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                     14: <h1 align="center"><font color="#00006A">Computing Health
                     15: Expectancies using IMaCh</font></h1>
                     16: 
                     17: <h1 align="center"><font color="#00006A" size="5">(a Maximum
                     18: Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
                     19: 
                     20: <p align="center">&nbsp;</p>
                     21: 
                     22: <p align="center"><a href="http://www.ined.fr/"><img
                     23: src="logo-ined.gif" border="0" width="151" height="76"></a><img
                     24: src="euroreves2.gif" width="151" height="75"></p>
                     25: 
                     26: <h3 align="center"><a href="http://www.ined.fr/"><font
                     27: color="#00006A">INED</font></a><font color="#00006A"> and </font><a
                     28: href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
                     29: 
                     30: <p align="center"><font color="#00006A" size="4"><strong>March
                     31: 2000</strong></font></p>
                     32: 
                     33: <hr size="3" color="#EC5E5E">
                     34: 
                     35: <p align="center"><font color="#00006A"><strong>Authors of the
                     36: program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
                     37: color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
                     38: color="#00006A"><strong>, senior researcher at the </strong></font><a
                     39: href="http://www.ined.fr"><font color="#00006A"><strong>Institut
                     40: National d'Etudes Démographiques</strong></font></a><font
                     41: color="#00006A"><strong> (INED, Paris) in the &quot;Mortality,
                     42: Health and Epidemiology&quot; Research Unit </strong></font></p>
                     43: 
                     44: <p align="center"><font color="#00006A"><strong>and Agnès
                     45: Lièvre<br clear="left">
                     46: </strong></font></p>
                     47: 
                     48: <h4><font color="#00006A">Contribution to the mathematics: C. R.
                     49: Heathcote </font><font color="#00006A" size="2">(Australian
                     50: National University, Canberra).</font></h4>
                     51: 
                     52: <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
                     53: href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
                     54: color="#00006A">) </font></h4>
                     55: 
                     56: <hr>
                     57: 
                     58: <ul>
                     59:     <li><a href="#intro">Introduction</a> </li>
                     60:     <li>The detailed statistical model (<a href="docmath.pdf">PDF
                     61:         version</a>),(<a href="docmath.ps">ps version</a>) </li>
                     62:     <li><a href="#data">On what kind of data can it be used?</a></li>
                     63:     <li><a href="#datafile">The data file</a> </li>
                     64:     <li><a href="#biaspar">The parameter file</a> </li>
                     65:     <li><a href="#running">Running Imach</a> </li>
                     66:     <li><a href="#output">Output files and graphs</a> </li>
                     67:     <li><a href="#example">Exemple</a> </li>
                     68: </ul>
                     69: 
                     70: <hr>
                     71: 
                     72: <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
                     73: 
                     74: <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
                     75: data</b>. Within the family of Health Expectancies (HE),
                     76: Disability-free life expectancy (DFLE) is probably the most
                     77: important index to monitor. In low mortality countries, there is
                     78: a fear that when mortality declines, the increase in DFLE is not
                     79: proportionate to the increase in total Life expectancy. This case
                     80: is called the <em>Expansion of morbidity</em>. Most of the data
                     81: collected today, in particular by the international <a
                     82: href="http://euroreves/reves">REVES</a> network on Health
                     83: expectancy, and most HE indices based on these data, are <em>cross-sectional</em>.
                     84: It means that the information collected comes from a single
                     85: cross-sectional survey: people from various ages (but mostly old
                     86: people) are surveyed on their health status at a single date.
                     87: Proportion of people disabled at each age, can then be measured
                     88: at that date. This age-specific prevalence curve is then used to
                     89: distinguish, within the stationary population (which, by
                     90: definition, is the life table estimated from the vital statistics
                     91: on mortality at the same date), the disable population from the
                     92: disability-free population. Life expectancy (LE) (or total
                     93: population divided by the yearly number of births or deaths of
                     94: this stationary population) is then decomposed into DFLE and DLE.
                     95: This method of computing HE is usually called the Sullivan method
                     96: (from the name of the author who first described it).</p>
                     97: 
                     98: <p>Age-specific proportions of people disable are very difficult
                     99: to forecast because each proportion corresponds to historical
                    100: conditions of the cohort and it is the result of the historical
                    101: flows from entering disability and recovering in the past until
                    102: today. The age-specific intensities (or incidence rates) of
                    103: entering disability or recovering a good health, are reflecting
                    104: actual conditions and therefore can be used at each age to
                    105: forecast the future of this cohort. For example if a country is
                    106: improving its technology of prosthesis, the incidence of
                    107: recovering the ability to walk will be higher at each (old) age,
                    108: but the prevalence of disability will only slightly reflect an
                    109: improve because the prevalence is mostly affected by the history
                    110: of the cohort and not by recent period effects. To measure the
                    111: period improvement we have to simulate the future of a cohort of
                    112: new-borns entering or leaving at each age the disability state or
                    113: dying according to the incidence rates measured today on
                    114: different cohorts. The proportion of people disabled at each age
                    115: in this simulated cohort will be much lower (using the exemple of
                    116: an improvement) that the proportions observed at each age in a
                    117: cross-sectional survey. This new prevalence curve introduced in a
                    118: life table will give a much more actual and realistic HE level
                    119: than the Sullivan method which mostly measured the History of
                    120: health conditions in this country.</p>
                    121: 
                    122: <p>Therefore, the main question is how to measure incidence rates
                    123: from cross-longitudinal surveys? This is the goal of the IMaCH
                    124: program. From your data and using IMaCH you can estimate period
                    125: HE and not only Sullivan's HE. Also the standard errors of the HE
                    126: are computed.</p>
                    127: 
                    128: <p>A cross-longitudinal survey consists in a first survey
                    129: (&quot;cross&quot;) where individuals from different ages are
                    130: interviewed on their health status or degree of disability. At
