809<o:p></o:p></span></pre>
1.4       lievre   1470: 
1.5     ! lievre   1471: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.13678<o:p></o:p></span></pre>
1.4       lievre   1472: 
1.5     ! lievre   1473: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">p22(100,106)=0.84513 <o:p></o:p></span></pre>
1.4       lievre   1474: 
1.5     ! lievre   1475: <h5
        !          1476: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1477: <a name="Stationary_prevalence_in_each_state">Stationary
        !          1478: prevalence in each state</span><span style="mso-bookmark:Stationary_prevalence_in_each_state"></span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>: </span><a href="plrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">plrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
1.4       lievre   1479: 
1.5     ! lievre   1480: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Prevalence<o:p></o:p></span></pre>
1.2       lievre   1481: 
1.5     ! lievre   1482: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Age 1-1 2-2<o:p></o:p></span></pre>
1.2       lievre   1483: 
1.5     ! lievre   1484: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
1.2       lievre   1485: 
1.5     ! lievre   1486: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#************ <o:p></o:p></span></pre>
1.2       lievre   1487: 
1.5     ! lievre   1488: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 0.90134 0.09866<o:p></o:p></span></pre>
1.2       lievre   1489: 
1.5     ! lievre   1490: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 0.89177 0.10823 <o:p></o:p></span></pre>
1.2       lievre   1491: 
1.5     ! lievre   1492: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 0.88139 0.11861 <o:p></o:p></span></pre>
1.2       lievre   1493: 
1.5     ! lievre   1494: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.87015 0.12985 <o:p></o:p></span></pre>
1.2       lievre   1495: 
1.5     ! lievre   1496: <p
        !          1497: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">At
        !          1498: age 70 the stationary prevalence is 0.90134 in state 1 and
1.3       lievre   1499: 0.09866 in state 2. This stationary prevalence differs from
1.2       lievre   1500: observed prevalence. Here is the point. The observed prevalence
                   1501: at age 70 results from the incidence of disability, incidence of
                   1502: recovery and mortality which occurred in the past of the cohort.
                   1503: Stationary prevalence results from a simulation with actual
                   1504: incidences and mortality (estimated from this cross-longitudinal
                   1505: survey). It is the best predictive value of the prevalence in the
                   1506: future if &quot;nothing changes in the future&quot;. This is
                   1507: exactly what demographers do with a Life table. Life expectancy
                   1508: is the expected mean time to survive if observed mortality rates
                   1509: (incidence of mortality) &quot;remains constant&quot; in the
1.5     ! lievre   1510: future. <o:p></o:p></span></p>
1.2       lievre   1511: 
1.5     ! lievre   1512: <h5
        !          1513: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1514: Standard deviation of stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
        !          1515: href="vplrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vplrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1516: 
        !          1517: <p
        !          1518: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">The
        !          1519: stationary prevalence has to be compared with the observed
1.2       lievre   1520: prevalence by age. But both are statistical estimates and
                   1521: subjected to stochastic errors due to the size of the sample, the
                   1522: design of the survey, and, for the stationary prevalence to the
                   1523: model used and fitted. It is possible to compute the standard
1.5     ! lievre   1524: deviation of the stationary prevalence at each age.<o:p></o:p></span></p>
1.2       lievre   1525: 
1.5     ! lievre   1526: <h5
        !          1527: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Observed
        !          1528: and stationary prevalence in state (2=disable) with the confident
        !          1529: interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="vbiaspar21.htm"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vbiaspar21.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1530: 
        !          1531: <p
        !          1532: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1533: graph exhibits the stationary prevalence in state (2) with the
        !          1534: confidence interval in red. The green curve is the observed
        !          1535: prevalence (or proportion of individuals in state (2)). Without
        !          1536: discussing the results (it is not the purpose here), we observe
        !          1537: that the green curve is rather below the stationary prevalence.
