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! 7: <title>Computing Health Expectancies using IMaCh</title>
! 8: <!-- Changed by: Agnes Lievre, 12-Oct-2000 -->
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! 15: <h1 align="center"><font color="#00006A">Computing Health
! 16: Expectancies using IMaCh</font></h1>
! 17:
! 18: <h1 align="center"><font color="#00006A" size="5">(a Maximum
! 19: Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
! 20:
! 21: <p align="center"> </p>
! 22:
! 23: <p align="center"><a href="http://www.ined.fr/"><img
! 24: src="logo-ined.gif" border="0" width="151" height="76"></a><img
! 25: src="euroreves2.gif" width="151" height="75"></p>
! 26:
! 27: <h3 align="center"><a href="http://www.ined.fr/"><font
! 28: color="#00006A">INED</font></a><font color="#00006A"> and </font><a
! 29: href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
! 30:
! 31: <p align="center"><font color="#00006A" size="4"><strong>March
! 32: 2000</strong></font></p>
! 33:
! 34: <hr size="3" color="#EC5E5E">
! 35:
! 36: <p align="center"><font color="#00006A"><strong>Authors of the
! 37: program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
! 38: color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
! 39: color="#00006A"><strong>, senior researcher at the </strong></font><a
! 40: href="http://www.ined.fr"><font color="#00006A"><strong>Institut
! 41: National d'Etudes Démographiques</strong></font></a><font
! 42: color="#00006A"><strong> (INED, Paris) in the "Mortality,
! 43: Health and Epidemiology" Research Unit </strong></font></p>
! 44:
! 45: <p align="center"><font color="#00006A"><strong>and Agnès
! 46: Lièvre<br clear="left">
! 47: </strong></font></p>
! 48:
! 49: <h4><font color="#00006A">Contribution to the mathematics: C. R.
! 50: Heathcote </font><font color="#00006A" size="2">(Australian
! 51: National University, Canberra).</font></h4>
! 52:
! 53: <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
! 54: href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
! 55: color="#00006A">) </font></h4>
! 56:
! 57: <hr>
! 58:
! 59: <ul>
! 60: <li><a href="#intro">Introduction</a> </li>
! 61: <li>The detailed statistical model (<a href="docmath.pdf">PDF
! 62: version</a>),(<a href="docmath.ps">ps version</a>) </li>
! 63: <li><a href="#data">On what kind of data can it be used?</a></li>
! 64: <li><a href="#datafile">The data file</a> </li>
! 65: <li><a href="#biaspar">The parameter file</a> </li>
! 66: <li><a href="#running">Running Imach</a> </li>
! 67: <li><a href="#output">Output files and graphs</a> </li>
! 68: <li><a href="#example">Exemple</a> </li>
! 69: </ul>
! 70:
! 71: <hr>
! 72:
! 73: <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
! 74:
! 75: <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
! 76: data</b> using the methodology pioneered by Laditka and Wolf (1).