                    131: least a second wave of interviews (&quot;longitudinal&quot;)
                    132: should measure each new individual health status. Health
                    133: expectancies are computed from the transitions observed between
                    134: waves and are computed for each degree of severity of disability
                    135: (number of life states). More degrees you consider, more time is
                    136: necessary to reach the Maximum Likelihood of the parameters
                    137: involved in the model. Considering only two states of disability
                    138: (disable and healthy) is generally enough but the computer
                    139: program works also with more health statuses.<br>
                    140: <br>
                    141: The simplest model is the multinomial logistic model where <i>pij</i>
                    142: is the probability to be observed in state <i>j</i> at the second
                    143: wave conditional to be observed in state <em>i</em> at the first
                    144: wave. Therefore a simple model is: log<em>(pij/pii)= aij +
                    145: bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
                    146: is a covariate. The advantage that this computer program claims,
                    147: comes from that if the delay between waves is not identical for
                    148: each individual, or if some individual missed an interview, the
                    149: information is not rounded or lost, but taken into account using
                    150: an interpolation or extrapolation. <i>hPijx</i> is the
                    151: probability to be observed in state <i>i</i> at age <i>x+h</i>
                    152: conditional to the observed state <i>i</i> at age <i>x</i>. The
                    153: delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
                    154: of unobserved intermediate states. This elementary transition (by
                    155: month or quarter trimester, semester or year) is modeled as a
                    156: multinomial logistic. The <i>hPx</i> matrix is simply the matrix
                    157: product of <i>nh*stepm</i> elementary matrices and the
                    158: contribution of each individual to the likelihood is simply <i>hPijx</i>.
                    159: <br>
                    160: </p>
                    161: 
                    162: <p>The program presented in this manual is a quite general
                    163: program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
                    164: <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
                    165: analyse transition data from longitudinal surveys. The first step
                    166: is the parameters estimation of a transition probabilities model
                    167: between an initial status and a final status. From there, the
                    168: computer program produces some indicators such as observed and
                    169: stationary prevalence, life expectancies and their variances and
                    170: graphs. Our transition model consists in absorbing and
                    171: non-absorbing states with the possibility of return across the
                    172: non-absorbing states. The main advantage of this package,
                    173: compared to other programs for the analysis of transition data
                    174: (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
                    175: individual information is used even if an interview is missing, a
                    176: status or a date is unknown or when the delay between waves is
                    177: not identical for each individual. The program can be executed
                    178: according to parameters: selection of a sub-sample, number of
                    179: absorbing and non-absorbing states, number of waves taken in
                    180: account (the user inputs the first and the last interview), a
                    181: tolerance level for the maximization function, the periodicity of
                    182: the transitions (we can compute annual, quaterly or monthly
                    183: transitions), covariates in the model. It works on Windows or on
                    184: Unix.<br>
                    185: </p>
                    186: 
                    187: <hr>
                    188: 
                    189: <h2><a name="data"><font color="#00006A">On what kind of data can
                    190: it be used?</font></a></h2>
                    191: 
                    192: <p>The minimum data required for a transition model is the
                    193: recording of a set of individuals interviewed at a first date and
                    194: interviewed again at least one another time. From the
                    195: observations of an individual, we obtain a follow-up over time of
                    196: the occurrence of a specific event. In this documentation, the
                    197: event is related to health status at older ages, but the program
                    198: can be applied on a lot of longitudinal studies in different
                    199: contexts. To build the data file explained into the next section,
                    200: you must have the month and year of each interview and the
                    201: corresponding health status. But in order to get age, date of
                    202: birth (month and year) is required (missing values is allowed for
                    203: month). Date of death (month and year) is an important
                    204: information also required if the individual is dead. Shorter
                    205: steps (i.e. a month) will more closely take into account the
                    206: survival time after the last interview.</p>
                    207: 
                    208: <hr>
                    209: 
                    210: <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
                    211: 
                    212: <p>In this example, 8,000 people have been interviewed in a
                    213: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
                    214: Some people missed 1, 2 or 3 interviews. Health statuses are
                    215: healthy (1) and disable (2). The survey is not a real one. It is
                    216: a simulation of the American Longitudinal Survey on Aging. The
                    217: disability state is defined if the individual missed one of four
                    218: ADL (Activity of daily living, like bathing, eating, walking).
                    219: Therefore, even is the individuals interviewed in the sample are
                    220: virtual, the information brought with this sample is close to the
                    221: situation of the United States. Sex is not recorded is this
                    222: sample.</p>
                    223: 
                    224: <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
                    225: in this first example) is an individual record which fields are: </p>
                    226: 
                    227: <ul>
                    228:     <li><b>Index number</b>: positive number (field 1) </li>
                    229:     <li><b>First covariate</b> positive number (field 2) </li>
                    230:     <li><b>Second covariate</b> positive number (field 3) </li>
                    231:     <li><a name="Weight"><b>Weight</b></a>: positive number
                    232:         (field 4) . In most surveys individuals are weighted
                    233:         according to the stratification of the sample.</li>
                    234:     <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
                    235:         coded as 99/9999 (field 5) </li>
                    236:     <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
                    237:         coded as 99/9999 (field 6) </li>
                    238:     <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
                    239:         dates are coded as 99/9999 (field 7) </li>
                    240:     <li><b>Status at first interview</b>: positive number.
                    241:         Missing values ar coded -1. (field 8) </li>
                    242:     <li><b>Date of second interview</b>: coded as mm/yyyy.