        !          1538: It suggests an increase of the disability prevalence in the
        !          1539: future.<o:p></o:p></span></p>
        !          1540: 
        !          1541: <p
        !          1542: 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"><img
        !          1543: src="vbiaspar21.gif" width="400" height="300" id="_x0000_i1038"></p>
        !          1544: 
        !          1545: <h5
        !          1546: style="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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Convergence
        !          1547: to the stationary prevalence of disability</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
        !          1548: href="pbiaspar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pbiaspar11.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
        !          1549: </span><img src="pbiaspar11.gif" width="400" height="300"
        !          1550: id="_x0000_i1039"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h5>
        !          1551: 
        !          1552: <p
        !          1553: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1554: graph plots the conditional transition probabilities from an
        !          1555: initial state (1=healthy in red at the bottom, or 2=disable in
1.2       lievre   1556: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
                   1557: age <em>x+h. </em>Conditional means at the condition to be alive
                   1558: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
                   1559: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
                   1560: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
                   1561: prevalence of disability</em>. In order to get the stationary
                   1562: prevalence at age 70 we should start the process at an earlier
                   1563: age, i.e.50. If the disability state is defined by severe
                   1564: disability criteria with only a few chance to recover, then the
                   1565: incidence of recovery is low and the time to convergence is
1.5     ! lievre   1566: probably longer. But we don't have experience yet.<o:p></o:p></span></p>
        !          1567: 
        !          1568: <h5
        !          1569: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1570: Life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
        !          1571: href="erbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">erbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1572: 
        !          1573: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Health expectancies <o:p></o:p></span></pre>
1.2       lievre   1574: 
1.5     ! lievre   1575: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age 1-1 1-2 2-1 2-2 <o:p></o:p></span></pre>
1.2       lievre   1576: 
1.5     ! lievre   1577: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 10.9226 3.0401 5.6488 6.2122 <o:p></o:p></span></pre>
1.2       lievre   1578: 
1.5     ! lievre   1579: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">71 10.4384 3.0461 5.2477 6.1599 <o:p></o:p></span></pre>
1.2       lievre   1580: 
1.5     ! lievre   1581: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">72 9.9667 3.0502 4.8663 6.1025 <o:p></o:p></span></pre>
        !          1582: 
        !          1583: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 9.5077 3.0524 4.5044 6.0401 <o:p></o:p></span></pre>
        !          1584: 
        !          1585: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For example 70 10.9226 3.0401 5.6488 6.2122 means:<o:p></o:p></span></pre>
        !          1586: 
        !          1587: <pre style="text-align:justify"><span lang="DE" style="mso-ansi-language:DE">e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122<o:p></o:p></span></pre>
        !          1588: 
        !          1589: <pre style="text-align:justify"><img src="expbiaspar21.gif"
        !          1590: width="400" height="300" id="_x0000_i1040"><img
        !          1591: src="expbiaspar11.gif" width="400" height="300" id="_x0000_i1041"></pre>
        !          1592: 
        !          1593: <p
        !          1594: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
        !          1595: example, life expectancy of a healthy individual at age 70 is
        !          1596: 10.92 in the healthy state and 3.04 in the disability state
1.3       lievre   1597: (=13.96 years). If he was disable at age 70, his life expectancy
                   1598: will be shorter, 5.64 in the healthy state and 6.21 in the
                   1599: disability state (=11.85 years). The total life expectancy is a
                   1600: weighted mean of both, 13.96 and 11.85; weight is the proportion
1.2       lievre   1601: of people disabled at age 70. In order to get a pure period index
1.5     ! lievre   1602: (i.e. based only on incidences) we use the </span><a
        !          1603: href="#Stationary prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:EN-GB">computed or
        !          1604: stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> at age 70 (i.e. computed from
        !          1605: incidences at earlier ages) instead of the </span><a
        !          1606: href="#Observed prevalence in each state"><span lang="EN-GB" style="mso-ansi-language:
        !          1607: EN-GB">observed prevalence</span><span lang="EN-GB" style="mso-ansi-language:
        !          1608: EN-GB"></a>
        !          1609: (for example at first exam) (</span><a href="#Health expectancies"><span lang="EN-GB" style="mso-ansi-language:EN-GB">see
        !          1610: below</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>).<o:p></o:p></span></p>
        !          1611: 
        !          1612: <h5
        !          1613: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1614: Variances of life expectancies by age and initial health status</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a
        !          1615: href="vrbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">vrbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1616: 
        !          1617: <p
        !          1618: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">For
        !          1619: example, the covariances of life expectancies Cov(ei,ej) at age
        !          1620: 50 are (line 3) <o:p></o:p></span></p>
        !          1621: 