! 77: Within the family of Health Expectancies (HE), Disability-free
! 78: life expectancy (DFLE) is probably the most important index to
! 79: monitor. In low mortality countries, there is a fear that when
! 80: mortality declines, the increase in DFLE is not proportionate to
! 81: the increase in total Life expectancy. This case is called the <em>Expansion
! 82: of morbidity</em>. Most of the data collected today, in
! 83: particular by the international <a href="http://euroreves/reves">REVES</a>
! 84: network on Health expectancy, and most HE indices based on these
! 85: data, are <em>cross-sectional</em>. It means that the information
! 86: collected comes from a single cross-sectional survey: people from
! 87: various ages (but mostly old people) are surveyed on their health
! 88: status at a single date. Proportion of people disabled at each
! 89: age, can then be measured at that date. This age-specific
! 90: prevalence curve is then used to distinguish, within the
! 91: stationary population (which, by definition, is the life table
! 92: estimated from the vital statistics on mortality at the same
! 93: date), the disable population from the disability-free
! 94: population. Life expectancy (LE) (or total population divided by
! 95: the yearly number of births or deaths of this stationary
! 96: population) is then decomposed into DFLE and DLE. This method of
! 97: computing HE is usually called the Sullivan method (from the name
! 98: of the author who first described it).</p>
! 99:
! 100: <p>Age-specific proportions of people disable are very difficult
! 101: to forecast because each proportion corresponds to historical
! 102: conditions of the cohort and it is the result of the historical
! 103: flows from entering disability and recovering in the past until
! 104: today. The age-specific intensities (or incidence rates) of
! 105: entering disability or recovering a good health, are reflecting
! 106: actual conditions and therefore can be used at each age to
! 107: forecast the future of this cohort. For example if a country is
! 108: improving its technology of prosthesis, the incidence of
! 109: recovering the ability to walk will be higher at each (old) age,
! 110: but the prevalence of disability will only slightly reflect an
! 111: improve because the prevalence is mostly affected by the history
! 112: of the cohort and not by recent period effects. To measure the
! 113: period improvement we have to simulate the future of a cohort of
! 114: new-borns entering or leaving at each age the disability state or
! 115: dying according to the incidence rates measured today on
! 116: different cohorts. The proportion of people disabled at each age
! 117: in this simulated cohort will be much lower (using the exemple of
! 118: an improvement) that the proportions observed at each age in a
! 119: cross-sectional survey. This new prevalence curve introduced in a
! 120: life table will give a much more actual and realistic HE level
! 121: than the Sullivan method which mostly measured the History of
! 122: health conditions in this country.</p>
! 123:
! 124: <p>Therefore, the main question is how to measure incidence rates
! 125: from cross-longitudinal surveys? This is the goal of the IMaCH
! 126: program. From your data and using IMaCH you can estimate period
! 127: HE and not only Sullivan's HE. Also the standard errors of the HE
! 128: are computed.</p>
! 129:
! 130: <p>A cross-longitudinal survey consists in a first survey
! 131: ("cross") where individuals from different ages are
! 132: interviewed on their health status or degree of disability. At
! 133: least a second wave of interviews ("longitudinal")
! 134: should measure each new individual health status. Health
! 135: expectancies are computed from the transitions observed between
! 136: waves and are computed for each degree of severity of disability
! 137: (number of life states). More degrees you consider, more time is
! 138: necessary to reach the Maximum Likelihood of the parameters
! 139: involved in the model. Considering only two states of disability
! 140: (disable and healthy) is generally enough but the computer
! 141: program works also with more health statuses.<br>
! 142: <br>
! 143: The simplest model is the multinomial logistic model where <i>pij</i>
! 144: is the probability to be observed in state <i>j</i> at the second
! 145: wave conditional to be observed in state <em>i</em> at the first
! 146: wave. Therefore a simple model is: log<em>(pij/pii)= aij +
! 147: bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
! 148: is a covariate. The advantage that this computer program claims,
! 149: comes from that if the delay between waves is not identical for
! 150: each individual, or if some individual missed an interview, the
! 151: information is not rounded or lost, but taken into account using
! 152: an interpolation or extrapolation. <i>hPijx</i> is the
! 153: probability to be observed in state <i>i</i> at age <i>x+h</i>
! 154: conditional to the observed state <i>i</i> at age <i>x</i>. The
! 155: delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
! 156: of unobserved intermediate states. This elementary transition (by
! 157: month or quarter trimester, semester or year) is modeled as a
! 158: multinomial logistic. The <i>hPx</i> matrix is simply the matrix
! 159: product of <i>nh*stepm</i> elementary matrices and the
! 160: contribution of each individual to the likelihood is simply <i>hPijx</i>.