                    243:         Missing dates are coded as 99/9999 (field 9) </li>
                    244:     <li><strong>Status at second interview</strong> positive
                    245:         number. Missing values ar coded -1. (field 10) </li>
                    246:     <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
                    247:         dates are coded as 99/9999 (field 11) </li>
                    248:     <li><strong>Status at third interview</strong> positive
                    249:         number. Missing values ar coded -1. (field 12) </li>
                    250:     <li><b>Date of fourth interview</b>: coded as mm/yyyy.
                    251:         Missing dates are coded as 99/9999 (field 13) </li>
                    252:     <li><strong>Status at fourth interview</strong> positive
                    253:         number. Missing values are coded -1. (field 14) </li>
                    254:     <li>etc</li>
                    255: </ul>
                    256: 
                    257: <p>&nbsp;</p>
                    258: 
                    259: <p>If your longitudinal survey do not include information about
                    260: weights or covariates, you must fill the column with a number
                    261: (e.g. 1) because a missing field is not allowed.</p>
                    262: 
                    263: <hr>
                    264: 
                    265: <h2><font color="#00006A">Your first example parameter file</font><a
                    266: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
                    267: 
                    268: <h2><a name="biaspar"></a>#Imach version 0.63, February 2000,
                    269: INED-EUROREVES </h2>
                    270: 
                    271: <p>This is a comment. Comments start with a '#'.</p>
                    272: 
                    273: <h4><font color="#FF0000">First uncommented line</font></h4>
                    274: 
                    275: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
                    276: 
                    277: <ul>
                    278:     <li><b>title=</b> 1st_example is title of the run. </li>
                    279:     <li><b>datafile=</b>data1.txt is the name of the data set.
                    280:         Our example is a six years follow-up survey. It consists
                    281:         in a baseline followed by 3 reinterviews. </li>
                    282:     <li><b>lastobs=</b> 8600 the program is able to run on a
                    283:         subsample where the last observation number is lastobs.
                    284:         It can be set a bigger number than the real number of
                    285:         observations (e.g. 100000). In this example, maximisation
                    286:         will be done on the 8600 first records. </li>
                    287:     <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
                    288:         than two interviews in the survey, the program can be run
                    289:         on selected transitions periods. firstpass=1 means the
                    290:         first interview included in the calculation is the
                    291:         baseline survey. lastpass=4 means that the information
                    292:         brought by the 4th interview is taken into account.</li>
                    293: </ul>
                    294: 
                    295: <p>&nbsp;</p>
                    296: 
                    297: <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
                    298: line</font></a></h4>
                    299: 
                    300: <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
                    301: 
                    302: <ul>
                    303:     <li><b>ftol=1e-8</b> Convergence tolerance on the function
                    304:         value in the maximisation of the likelihood. Choosing a
                    305:         correct value for ftol is difficult. 1e-8 is a correct
                    306:         value for a 32 bits computer.</li>
                    307:     <li><b>stepm=1</b> Time unit in months for interpolation.
                    308:         Examples:<ul>
                    309:             <li>If stepm=1, the unit is a month </li>
                    310:             <li>If stepm=4, the unit is a trimester</li>
                    311:             <li>If stepm=12, the unit is a year </li>
                    312:             <li>If stepm=24, the unit is two years</li>
                    313:             <li>... </li>
                    314:         </ul>
                    315:     </li>
                    316:     <li><b>ncov=2</b> Number of covariates to be add to the
                    317:         model. The intercept and the age parameter are counting
                    318:         for 2 covariates. For example, if you want to add gender
                    319:         in the covariate vector you must write ncov=3 else
                    320:         ncov=2. </li>
                    321:     <li><b>nlstate=2</b> Number of non-absorbing (live) states.
                    322:         Here we have two alive states: disability-free is coded 1
                    323:         and disability is coded 2. </li>
                    324:     <li><b>ndeath=1</b> Number of absorbing states. The absorbing
                    325:         state death is coded 3. </li>
                    326:     <li><b>maxwav=4</b> Maximum number of waves. The program can
                    327:         not include more than 4 interviews. </li>
                    328:     <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
                    329:         Maximisation Likelihood Estimation. <ul>
                    330:             <li>If mle=1 the program does the maximisation and
                    331:                 the calculation of heath expectancies </li>
                    332:             <li>If mle=0 the program only does the calculation of
                    333:                 the health expectancies. </li>
                    334:         </ul>
                    335:     </li>
                    336:     <li><b>weight=0</b> Possibility to add weights. <ul>
                    337:             <li>If weight=0 no weights are included </li>
                    338:             <li>If weight=1 the maximisation integrates the
                    339:                 weights which are in field <a href="#Weight">4</a></li>
                    340:         </ul>
                    341:     </li>
                    342: </ul>
                    343: 
                    344: <h4><font color="#FF0000">Guess values for optimization</font><font
                    345: color="#00006A"> </font></h4>
                    346: 
                    347: <p>You must write the initial guess values of the parameters for
                    348: optimization. The number of parameters, <em>N</em> depends on the
                    349: number of absorbing states and non-absorbing states and on the
                    350: number of covariates. <br>
                    351: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
                    352: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em>&nbsp;. <br>
                    353: <br>
                    354: Thus in the simple case with 2 covariates (the model is log
                    355: (pij/pii) = aij + bij * age where intercept and age are the two
                    356: covariates), and 2 health degrees (1 for disability-free and 2
                    357: for disability) and 1 absorbing state (3), you must enter 8
                    358: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
                    359: start with zeros as in this example, but if you have a more
                    360: precise set (for example from an earlier run) you can enter it
                    361: and it will speed up them<br>
                    362: Each of the four lines starts with indices &quot;ij&quot;: <br>
                    363: <br>
                    364: <b>ij aij bij</b> </p>
                    365: 
                    366: <blockquote>
                    367:     <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
                    368: 12 -14.155633  0.110794 
                    369: 13  -7.925360  0.032091 
                    370: 21  -1.890135 -0.029473 
                    371: 23  -6.234642  0.022315 </pre>
                    372: </blockquote>
                    373: 
                    374: <p>or, to simplify: </p>
                    375: 
                    376: <blockquote>
                    377:     <pre>12 0.0 0.0
                    378: 13 0.0 0.0
                    379: 21 0.0 0.0
                    380: 23 0.0 0.0</pre>
                    381: </blockquote>
                    382: 
                    383: <h4><font color="#FF0000">Guess values for computing variances</font></h4>
                    384: 
                    385: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
                    386: used as an input to get the vairous output data files (Health
                    387: expectancies, stationary prevalence etc.) and figures without
                    388: rerunning the rather long maximisation phase (mle=0). </p>
                    389: 
                    390: <p>The scales are small values for the evaluation of numerical
                    391: derivatives. These derivatives are used to compute the hessian
                    392: matrix of the parameters, that is the inverse of the covariance
                    393: matrix, and the variances of health expectancies. Each line
                    394: consists in indices &quot;ij&quot; followed by the initial scales
                    395: (zero to simplify) associated with aij and bij. </p>
                    396: 
                    397: <ul>
                    398:     <li>If mle=1 you can enter zeros:</li>
                    399: </ul>
                    400: 
                    401: <blockquote>
                    402:     <pre># Scales (for hessian or gradient estimation)
                    403: 12 0. 0. 