        !          1622: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp; </span></span><span lang="DE" style="mso-ansi-language:DE">Cov(e1,e1)=0.4776<span style="mso-spacerun: yes">&nbsp; </span>Cov(e1,e2)=0.0488=Cov(e2,e1)<span style="mso-spacerun: yes">&nbsp; </span>Cov(e2,e2)=0.0424<o:p></o:p></span></pre>
        !          1623: 
        !          1624: <h5
        !          1625: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1626: <a name="Health_expectancies">Health expectancies</a> with
        !          1627: standard errors in parentheses</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="trbiaspar.txt"><span lang="EN-GB" style="font-family:&quot;Courier New&quot;;
        !          1628: mso-ansi-language:EN-GB">trbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1629: 
        !          1630: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) <o:p></o:p></span></pre>
        !          1631: 
        !          1632: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) <o:p></o:p></span></pre>
        !          1633: 
        !          1634: <p
        !          1635: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Thus,
        !          1636: at age 70 the total life expectancy, e..=13.76years is the
        !          1637: weighted mean of e1.=13.96 and e2.=11.85 by the stationary
1.3       lievre   1638: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
                   1639: state 2, respectively (the sum is equal to one). e.1=10.40 is the
1.2       lievre   1640: Disability-free life expectancy at age 70 (it is again a weighted
1.3       lievre   1641: mean of e11 and e21). e.2=3.35 is also the life expectancy at age
1.5     ! lievre   1642: 70 to be spent in the disability state.<o:p></o:p></span></p>
1.2       lievre   1643: 
1.5     ! lievre   1644: <h5
        !          1645: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-Total
        !          1646: life expectancy by age and health expectancies in states
        !          1647: (1=healthy) and (2=disable)</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="ebiaspar1.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ebiaspar1.gif</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
        !          1648: 
        !          1649: <p
        !          1650: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1651: figure represents the health expectancies and the total life
        !          1652: expectancy with the confident interval in dashed curve. <o:p></o:p></span></p>
        !          1653: 
        !          1654: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><img
        !          1655: src="ebiaspar1.gif" width="400" height="300" id="_x0000_i1042"></pre>
        !          1656: 
        !          1657: <p
        !          1658: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Standard
        !          1659: deviations (obtained from the information matrix of the model) of
        !          1660: these quantities are very useful. Cross-longitudinal surveys are
        !          1661: costly and do not involve huge samples, generally a few
        !          1662: thousands; therefore it is very important to have an idea of the
        !          1663: standard deviation of our estimates. It has been a big challenge
        !          1664: to compute the Health Expectancy standard deviations. Don't be
        !          1665: confuse: life expectancy is, as any expected value, the mean of a
        !          1666: distribution; but here we are not computing the standard
        !          1667: deviation of the distribution, but the standard deviation of the
        !          1668: estimate of the mean.<o:p></o:p></span></p>
        !          1669: 
        !          1670: <p
        !          1671: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Our
        !          1672: health expectancies estimates vary according to the sample size
        !          1673: (and the standard deviations give confidence intervals of the
        !          1674: estimate) but also according to the model fitted. Let us explain
        !          1675: it in more details.<o:p></o:p></span></p>
        !          1676: 
        !          1677: <p
        !          1678: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Choosing
        !          1679: a model means at least two kind of choices. First we have to
        !          1680: decide the number of disability states. Second we have to design,
        !          1681: within the logit model family, the model: variables, covariables,
        !          1682: confounding factors etc. to be included.<o:p></o:p></span></p>
        !          1683: 
        !          1684: <p
        !          1685: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">More
        !          1686: disability states we have, better is our demographical approach
        !          1687: of the disability process, but smaller are the number of
1.2       lievre   1688: transitions between each state and higher is the noise in the
                   1689: measurement. We do not have enough experiments of the various
                   1690: models to summarize the advantages and disadvantages, but it is
                   1691: important to say that even if we had huge and unbiased samples,
                   1692: the total life expectancy computed from a cross-longitudinal
                   1693: survey, varies with the number of states. If we define only two
                   1694: states, alive or dead, we find the usual life expectancy where it
                   1695: is assumed that at each age, people are at the same risk to die.
                   1696: If we are differentiating the alive state into healthy and
                   1697: disable, and as the mortality from the disability state is higher
                   1698: than the mortality from the healthy state, we are introducing
                   1699: heterogeneity in the risk of dying. The total mortality at each
                   1700: age is the weighted mean of the mortality in each state by the
                   1701: prevalence in each state. Therefore if the proportion of people
                   1702: at each age and in each state is different from the stationary
                   1703: equilibrium, there is no reason to find the same total mortality
                   1704: at a particular age. Life expectancy, even if it is a very useful
                   1705: tool, has a very strong hypothesis of homogeneity of the
                   1706: population. Our main purpose is not to measure differential
                   1707: mortality but to measure the expected time in a healthy or