! 161: <br>
! 162: </p>
! 163:
! 164: <p>The program presented in this manual is a quite general
! 165: program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
! 166: <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
! 167: analyse transition data from longitudinal surveys. The first step
! 168: is the parameters estimation of a transition probabilities model
! 169: between an initial status and a final status. From there, the
! 170: computer program produces some indicators such as observed and
! 171: stationary prevalence, life expectancies and their variances and
! 172: graphs. Our transition model consists in absorbing and
! 173: non-absorbing states with the possibility of return across the
! 174: non-absorbing states. The main advantage of this package,
! 175: compared to other programs for the analysis of transition data
! 176: (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
! 177: individual information is used even if an interview is missing, a
! 178: status or a date is unknown or when the delay between waves is
! 179: not identical for each individual. The program can be executed
! 180: according to parameters: selection of a sub-sample, number of
! 181: absorbing and non-absorbing states, number of waves taken in
! 182: account (the user inputs the first and the last interview), a
! 183: tolerance level for the maximization function, the periodicity of
! 184: the transitions (we can compute annual, quaterly or monthly
! 185: transitions), covariates in the model. It works on Windows or on
! 186: Unix.<br>
! 187: </p>
! 188:
! 189: <hr>
! 190:
! 191: <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
! 192: Methods for Analyzing Active Life Expectancy". <i>Journal of
! 193: Aging and Health</i>. Vol 10, No. 2. </p>
! 194:
! 195: <hr>
! 196:
! 197: <h2><a name="data"><font color="#00006A">On what kind of data can
! 198: it be used?</font></a></h2>
! 199:
! 200: <p>The minimum data required for a transition model is the
! 201: recording of a set of individuals interviewed at a first date and
! 202: interviewed again at least one another time. From the
! 203: observations of an individual, we obtain a follow-up over time of
! 204: the occurrence of a specific event. In this documentation, the
! 205: event is related to health status at older ages, but the program
! 206: can be applied on a lot of longitudinal studies in different
! 207: contexts. To build the data file explained into the next section,
! 208: you must have the month and year of each interview and the
! 209: corresponding health status. But in order to get age, date of
! 210: birth (month and year) is required (missing values is allowed for
! 211: month). Date of death (month and year) is an important
! 212: information also required if the individual is dead. Shorter
! 213: steps (i.e. a month) will more closely take into account the
! 214: survival time after the last interview.</p>
! 215:
! 216: <hr>
! 217:
! 218: <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
! 219:
! 220: <p>In this example, 8,000 people have been interviewed in a
! 221: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
! 222: Some people missed 1, 2 or 3 interviews. Health statuses are
! 223: healthy (1) and disable (2). The survey is not a real one. It is
! 224: a simulation of the American Longitudinal Survey on Aging. The
! 225: disability state is defined if the individual missed one of four
! 226: ADL (Activity of daily living, like bathing, eating, walking).
! 227: Therefore, even is the individuals interviewed in the sample are
! 228: virtual, the information brought with this sample is close to the
! 229: situation of the United States. Sex is not recorded is this
! 230: sample.</p>
! 231:
! 232: <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
! 233: in this first example) is an individual record which fields are: </p>
! 234:
! 235: <ul>
! 236: <li><b>Index number</b>: positive number (field 1) </li>
! 237: <li><b>First covariate</b> positive number (field 2) </li>
! 238: <li><b>Second covariate</b> positive number (field 3) </li>
! 239: <li><a name="Weight"><b>Weight</b></a>: positive number
! 240: (field 4) . In most surveys individuals are weighted
! 241: according to the stratification of the sample.</li>
! 242: <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
! 243: coded as 99/9999 (field 5) </li>
! 244: <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
! 245: coded as 99/9999 (field 6) </li>
! 246: <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
! 247: dates are coded as 99/9999 (field 7) </li>
! 248: <li><b>Status at first interview</b>: positive number.
! 249: Missing values ar coded -1. (field 8) </li>
! 250: <li><b>Date of second interview</b>: coded as mm/yyyy.
! 251: Missing dates are coded as 99/9999 (field 9) </li>
! 252: <li><strong>Status at second interview</strong> positive
! 253: number. Missing values ar coded -1. (field 10) </li>
! 254: <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
! 255: dates are coded as 99/9999 (field 11) </li>
! 256: <li><strong>Status at third interview</strong> positive
! 257: number. Missing values ar coded -1. (field 12) </li>
! 258: <li><b>Date of fourth interview</b>: coded as mm/yyyy.