                    404: 13 0. 0. 
                    405: 21 0. 0. 
                    406: 23 0. 0. </pre>
                    407: </blockquote>
                    408: 
                    409: <ul>
                    410:     <li>If mle=0 you must enter a covariance matrix (usually
                    411:         obtained from an earlier run).</li>
                    412: </ul>
                    413: 
                    414: <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
                    415: 
                    416: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
                    417: used as an input to get the vairous output data files (Health
                    418: expectancies, stationary prevalence etc.) and figures without
                    419: rerunning the rather long maximisation phase (mle=0). </p>
                    420: 
                    421: <p>Each line starts with indices &quot;ijk&quot; followed by the
                    422: covariances between aij and bij: </p>
                    423: 
                    424: <pre>
                    425:    121 Var(a12) 
                    426:    122 Cov(b12,a12)  Var(b12) 
                    427:           ...
                    428:    232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) </pre>
                    429: 
                    430: <ul>
                    431:     <li>If mle=1 you can enter zeros. </li>
                    432: </ul>
                    433: 
                    434: <blockquote>
                    435:     <pre># Covariance matrix
                    436: 121 0.
                    437: 122 0. 0.
                    438: 131 0. 0. 0. 
                    439: 132 0. 0. 0. 0. 
                    440: 211 0. 0. 0. 0. 0. 
                    441: 212 0. 0. 0. 0. 0. 0. 
                    442: 231 0. 0. 0. 0. 0. 0. 0. 
                    443: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
                    444: </blockquote>
                    445: 
                    446: <ul>
                    447:     <li>If mle=0 you must enter a covariance matrix (usually
                    448:         obtained from an earlier run).<br>
                    449:         </li>
                    450: </ul>
                    451: 
                    452: <h4><a name="biaspar-l"></a><font color="#FF0000">last
                    453: uncommented line</font></h4>
                    454: 
                    455: <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
                    456: 
                    457: <p>Once we obtained the estimated parameters, the program is able
                    458: to calculated stationary prevalence, transitions probabilities
                    459: and life expectancies at any age. Choice of age ranges is useful
                    460: for extrapolation. In our data file, ages varies from age 70 to
                    461: 102. Setting bage=50 and fage=100, makes the program computing
                    462: life expectancy from age bage to age fage. As we use a model, we
                    463: can compute life expectancy on a wider age range than the age
                    464: range from the data. But the model can be rather wrong on big
                    465: intervals.</p>
                    466: 
                    467: <p>Similarly, it is possible to get extrapolated stationary
                    468: prevalence by age raning from agemin to agemax. </p>
                    469: 
                    470: <ul>
                    471:     <li><b>agemin=</b> Minimum age for calculation of the
                    472:         stationary prevalence </li>
                    473:     <li><b>agemax=</b> Maximum age for calculation of the
                    474:         stationary prevalence </li>
                    475:     <li><b>bage=</b> Minimum age for calculation of the health
                    476:         expectancies </li>
                    477:     <li><b>fage=</b> Maximum ages for calculation of the health
                    478:         expectancies </li>
                    479: </ul>
                    480: 
                    481: <hr>
                    482: 
                    483: <h2><a name="running"></a><font color="#00006A">Running Imach
                    484: with this example</font></h2>
                    485: 
                    486: <p>We assume that you entered your <a href="biaspar.txt">1st_example
                    487: parameter file</a> as explained <a href="#biaspar">above</a>. To
                    488: run the program you should click on the imach.exe icon and enter
                    489: the name of the parameter file which is for example <a
                    490: href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
                    491: (you also can click on the biaspar.txt icon located in <br>
                    492: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
                    493: the mouse on the imach window).<br>
                    494: </p>
                    495: 
                    496: <p>The time to converge depends on the step unit that you used (1
                    497: month is cpu consuming), on the number of cases, and on the
                    498: number of variables.</p>
                    499: 
                    500: <p>The program outputs many files. Most of them are files which
                    501: will be plotted for better understanding.</p>
                    502: 
                    503: <hr>
                    504: 
                    505: <h2><a name="output"><font color="#00006A">Output of the program
                    506: and graphs</font> </a></h2>
                    507: 
                    508: <p>Once the optimization is finished, some graphics can be made
                    509: with a grapher. We use Gnuplot which is an interactive plotting
                    510: program copyrighted but freely distributed. Imach outputs the
                    511: source of a gnuplot file, named 'graph.gp', which can be directly
                    512: input into gnuplot.<br>
                    513: When the running is finished, the user should enter a caracter
                    514: for plotting and output editing. </p>
                    515: 
                    516: <p>These caracters are:</p>
                    517: 
                    518: <ul>
                    519:     <li>'c' to start again the program from the beginning.</li>
                    520:     <li>'g' to made graphics. The output graphs are in GIF format
                    521:         and you have no control over which is produced. If you
                    522:         want to modify the graphics or make another one, you
                    523:         should modify the parameters in the file <b>graph.gp</b>
                    524:         located in imach\bin. A gnuplot reference manual is
                    525:         available <a
                    526:         href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.