                   1708: disability state in order to maximise the former and minimize the
                   1709: latter. But the differential in mortality complexifies the
1.5     ! lievre   1710: measurement.<o:p></o:p></span></p>
1.2       lievre   1711: 
1.5     ! lievre   1712: <p
        !          1713: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Incidences
        !          1714: of disability or recovery are not affected by the number of
        !          1715: states if these states are independant. But incidences estimates
        !          1716: are dependant on the specification of the model. More covariates
        !          1717: we added in the logit model better is the model, but some
        !          1718: covariates are not well measured, some are confounding factors
        !          1719: like in any statistical model. The procedure to &quot;fit the
        !          1720: best model' is similar to logistic regression which itself is
        !          1721: similar to regression analysis. We haven't yet been so far
        !          1722: because we also have a severe limitation which is the speed of
        !          1723: the convergence. On a Pentium III, 500 MHz, even the simplest
        !          1724: model, estimated by month on 8,000 people may take 4 hours to
        !          1725: converge. Also, the program is not yet a statistical package,
        !          1726: which permits a simple writing of the variables and the model to
        !          1727: take into account in the maximisation. The actual program allows
        !          1728: only to add simple variables like age+sex or age+sex+ age*sex but
        !          1729: will never be general enough. But what is to remember, is that
1.2       lievre   1730: incidences or probability of change from one state to another is
1.5     ! lievre   1731: affected by the variables specified into the model.<o:p></o:p></span></p>
1.2       lievre   1732: 
1.5     ! lievre   1733: <p
        !          1734: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Also,
        !          1735: the age range of the people interviewed has a link with the age
        !          1736: range of the life expectancy which can be estimated by
1.2       lievre   1737: extrapolation. If your sample ranges from age 70 to 95, you can
                   1738: clearly estimate a life expectancy at age 70 and trust your
                   1739: confidence interval which is mostly based on your sample size,
                   1740: but if you want to estimate the life expectancy at age 50, you
                   1741: should rely in your model, but fitting a logistic model on a age
1.5     ! lievre   1742: range of 70-95 and estimating probabilities of transition out of
1.2       lievre   1743: this age range, say at age 50 is very dangerous. At least you
                   1744: should remember that the confidence interval given by the
                   1745: standard deviation of the health expectancies, are under the
                   1746: strong assumption that your model is the 'true model', which is
1.5     ! lievre   1747: probably not the case.<o:p></o:p></span></p>
        !          1748: 
        !          1749: <h5
        !          1750: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1751: Copy of the parameter file</span><span lang="EN-GB" style="mso-ansi-language:
        !          1752: EN-GB">: </span><a href="orbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          1753: EN-GB">orbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
1.2       lievre   1754: 
1.5     ! lievre   1755: <p
        !          1756: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          1757: copy of the parameter file can be useful to re-run the program
        !          1758: while saving the old output files. <o:p></o:p></span></p>
1.2       lievre   1759: 
1.5     ! lievre   1760: <h5
        !          1761: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1762: Prevalence forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="frbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></h5>
1.2       lievre   1763: 
1.5     ! lievre   1764: <p
        !          1765: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First,
        !          1766: we have estimated the observed prevalence between 1/1/1984 and
        !          1767: 1/6/1988. <span style="mso-spacerun:
        !          1768: yes">&nbsp;</span>The mean date of interview (weighed average of
        !          1769: the interviews performed between1/1/1984 and 1/6/1988) is
        !          1770: estimated to be 13/9/1985, as written on the top on the file.
        !          1771: Then we forecast the probability to be in each state. <o:p></o:p></span></p>
1.4       lievre   1772: 
1.5     ! lievre   1773: <p
        !          1774: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Example,
        !          1775: at date 1/1/1989 : <o:p></o:p></span></p>
1.4       lievre   1776: 
1.5     ! lievre   1777: <p class="MsoNormal"><span lang="DE" style="mso-ansi-language:DE"># StartingAge FinalAge P.1 P.2 P.3<o:p></o:p></span></p>
1.4       lievre   1778: 
1.5     ! lievre   1779: <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></p>
1.4       lievre   1780: 
1.5     ! lievre   1781: <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 0.807 0.078 0.115 <o:p></o:p></span></p>
1.4       lievre   1782: 
1.5     ! lievre   1783: <p
        !          1784: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
        !          1785: the minimum age is 70 on the 13/9/1985, the youngest forecasted
        !          1786: age is 73. This means that at age a person aged 70 at 13/9/1989
        !          1787: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
        !          1788: Similarly, the probability to be in state 2 is 0.078 and the
        !          1789: probability to die is 0.115. Then, on the 1/1/1989, the
        !          1790: prevalence of disability at age 73 is estimated to be 0.088.<o:p></o:p></span></p>
1.4       lievre   1791: 
1.5     ! lievre   1792: <h5
        !          1793: 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"><span lang="EN-GB" style="font-size:12.0pt;color:#EC5E5E;mso-ansi-language:EN-GB">-
        !          1794: Population forecasting</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">: </span><a href="poprbiaspar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          1795: EN-GB">poprbiaspar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          1796: EN-GB"><o:p></o:p></span></a></h5>