! 259: Missing dates are coded as 99/9999 (field 13) </li>
! 260: <li><strong>Status at fourth interview</strong> positive
! 261: number. Missing values are coded -1. (field 14) </li>
! 262: <li>etc</li>
! 263: </ul>
! 264:
! 265: <p> </p>
! 266:
! 267: <p>If your longitudinal survey do not include information about
! 268: weights or covariates, you must fill the column with a number
! 269: (e.g. 1) because a missing field is not allowed.</p>
! 270:
! 271: <hr>
! 272:
! 273: <h2><font color="#00006A">Your first example parameter file</font><a
! 274: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
! 275:
! 276: <h2><a name="biaspar"></a>#Imach version 0.63, February 2000,
! 277: INED-EUROREVES </h2>
! 278:
! 279: <p>This is a comment. Comments start with a '#'.</p>
! 280:
! 281: <h4><font color="#FF0000">First uncommented line</font></h4>
! 282:
! 283: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
! 284:
! 285: <ul>
! 286: <li><b>title=</b> 1st_example is title of the run. </li>
! 287: <li><b>datafile=</b>data1.txt is the name of the data set.
! 288: Our example is a six years follow-up survey. It consists
! 289: in a baseline followed by 3 reinterviews. </li>
! 290: <li><b>lastobs=</b> 8600 the program is able to run on a
! 291: subsample where the last observation number is lastobs.
! 292: It can be set a bigger number than the real number of
! 293: observations (e.g. 100000). In this example, maximisation
! 294: will be done on the 8600 first records. </li>
! 295: <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
! 296: than two interviews in the survey, the program can be run
! 297: on selected transitions periods. firstpass=1 means the
! 298: first interview included in the calculation is the
! 299: baseline survey. lastpass=4 means that the information
! 300: brought by the 4th interview is taken into account.</li>
! 301: </ul>
! 302:
! 303: <p> </p>
! 304:
! 305: <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
! 306: line</font></a></h4>
! 307:
! 308: <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
! 309:
! 310: <ul>
! 311: <li><b>ftol=1e-8</b> Convergence tolerance on the function
! 312: value in the maximisation of the likelihood. Choosing a
! 313: correct value for ftol is difficult. 1e-8 is a correct
! 314: value for a 32 bits computer.</li>
! 315: <li><b>stepm=1</b> Time unit in months for interpolation.
! 316: Examples:<ul>
! 317: <li>If stepm=1, the unit is a month </li>
! 318: <li>If stepm=4, the unit is a trimester</li>
! 319: <li>If stepm=12, the unit is a year </li>
! 320: <li>If stepm=24, the unit is two years</li>
! 321: <li>... </li>
! 322: </ul>
! 323: </li>
! 324: <li><b>ncov=2</b> Number of covariates in the datafile. The
! 325: intercept and the age parameter are counting for 2
! 326: covariates.</li>
! 327: <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
! 328: Here we have two alive states: disability-free is coded 1
! 329: and disability is coded 2. </li>
! 330: <li><b>ndeath=1</b> Number of absorbing states. The absorbing
! 331: state death is coded 3. </li>
! 332: <li><b>maxwav=4</b> Number of waves in the datafile.</li>
! 333: <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
! 334: Maximisation Likelihood Estimation. <ul>
! 335: <li>If mle=1 the program does the maximisation and
! 336: the calculation of health expectancies </li>
! 337: <li>If mle=0 the program only does the calculation of
! 338: the health expectancies. </li>
! 339: </ul>
! 340: </li>
! 341: <li><b>weight=0</b> Possibility to add weights. <ul>
! 342: <li>If weight=0 no weights are included </li>
! 343: <li>If weight=1 the maximisation integrates the
! 344: weights which are in field <a href="#Weight">4</a></li>
! 345: </ul>
! 346: </li>
! 347: </ul>
! 348:
! 349: <h4><font color="#FF0000">Covariates</font></h4>
! 350:
! 351: <p>Intercept and age are systematically included in the model.