                    527:     </li>
                    528:     <li>'e' opens the <strong>index.htm</strong> file to edit the
                    529:         output files and graphs. </li>
                    530:     <li>'q' for exiting.</li>
                    531: </ul>
                    532: 
                    533: <h5><font size="4"><strong>Results files </strong></font><br>
                    534: <br>
                    535: <font color="#EC5E5E" size="3"><strong>- </strong></font><a
                    536: name="Observed prevalence in each state"><font color="#EC5E5E"
                    537: size="3"><strong>Observed prevalence in each state</strong></font></a><font
                    538: color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
                    539: </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
                    540: </h5>
                    541: 
                    542: <p>The first line is the title and displays each field of the
                    543: file. The first column is age. The fields 2 and 6 are the
                    544: proportion of individuals in states 1 and 2 respectively as
                    545: observed during the first exam. Others fields are the numbers of
                    546: people in states 1, 2 or more. The number of columns increases if
                    547: the number of states is higher than 2.<br>
                    548: The header of the file is </p>
                    549: 
                    550: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
                    551: 70 1.00000 631 631 70 0.00000 0 631
                    552: 71 0.99681 625 627 71 0.00319 2 627 
                    553: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
                    554: 
                    555: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
                    556:     70 0.95721 604 631 70 0.04279 27 631</pre>
                    557: 
                    558: <p>It means that at age 70, the prevalence in state 1 is 1.000
                    559: and in state 2 is 0.00 . At age 71 the number of individuals in
                    560: state 1 is 625 and in state 2 is 2, hence the total number of
                    561: people aged 71 is 625+2=627. <br>
                    562: </p>
                    563: 
                    564: <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
                    565: covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
                    566: 
                    567: <p>This file contains all the maximisation results: </p>
                    568: 
                    569: <pre> Number of iterations=47
                    570:  -2 log likelihood=46553.005854373667  
                    571:  Estimated parameters: a12 = -12.691743 b12 = 0.095819 
                    572:                        a13 = -7.815392   b13 = 0.031851 
                    573:                        a21 = -1.809895 b21 = -0.030470 
                    574:                        a23 = -7.838248  b23 = 0.039490  
                    575:  Covariance matrix: Var(a12) = 1.03611e-001
                    576:                     Var(b12) = 1.51173e-005
                    577:                     Var(a13) = 1.08952e-001
                    578:                     Var(b13) = 1.68520e-005  
                    579:                     Var(a21) = 4.82801e-001
                    580:                     Var(b21) = 6.86392e-005
                    581:                     Var(a23) = 2.27587e-001
                    582:                     Var(b23) = 3.04465e-005 
                    583:  </pre>
                    584: 
                    585: <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
                    586: </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
                    587: 
                    588: <p>Here are the transitions probabilities Pij(x, x+nh) where nh
                    589: is a multiple of 2 years. The first column is the starting age x
                    590: (from age 50 to 100), the second is age (x+nh) and the others are
                    591: the transition probabilities p11, p12, p13, p21, p22, p23. For
                    592: example, line 5 of the file is: </p>
                    593: 
                    594: <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>
                    595: 
                    596: <p>and this means: </p>
                    597: 
                    598: <pre>p11(100,106)=0.03286
                    599: p12(100,106)=0.23512
                    600: p13(100,106)=0.73202
                    601: p21(100,106)=0.02330
                    602: p22(100,106)=0.19210 
                    603: p22(100,106)=0.78460 </pre>
                    604: 
                    605: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
                    606: name="Stationary prevalence in each state"><font color="#EC5E5E"
                    607: size="3"><b>Stationary prevalence in each state</b></font></a><b>:
                    608: </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
                    609: 
                    610: <pre>#Age 1-1 2-2 
                    611: 70 0.92274 0.07726 
                    612: 71 0.91420 0.08580 
                    613: 72 0.90481 0.09519 
                    614: 73 0.89453 0.10547</pre>
                    615: 
                    616: <p>At age 70 the stationary prevalence is 0.92274 in state 1 and
                    617: 0.07726 in state 2. This stationary prevalence differs from
                    618: observed prevalence. Here is the point. The observed prevalence
                    619: at age 70 results from the incidence of disability, incidence of
                    620: recovery and mortality which occurred in the past of the cohort.
                    621: Stationary prevalence results from a simulation with actual
                    622: incidences and mortality (estimated from this cross-longitudinal
                    623: survey). It is the best predictive value of the prevalence in the
                    624: future if &quot;nothing changes in the future&quot;. This is
                    625: exactly what demographers do with a Life table. Life expectancy
                    626: is the expected mean time to survive if observed mortality rates
                    627: (incidence of mortality) &quot;remains constant&quot; in the
                    628: future. </p>
                    629: 
                    630: <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
                    631: stationary prevalence</b></font><b>: </b><a
                    632: href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
                    633: 
                    634: <p>The stationary prevalence has to be compared with the observed
                    635: prevalence by age. But both are statistical estimates and
                    636: subjected to stochastic errors due to the size of the sample, the
                    637: design of the survey, and, for the stationary prevalence to the
                    638: model used and fitted. It is possible to compute the standard
                    639: deviation of the stationary prevalence at each age.</p>
                    640: 
                    641: <h6><font color="#EC5E5E" size="3">Observed and stationary
                    642: prevalence in state (2=disable) with the confident interval</font>:<b>
                    643: vbiaspar2.gif</b></h6>
                    644: 
                    645: <p><br>
                    646: This graph exhibits the stationary prevalence in state (2) with
                    647: the confidence interval in red. The green curve is the observed
                    648: prevalence (or proportion of individuals in state (2)). Without
                    649: discussing the results (it is not the purpose here), we observe
                    650: that the green curve is rather below the stationary prevalence.