1.4       lievre   1797: 
1.5     ! lievre   1798: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Age P.1 P.2 P.3 [Population]<o:p></o:p></span></pre>
1.4       lievre   1799: 
1.5     ! lievre   1800: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1989 <o:p></o:p></span></pre>
        !          1801: 
        !          1802: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">75 572685.22 83798.08 <o:p></o:p></span></pre>
        !          1803: 
        !          1804: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">74 621296.51 79767.99 <o:p></o:p></span></pre>
        !          1805: 
        !          1806: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">73 645857.70 69320.60 <o:p></o:p></span></pre>
        !          1807: 
        !          1808: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># Forecasting at date 1/1/1990<o:p></o:p></span></pre>
        !          1809: 
        !          1810: <pre style="text-align:justify">76 442986.68 92721.14 120775.48</pre>
        !          1811: 
        !          1812: <pre style="text-align:justify">75 487781.02 91367.97 121915.51</pre>
        !          1813: 
        !          1814: <pre style="text-align:justify">74 512892.07 85003.47 117282.76 </pre>
1.2       lievre   1815: 
1.5     ! lievre   1816: <pre style="text-align:justify">&nbsp;<o:p></o:p></pre>
1.2       lievre   1817: 
1.5     ! lievre   1818: <p class="MsoNormal"><span lang="EN-GB" style="mso-ansi-language:EN-GB">From the population file, we estimate the
        !          1819: number of people in each state. At age 73, 645857 persons are in
        !          1820: state 1 and 69320 are in state 2. One year latter, 512892 are
        !          1821: still in state 1, 85003 are in state 2 and 117282 died before
        !          1822: 1/1/1990.<o:p></o:p></span></p>
1.2       lievre   1823: 
1.5     ! lievre   1824: <pre style="text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
1.2       lievre   1825: 
1.5     ! lievre   1826: <hr>
        !          1827: 
        !          1828: <h2
        !          1829: 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"><a
        !          1830: name="example"><span lang="EN-GB" style="color:#00006A;mso-ansi-language:EN-GB"></a>Trying an example</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></h2>
        !          1831: 
        !          1832: <p
        !          1833: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Since
        !          1834: you know how to run the program, it is time to test it on your
        !          1835: own computer. Try for example on a parameter file named </span><a
        !          1836: href="..\mytry\imachpar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> which is a copy of </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">
        !          1837: included in the subdirectory of imach, </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;
        !          1838: mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:
        !          1839: EN-GB">. Edit it to change
        !          1840: the name of the data file to </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:
        !          1841: EN-GB">..\data\mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> if you don't want
        !          1842: to copy it on the same directory. The file </span><span lang="EN-GB" style="font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mydata.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"> is a
        !          1843: smaller file of 3,000 people but still with 4 waves. <o:p></o:p></span></p>
        !          1844: 
        !          1845: <p
        !          1846: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Click
        !          1847: on the imach.exe icon to open a window. Answer to the question: '<strong>Enter
        !          1848: the parameter file name:'<o:p></o:p></span></strong></p>
        !          1849: 
        !          1850: <table border="1" cellpadding="0"
        !          1851: style="mso-cellspacing:1.5pt;mso-padding-alt:
        !          1852:  0cm 0cm 0cm 0cm">
1.2       lievre   1853:     <tr>
1.5     ! lievre   1854:         <td width="100%"
        !          1855:         style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">IMACH,
        !          1856:         Version 0.7</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong><p style="text-align:justify"><strong><span lang="EN-GB" style="mso-ansi-language:
        !          1857:   EN-GB">Enter
        !          1858:         the parameter file name: ..\mytry\imachpar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></strong></p>
1.2       lievre   1859:         </td>
                   1860:     </tr>
                   1861: </table>
                   1862: 
1.5     ! lievre   1863: <p
        !          1864: style="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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Most
        !          1865: of the data files or image files generated, will use the
1.2       lievre   1866: 'imachpar' string into their name. The running time is about 2-3
                   1867: minutes on a Pentium III. If the execution worked correctly, the
                   1868: outputs files are created in the current directory, and should be
1.5     ! lievre   1869: the same as the mypar files initially included in the directory </span><span lang="EN-GB" style="font-size:10.0pt;font-family:&quot;Courier New&quot;;mso-ansi-language:EN-GB">mytry</span><span lang="EN-GB" style="mso-ansi-language:EN-GB">.<o:p></o:p></span></p>
        !          1870: 
        !          1871: <pre
        !          1872: style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l5 level1 lfo43"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Output on the screen</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> The output screen looks like </span><a
        !          1873: href="imachrun.LOG"><span lang="EN-GB" style="mso-ansi-language:EN-GB">this Log file</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></pre>
        !          1874: 
        !          1875: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          1876: 
        !          1877: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">#title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3<o:p></o:p></span></pre>
        !          1878: 
        !          1879: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></span></pre>
        !          1880: 