                    651: It suggests an increase of the disability prevalence in the
                    652: future.</p>
                    653: 
                    654: <p><img src="vbiaspar2.gif" width="400" height="300"></p>
                    655: 
                    656: <h6><font color="#EC5E5E" size="3"><b>Convergence to the
                    657: stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>
                    658: <img src="pbiaspar1.gif" width="400" height="300"> </h6>
                    659: 
                    660: <p>This graph plots the conditional transition probabilities from
                    661: an initial state (1=healthy in red at the bottom, or 2=disable in
                    662: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
                    663: age <em>x+h. </em>Conditional means at the condition to be alive
                    664: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
                    665: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
                    666: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
                    667: prevalence of disability</em>. In order to get the stationary
                    668: prevalence at age 70 we should start the process at an earlier
                    669: age, i.e.50. If the disability state is defined by severe
                    670: disability criteria with only a few chance to recover, then the
                    671: incidence of recovery is low and the time to convergence is
                    672: probably longer. But we don't have experience yet.</p>
                    673: 
                    674: <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
                    675: and initial health status</b></font><b>: </b><a
                    676: href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
                    677: 
                    678: <pre># Health expectancies 
                    679: # Age 1-1 1-2 2-1 2-2 
                    680: 70 10.7297 2.7809 6.3440 5.9813 
                    681: 71 10.3078 2.8233 5.9295 5.9959 
                    682: 72 9.8927 2.8643 5.5305 6.0033 
                    683: 73 9.4848 2.9036 5.1474 6.0035 </pre>
                    684: 
                    685: <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:
                    686: e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>
                    687: 
                    688: <pre><img src="exbiaspar1.gif" width="400" height="300"><img
                    689: src="exbiaspar2.gif" width="400" height="300"></pre>
                    690: 
                    691: <p>For example, life expectancy of a healthy individual at age 70
                    692: is 10.73 in the healthy state and 2.78 in the disability state
                    693: (=13.51 years). If he was disable at age 70, his life expectancy
                    694: will be shorter, 6.34 in the healthy state and 5.98 in the
                    695: disability state (=12.32 years). The total life expectancy is a
                    696: weighted mean of both, 13.51 and 12.32; weight is the proportion
                    697: of people disabled at age 70. In order to get a pure period index
                    698: (i.e. based only on incidences) we use the <a
                    699: href="#Stationary prevalence in each state">computed or
                    700: stationary prevalence</a> at age 70 (i.e. computed from
                    701: incidences at earlier ages) instead of the <a
                    702: href="#Observed prevalence in each state">observed prevalence</a>
                    703: (for example at first exam) (<a href="#Health expectancies">see
                    704: below</a>).</p>
                    705: 
                    706: <h5><font color="#EC5E5E" size="3"><b>- Variances of life
                    707: expectancies by age and initial health status</b></font><b>: </b><a
                    708: href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
                    709: 
                    710: <p>For example, the covariances of life expectancies Cov(ei,ej)
                    711: at age 50 are (line 3) </p>
                    712: 
                    713: <pre>   Cov(e1,e1)=0.4667  Cov(e1,e2)=0.0605=Cov(e2,e1)  Cov(e2,e2)=0.0183</pre>
                    714: 
                    715: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
                    716: name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
                    717: expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
                    718: with standard errors in parentheses</b></font><b>: </b><a
                    719: href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
                    720: 
                    721: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
                    722: 
                    723: <pre>70 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09) </pre>
                    724: 
                    725: <p>Thus, at age 70 the total life expectancy, e..=13.42 years is
                    726: the weighted mean of e1.=13.51 and e2.=12.32 by the stationary
                    727: prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in
                    728: state 2, respectively (the sum is equal to one). e.1=10.39 is the
                    729: Disability-free life expectancy at age 70 (it is again a weighted
                    730: mean of e11 and e21). e.2=3.03 is also the life expectancy at age
                    731: 70 to be spent in the disability state.</p>
                    732: 
                    733: <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by
                    734: age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
                    735: ebiaspar.gif</b></h6>
                    736: 
                    737: <p>This figure represents the health expectancies and the total
                    738: life expectancy with the confident interval in dashed curve. </p>
                    739: 
                    740: <pre>        <img src="ebiaspar.gif" width="400" height="300"></pre>
                    741: 
                    742: <p>Standard deviations (obtained from the information matrix of
                    743: the model) of these quantities are very useful.
                    744: Cross-longitudinal surveys are costly and do not involve huge
                    745: samples, generally a few thousands; therefore it is very
                    746: important to have an idea of the standard deviation of our
                    747: estimates. It has been a big challenge to compute the Health
                    748: Expectancy standard deviations. Don't be confuse: life expectancy
                    749: is, as any expected value, the mean of a distribution; but here
                    750: we are not computing the standard deviation of the distribution,
                    751: but the standard deviation of the estimate of the mean.</p>
                    752: 
                    753: <p>Our health expectancies estimates vary according to the sample
                    754: size (and the standard deviations give confidence intervals of
                    755: the estimate) but also according to the model fitted. Let us
                    756: explain it in more details.</p>
                    757: 
                    758: <p>Choosing a model means ar least two kind of choices. First we
                    759: have to decide the number of disability states. Second we have to
                    760: design, within the logit model family, the model: variables,
                    761: covariables, confonding factors etc. to be included.</p>
                    762: 
                    763: <p>More disability states we have, better is our demographical
                    764: approach of the disability process, but smaller are the number of
                    765: transitions between each state and higher is the noise in the
                    766: measurement. We do not have enough experiments of the various
                    767: models to summarize the advantages and disadvantages, but it is
                    768: important to say that even if we had huge and unbiased samples,
                    769: the total life expectancy computed from a cross-longitudinal
                    770: survey, varies with the number of states. If we define only two
                    771: states, alive or dead, we find the usual life expectancy where it
                    772: is assumed that at each age, people are at the same risk to die.
                    773: If we are differentiating the alive state into healthy and
                    774: disable, and as the mortality from the disability state is higher
                    775: than the mortality from the healthy state, we are introducing
                    776: heterogeneity in the risk of dying. The total mortality at each
                    777: age is the weighted mean of the mortality in each state by the
                    778: prevalence in each state. Therefore if the proportion of people
                    779: at each age and in each state is different from the stationary
                    780: equilibrium, there is no reason to find the same total mortality
                    781: at a particular age. Life expectancy, even if it is a very useful
                    782: tool, has a very strong hypothesis of homogeneity of the
                    783: population. Our main purpose is not to measure differential
                    784: mortality but to measure the expected time in a healthy or
                    785: disability state in order to maximise the former and minimize the
                    786: latter. But the differential in mortality complexifies the
                    787: measurement.</p>
                    788: 
                    789: <p>Incidences of disability or recovery are not affected by the
                    790: number of states if these states are independant. But incidences
                    791: estimates are dependant on the specification of the model. More
                    792: covariates we added in the logit model better is the model, but
                    793: some covariates are not well measured, some are confounding
                    794: factors like in any statistical model. The procedure to &quot;fit
                    795: the best model' is similar to logistic regression which itself is
                    796: similar to regression analysis. We haven't yet been sofar because
                    797: we also have a severe limitation which is the speed of the
                    798: convergence. On a Pentium III, 500 MHz, even the simplest model,
                    799: estimated by month on 8,000 people may take 4 hours to converge.
                    800: Also, the program is not yet a statistical package, which permits
                    801: a simple writing of the variables and the model to take into
                    802: account in the maximisation. The actual program allows only to
                    803: add simple variables without covariations, like age+sex but
                    804: without age+sex+ age*sex . This can be done from the source code
                    805: (you have to change three lines in the source code) but will
                    806: never be general enough. But what is to remember, is that
                    807: incidences or probability of change from one state to another is
                    808: affected by the variables specified into the model.</p>
                    809: 
                    810: <p>Also, the age range of the people interviewed has a link with
                    811: the age range of the life expectancy which can be estimated by
                    812: extrapolation. If your sample ranges from age 70 to 95, you can
                    813: clearly estimate a life expectancy at age 70 and trust your
                    814: confidence interval which is mostly based on your sample size,
                    815: but if you want to estimate the life expectancy at age 50, you
                    816: should rely in your model, but fitting a logistic model on a age
                    817: range of 70-95 and estimating probabilties of transition out of
                    818: this age range, say at age 50 is very dangerous. At least you
                    819: should remember that the confidence interval given by the
                    820: standard deviation of the health expectancies, are under the
                    821: strong assumption that your model is the 'true model', which is
                    822: probably not the case.</p>
                    823: 
                    824: <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
                    825: file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
                    826: 
                    827: <p>This copy of the parameter file can be useful to re-run the
                    828: program while saving the old output files. </p>
                    829: 
                    830: <hr>
                    831: 
                    832: <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
                    833: 
                    834: <p>Since you know how to run the program, it is time to test it
                    835: on your own computer. Try for example on a parameter file named <a
                    836: href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a
                    837: copy of <font size="2" face="Courier New">mypar.txt</font>
                    838: included in the subdirectory of imach, <font size="2"
                    839: face="Courier New">mytry</font>. Edit it to change the name of
                    840: the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>
                    841: if you don't want to copy it on the same directory. The file <font
                    842: face="Courier New">mydata.txt</font> is a smaller file of 3,000
                    843: people but still with 4 waves. </p>
                    844: 
                    845: <p>Click on the imach.exe icon to open a window. Answer to the
                    846: question:'<strong>Enter the parameter file name:'</strong></p>
                    847: 
                    848: <table border="1">
                    849:     <tr>
                    850:         <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter
                    851:         the parameter file name: ..\mytry\imachpar.txt</strong></p>
                    852:         </td>
                    853:     </tr>
                    854: </table>
                    855: 
                    856: <p>Most of the data files or image files generated, will use the
                    857: 'imachpar' string into their name. The running time is about 2-3
                    858: minutes on a Pentium III. If the execution worked correctly, the
                    859: outputs files are created in the current directory, and should be
                    860: the same as the mypar files initially included in the directory <font
                    861: size="2" face="Courier New">mytry</font>.</p>
                    862: 
                    863: <ul>
                    864:     <li><pre><u>Output on the screen</u> The output screen looks like <a
                    865: href="imachrun.LOG">this Log file</a>
                    866: #
                    867: 
                    868: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
                    869: ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
                    870:     </li>
                    871:     <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
                    872: 
                    873: Warning, no any valid information for:126 line=126
                    874: Warning, no any valid information for:2307 line=2307
                    875: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
                    876: <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
                    877: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
                    878:  prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
                    879: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
                    880:     </li>
                    881: </ul>
                    882: 
                    883: <p>&nbsp;</p>
                    884: 
                    885: <ul>
                    886:     <li>Maximisation with the Powell algorithm. 8 directions are
                    887:         given corresponding to the 8 parameters. this can be
                    888:         rather long to get convergence.<br>
                    889:         <font size="1" face="Courier New"><br>
                    890:         Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
                    891:         0.000000000000 3<br>
                    892:         0.000000000000 4 0.000000000000 5 0.000000000000 6
                    893:         0.000000000000 7 <br>
                    894:         0.000000000000 8 0.000000000000<br>
                    895:         1..........2.................3..........4.................5.........<br>
                    896:         6................7........8...............<br>
                    897:         Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
                    898:         <br>
                    899:         2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
                    900:         5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
                    901:         8 0.051272038506<br>
                    902:         1..............2...........3..............4...........<br>
                    903:         5..........6................7...........8.........<br>
                    904:         #Number of iterations = 23, -2 Log likelihood =
                    905:         6744.954042573691<br>
                    906:         # Parameters<br>
                    907:         12 -12.966061 0.135117 <br>
                    908:         13 -7.401109 0.067831 <br>
                    909:         21 -0.672648 -0.006627 <br>
                    910:         23 -5.051297 0.051271 </font><br>
                    911:         </li>
                    912:     <li><pre><font size="2">Calculation of the hessian matrix. Wait...