        !          1881: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92<o:p></o:p></span></pre>
        !          1882: 
        !          1883: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          1884: 
        !          1885: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:126 line=126<o:p></o:p></span></pre>
        !          1886: 
        !          1887: <pre style="margin-left:18.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Warning, no any valid information for:2307 line=2307<o:p></o:p></span></pre>
1.2       lievre   1888: 
1.5     ! lievre   1889: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Delay (in months) between two waves Min=21 Max=51 Mean=24.495826<o:p></o:p></span></pre>
1.2       lievre   1890: 
1.5     ! lievre   1891: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-GB">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></pre>
        !          1892: 
        !          1893: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14<o:p></o:p></span></pre>
1.2       lievre   1894: 
1.5     ! lievre   1895: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"> prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1<o:p></o:p></span></pre>
1.2       lievre   1896: 
1.5     ! lievre   1897: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 <o:p></o:p></span></pre>
1.2       lievre   1898: 
1.5     ! lievre   1899: <ul type="disc">
        !          1900:     <li class="MsoNormal"
        !          1901:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          1902:      mso-list:l6 level1 lfo46;tab-stops:list 36.0pt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Maximisation
        !          1903:         with the Powell algorithm. 8 directions are given
        !          1904:         corresponding to the 8 parameters. This can be rather
        !          1905:         long to get convergence.<br>
        !          1906: </span><span lang="EN-GB" style="font-size:7.5pt;font-family:&quot;Courier New&quot;;
        !          1907:      mso-ansi-language:EN-GB">        <br>
1.2       lievre   1908:         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
                   1909:         0.000000000000 3<br>
                   1910:         0.000000000000 4 0.000000000000 5 0.000000000000 6
                   1911:         0.000000000000 7 <br>
                   1912:         0.000000000000 8 0.000000000000<br>
                   1913:         1..........2.................3..........4.................5.........<br>
                   1914:         6................7........8...............<br>
                   1915:         Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
                   1916:         <br>
                   1917:         2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
                   1918:         5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
                   1919:         8 0.051272038506<br>
                   1920:         1..............2...........3..............4...........<br>
                   1921:         5..........6................7...........8.........<br>
                   1922:         #Number of iterations = 23, -2 Log likelihood =
                   1923:         6744.954042573691<br>
                   1924:         # Parameters<br>
                   1925:         12 -12.966061 0.135117 <br>
                   1926:         13 -7.401109 0.067831 <br>
                   1927:         21 -0.672648 -0.006627 <br>
1.5     ! lievre   1928:         23 -5.051297 0.051271 </span><span lang="EN-GB" style="mso-ansi-language:
        !          1929:      EN-GB"><o:p></o:p></span></li>
1.2       lievre   1930: </ul>
                   1931: 
1.5     ! lievre   1932: <pre
        !          1933: style="margin-left:36.0pt;text-align:justify;text-indent:-18.0pt;
        !          1934: mso-list:l6 level1 lfo46"><span lang="EN-GB" style="font-family:Symbol;mso-ansi-language:EN-GB">·<span style="font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="EN-GB" style="mso-ansi-language:EN-GB">Calculation of the hessian matrix. Wait...<o:p></o:p></span></pre>
        !          1935: 
        !          1936: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78<o:p></o:p></span></pre>
        !          1937: 
        !          1938: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          1939: 
        !          1940: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Inverting the hessian to get the covariance matrix. </span>Wait...</pre>
        !          1941: 
        !          1942: <pre style="margin-left:18.0pt;text-align:justify">&nbsp;<o:p></o:p></pre>
1.2       lievre   1943: 
1.5     ! lievre   1944: <pre style="margin-left:18.0pt;text-align:justify">#Hessian matrix#</pre>
        !          1945: 
        !          1946: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 <o:p></o:p></span></pre>
        !          1947: 
        !          1948: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 <o:p></o:p></span></pre>
        !          1949: 
        !          1950: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 <o:p></o:p></span></pre>
        !          1951: 
        !          1952: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 <o:p></o:p></span></pre>
        !          1953: 
        !          1954: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 <o:p></o:p></span></pre>
        !          1955: 
        !          1956: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 <o:p></o:p></span></pre>
        !          1957: 
        !          1958: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 <o:p></o:p></span></pre>
        !          1959: 
        !          1960: <pre style="margin-left:18.0pt"><span lang="DE" style="mso-ansi-language:DE">3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 <o:p></o:p></span></pre>
        !          1961: 
        !          1962: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1963: DE"># Scales<o:p></o:p></span></pre>
        !          1964: 
        !          1965: <pre style="margin-left:18.0pt;text-align:
        !          1966: justify"><span lang="DE" style="mso-ansi-language:DE">12 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
        !          1967: 
        !          1968: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1969: DE">13 1.00000e-004 1.00000e-006<o:p></o:p></span></pre>
        !          1970: 
        !          1971: <pre style="margin-left:
        !          1972: 18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE">21 1.00000e-003 1.00000e-005<o:p></o:p></span></pre>
        !          1973: 
        !          1974: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1975: DE">23 1.00000e-004 1.00000e-005<o:p></o:p></span></pre>
        !          1976: 
        !          1977: <pre style="margin-left:
        !          1978: 18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:DE"># Covariance<o:p></o:p></span></pre>
        !          1979: 
        !          1980: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1981: DE"><span style="mso-spacerun: yes">&nbsp; </span>1 5.90661e-001<o:p></o:p></span></pre>
        !          1982: 
        !          1983: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1984: DE"><span style="mso-spacerun: yes">&nbsp; </span>2 -7.26732e-003 8.98810e-005<o:p></o:p></span></pre>
        !          1985: 
        !          1986: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1987: DE"><span style="mso-spacerun: yes">&nbsp; </span>3 8.80177e-002 -1.12706e-003 5.15824e-001<o:p></o:p></span></pre>
        !          1988: 
        !          1989: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1990: DE"><span style="mso-spacerun: yes">&nbsp; </span>4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005<o:p></o:p></span></pre>
        !          1991: 
        !          1992: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1993: DE"><span style="mso-spacerun: yes">&nbsp; </span>5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000<o:p></o:p></span></pre>
        !          1994: 
        !          1995: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1996: DE"><span style="mso-spacerun: yes">&nbsp; </span>6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004<o:p></o:p></span></pre>
        !          1997: 
        !          1998: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          1999: DE"><span style="mso-spacerun: yes">&nbsp; </span>7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000<o:p></o:p></span></pre>
        !          2000: 
        !          2001: <pre style="margin-left:18.0pt;text-align:justify"><span lang="DE" style="mso-ansi-language:
        !          2002: DE"><span style="mso-spacerun: yes">&nbsp; </span>8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004<o:p></o:p></span></pre>
        !          2003: 
        !          2004: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB"># agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).<o:p></o:p></span></pre>
        !          2005: 
        !          2006: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          2007: 
        !          2008: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">&nbsp;<o:p></o:p></span></pre>
        !          2009: 
        !          2010: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></span></pre>
        !          2011: 
        !          2012: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing prevalence limit: result on file 'plrmypar.txt' <o:p></o:p></span></pre>
        !          2013: 
        !          2014: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing pij: result on file 'pijrmypar.txt' <o:p></o:p></span></pre>
        !          2015: 
        !          2016: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Health Expectancies: result on file 'ermypar.txt' <o:p></o:p></span></pre>
        !          2017: 
        !          2018: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of DFLEs: file 'vrmypar.txt' <o:p></o:p></span></pre>
        !          2019: 
        !          2020: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Total LEs with variances: file 'trmypar.txt' <o:p></o:p></span></pre>
        !          2021: 
        !          2022: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' <o:p></o:p></span></pre>
        !          2023: 
        !          2024: <pre style="margin-left:18.0pt;text-align:justify"><span lang="EN-GB" style="mso-ansi-language:EN-GB">End of Imach<o:p></o:p></span></pre>
        !          2025: 
        !          2026: <p
        !          2027: 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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Once
        !          2028: the running is finished, the program requires a caracter:<o:p></o:p></span></p>
        !          2029: 
        !          2030: <table border="1" cellpadding="0"
        !          2031: style="mso-cellspacing:1.5pt;mso-padding-alt:
        !          2032:  0cm 0cm 0cm 0cm">
1.2       lievre   2033:     <tr>
1.5     ! lievre   2034:         <td width="100%"
        !          2035:         style="width:100.0%;padding:.75pt .75pt .75pt .75pt"><strong><span lang="EN-GB" style="mso-ansi-language:EN-GB">Type
        !          2036:         e to edit output files, c to start again, and q for
        !          2037:         exiting:</span><span lang="EN-GB" style="mso-ansi-language:
        !          2038:   EN-GB"><o:p></o:p></span></strong></td>
1.2       lievre   2039:     </tr>
                   2040: </table>
                   2041: 
1.5     ! lievre   2042: <p
        !          2043: style="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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">First
        !          2044: you should enter <strong>e </strong>to edit the master file
        !          2045: mypar.htm. <o:p></o:p></span></p>
        !          2046: 
        !          2047: <ul type="disc">
        !          2048:     <li class="MsoNormal"
        !          2049:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          2050:      mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Outputs
        !          2051:         files</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u> <br>
1.3       lievre   2052:         <br>
1.5     ! lievre   2053:         - Observed prevalence in each state: </span><a
        !          2054:         href="..\mytry\prmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2055:         - Estimated parameters and the covariance matrix: </span><a
        !          2056:         href="..\mytry\rmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">rmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2057:         - Stationary prevalence in each state: </span><a
        !          2058:         href="..\mytry\plrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          2059:      EN-GB">plrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          2060:      EN-GB"></a> <br>
        !          2061:         - Transition probabilities: </span><a