                    913: 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
                    914: 
                    915: Inverting the hessian to get the covariance matrix. Wait...
                    916: 
                    917: #Hessian matrix#
                    918: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 
                    919: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 
                    920: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 
                    921: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 
                    922: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 
                    923: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 
                    924: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 
                    925: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 
                    926: # Scales
                    927: 12 1.00000e-004 1.00000e-006
                    928: 13 1.00000e-004 1.00000e-006
                    929: 21 1.00000e-003 1.00000e-005
                    930: 23 1.00000e-004 1.00000e-005
                    931: # Covariance
                    932:   1 5.90661e-001
                    933:   2 -7.26732e-003 8.98810e-005
                    934:   3 8.80177e-002 -1.12706e-003 5.15824e-001
                    935:   4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
                    936:   5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
                    937:   6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
                    938:   7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
                    939:   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
                    940: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
                    941: 
                    942: 
                    943: agemin=70 agemax=100 bage=50 fage=100
                    944: Computing prevalence limit: result on file 'plrmypar.txt' 
                    945: Computing pij: result on file 'pijrmypar.txt' 
                    946: Computing Health Expectancies: result on file 'ermypar.txt' 
                    947: Computing Variance-covariance of DFLEs: file 'vrmypar.txt' 
                    948: Computing Total LEs with variances: file 'trmypar.txt' 
                    949: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' 
                    950: End of Imach
                    951: </font></pre>
                    952:     </li>
                    953: </ul>
                    954: 
                    955: <p><font size="3">Once the running is finished, the program
                    956: requires a caracter:</font></p>
                    957: 
                    958: <table border="1">
                    959:     <tr>
                    960:         <td width="100%"><strong>Type g for plotting (available
                    961:         if mle=1), e to edit output files, c to start again,</strong><p><strong>and
                    962:         q for exiting:</strong></p>
                    963:         </td>
                    964:     </tr>
                    965: </table>
                    966: 
                    967: <p><font size="3">First you should enter <strong>g</strong> to
                    968: make the figures and then you can edit all the results by typing <strong>e</strong>.
                    969: </font></p>
                    970: 
                    971: <ul>
                    972:     <li><u>Outputs files</u> <br>
                    973:         - index.htm, this file is the master file on which you
                    974:         should click first.<br>
                    975:         - Observed prevalence in each state: <a
                    976:         href="..\mytry\prmypar.txt">mypar.txt</a> <br>
                    977:         - Estimated parameters and the covariance matrix: <a
                    978:         href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
                    979:         - Stationary prevalence in each state: <a
                    980:         href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
                    981:         - Transition probabilities: <a
                    982:         href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
                    983:         - Copy of the parameter file: <a
                    984:         href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
                    985:         - Life expectancies by age and initial health status: <a
                    986:         href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
                    987:         - Variances of life expectancies by age and initial
                    988:         health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
                    989:         <br>
                    990:         - Health expectancies with their variances: <a
                    991:         href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
                    992:         - Standard deviation of stationary prevalence: <a
                    993:         href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>
                    994:         <br>
                    995:         </li>
                    996:     <li><u>Graphs</u> <br>
                    997:         <br>
                    998:         -<a href="..\mytry\vmypar1.gif">Observed and stationary
                    999:         prevalence in state (1) with the confident interval</a> <br>
                   1000:         -<a href="..\mytry\vmypar2.gif">Observed and stationary
                   1001:         prevalence in state (2) with the confident interval</a> <br>
                   1002:         -<a href="..\mytry\exmypar1.gif">Health life expectancies
                   1003:         by age and initial health state (1)</a> <br>
                   1004:         -<a href="..\mytry\exmypar2.gif">Health life expectancies
                   1005:         by age and initial health state (2)</a> <br>
                   1006:         -<a href="..\mytry\emypar.gif">Total life expectancy by
                   1007:         age and health expectancies in states (1) and (2).</a> </li>
                   1008: </ul>
                   1009: 
                   1010: <p>This software have been partly granted by <a
                   1011: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
                   1012: action from the European Union. It will be copyrighted
                   1013: identically to a GNU software product, i.e. program and software
                   1014: can be distributed freely for non commercial use. Sources are not
                   1015: widely distributed today. You can get them by asking us with a
                   1016: simple justification (name, email, institute) <a
                   1017: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
                   1018: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
                   1019: 
                   1020: <p>Latest version (0.63 of 16 march 2000) can be accessed at <a
                   1021: href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
                   1022: </p>
                   1023: </body>
                   1024: </html>

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