        !          2062:         href="..\mytry\pijrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">pijrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2063:         - Copy of the parameter file: </span><a
        !          2064:         href="..\mytry\ormypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">ormypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2065:         - Life expectancies by age and initial health status: </span><a
        !          2066:         href="..\mytry\ermypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          2067:      EN-GB">ermypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          2068:      EN-GB"></a> <br>
1.2       lievre   2069:         - Variances of life expectancies by age and initial
1.5     ! lievre   2070:         health status: </span><a href="..\mytry\vrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          2071:      EN-GB">vrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          2072:      EN-GB"></a>
        !          2073:         <br>
        !          2074:         - Health expectancies with their variances: </span><a
        !          2075:         href="..\mytry\trmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          2076:      EN-GB">trmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          2077:      EN-GB"></a> <br>
        !          2078:         - Standard deviation of stationary prevalence: </span><a
        !          2079:         href="..\mytry\vplrmypar.txt"><span lang="EN-GB" style="mso-ansi-language:
        !          2080:      EN-GB">vplrmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:
        !          2081:      EN-GB"></a><br>
        !          2082:         - Prevalences forecasting: </span><a href="frmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">frmypar.txt</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>
1.2       lievre   2083:         <br>
1.5     ! lievre   2084:         - Population forecasting (if popforecast=1): </span><a
        !          2085:         href="poprmypar.txt"><span lang="EN-GB" style="mso-ansi-language:EN-GB">poprmypar.txt</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
        !          2086:     <li class="MsoNormal"
        !          2087:     style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
        !          2088:      mso-list:l9 level1 lfo49;tab-stops:list 36.0pt"><u><span lang="EN-GB" style="mso-ansi-language:EN-GB">Graphs</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></u>
1.2       lievre   2089:         <br>
                   2090:         <br>
1.5     ! lievre   2091:         -</span><a href="..\mytry\pemypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
        !          2092:      EN-GB">One-step transition
        !          2093:         probabilities</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
        !          2094:         -</span><a href="..\mytry\pmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
        !          2095:      EN-GB">Convergence to the
        !          2096:         stationary prevalence</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a><br>
        !          2097:         -</span><a href="..\mytry\vmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:
        !          2098:      EN-GB">Observed and stationary
        !          2099:         prevalence in state (1) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2100:         -</span><a href="..\mytry\vmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:
        !          2101:      EN-GB">Observed and stationary
        !          2102:         prevalence in state (2) with the confident interval</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> <br>
        !          2103:         -</span><a href="..\mytry\expmypar11.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
        !          2104:         expectancies by age and initial health state (1)</span><span lang="EN-GB" style="mso-ansi-language:
        !          2105:      EN-GB"></a> <br>
        !          2106:         -</span><a href="..\mytry\expmypar21.gif"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Health life
        !          2107:         expectancies by age and initial health state (2)</span><span lang="EN-GB" style="mso-ansi-language:
        !          2108:      EN-GB"></a> <br>
        !          2109:         -</span><a href="..\mytry\emypar1.gif"><span lang="EN-GB" style="mso-ansi-language:
        !          2110:      EN-GB">Total life expectancy by
        !          2111:         age and health expectancies in states (1) and (2).</span><span style="mso-ansi-language:EN-GB"></a> <span lang="EN-GB"><o:p></o:p></span></span></li>
1.2       lievre   2112: </ul>
                   2113: 
1.5     ! lievre   2114: <p
        !          2115: style="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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">This
        !          2116: software have been partly granted by </span><a
        !          2117: href="http://euroreves.ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Euro-REVES</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a>, a concerted
1.2       lievre   2118: action from the European Union. It will be copyrighted
                   2119: identically to a GNU software product, i.e. program and software
                   2120: can be distributed freely for non commercial use. Sources are not
                   2121: widely distributed today. You can get them by asking us with a
1.5     ! lievre   2122: simple justification (name, email, institute) </span><a
        !          2123: href="mailto:brouard@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:brouard@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> and </span><a
        !          2124: href="mailto:lievre@ined.fr"><span lang="EN-GB" style="mso-ansi-language:EN-GB">mailto:lievre@ined.fr</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"></a> .<o:p></o:p></span></p>
        !          2125: 
        !          2126: <p
        !          2127: style="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"><span lang="EN-GB" style="mso-ansi-language:EN-GB">Latest
        !          2128: version (0.7 of February 2002) can be accessed at </span><a
        !          2129: href="http://euroreves.ined.fr/imach"><span lang="EN-GB" style="mso-ansi-language:EN-GB">http://euroreves.ined.fr/imach</span><span lang="EN-GB" style="mso-ansi-language:EN-GB"><o:p></o:p></span></a></p>
1.2       lievre   2130: </body>
                   2131: </html>

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