! 352: Additional covariates can be included with the command </p>
! 353:
! 354: <pre>model=<em>list of covariates</em></pre>
! 355:
! 356: <ul>
! 357: <li>if<strong> model=. </strong>then no covariates are
! 358: included</li>
! 359: <li>if <strong>model=V1</strong> the model includes the first
! 360: covariate (field 2)</li>
! 361: <li>if <strong>model=V2 </strong>the model includes the
! 362: second covariate (field 3)</li>
! 363: <li>if <strong>model=V1+V2 </strong>the model includes the
! 364: first and the second covariate (fields 2 and 3)</li>
! 365: <li>if <strong>model=V1*V2 </strong>the model includes the
! 366: product of the first and the second covariate (fields 2
! 367: and 3)</li>
! 368: </ul>
! 369:
! 370: <h4><font color="#FF0000">Guess values for optimization</font><font
! 371: color="#00006A"> </font></h4>
! 372:
! 373: <p>You must write the initial guess values of the parameters for
! 374: optimization. The number of parameters, <em>N</em> depends on the
! 375: number of absorbing states and non-absorbing states and on the
! 376: number of covariates. <br>
! 377: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
! 378: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br>
! 379: <br>
! 380: Thus in the simple case with 2 covariates (the model is log
! 381: (pij/pii) = aij + bij * age where intercept and age are the two
! 382: covariates), and 2 health degrees (1 for disability-free and 2
! 383: for disability) and 1 absorbing state (3), you must enter 8
! 384: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
! 385: start with zeros as in this example, but if you have a more
! 386: precise set (for example from an earlier run) you can enter it
! 387: and it will speed up them<br>
! 388: Each of the four lines starts with indices "ij": <br>
! 389: <br>
! 390: <b>ij aij bij</b> </p>
! 391:
! 392: <blockquote>
! 393: <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
! 394: 12 -14.155633 0.110794
! 395: 13 -7.925360 0.032091
! 396: 21 -1.890135 -0.029473
! 397: 23 -6.234642 0.022315 </pre>
! 398: </blockquote>
! 399:
! 400: <p>or, to simplify: </p>
! 401:
! 402: <blockquote>
! 403: <pre>12 0.0 0.0
! 404: 13 0.0 0.0
! 405: 21 0.0 0.0
! 406: 23 0.0 0.0</pre>
! 407: </blockquote>
! 408:
! 409: <h4><font color="#FF0000">Guess values for computing variances</font></h4>
! 410:
! 411: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
! 412: used as an input to get the vairous output data files (Health
! 413: expectancies, stationary prevalence etc.) and figures without
! 414: rerunning the rather long maximisation phase (mle=0). </p>
! 415:
! 416: <p>The scales are small values for the evaluation of numerical
! 417: derivatives. These derivatives are used to compute the hessian
! 418: matrix of the parameters, that is the inverse of the covariance
! 419: matrix, and the variances of health expectancies. Each line
! 420: consists in indices "ij" followed by the initial scales
! 421: (zero to simplify) associated with aij and bij. </p>
! 422:
! 423: <ul>
! 424: <li>If mle=1 you can enter zeros:</li>
! 425: </ul>
! 426:
! 427: <blockquote>
! 428: <pre># Scales (for hessian or gradient estimation)
! 429: 12 0. 0.
! 430: 13 0. 0.
! 431: 21 0. 0.
! 432: 23 0. 0. </pre>
! 433: </blockquote>
! 434:
! 435: <ul>
! 436: <li>If mle=0 you must enter a covariance matrix (usually
! 437: obtained from an earlier run).</li>
! 438: </ul>
! 439:
! 440: <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
! 441:
! 442: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
! 443: used as an input to get the vairous output data files (Health
! 444: expectancies, stationary prevalence etc.) and figures without
! 445: rerunning the rather long maximisation phase (mle=0). </p>
! 446:
! 447: <p>Each line starts with indices "ijk" followed by the
! 448: covariances between aij and bij: </p>
! 449:
! 450: <pre>
! 451: 121 Var(a12)
! 452: 122 Cov(b12,a12) Var(b12)
! 453: ...
! 454: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
! 455:
! 456: <ul>
! 457: <li>If mle=1 you can enter zeros. </li>
! 458: </ul>
! 459:
! 460: <blockquote>
! 461: <pre># Covariance matrix
! 462: 121 0.
! 463: 122 0. 0.
! 464: 131 0. 0. 0.
! 465: 132 0. 0. 0. 0.
! 466: 211 0. 0. 0. 0. 0.
! 467: 212 0. 0. 0. 0. 0. 0.
! 468: 231 0. 0. 0. 0. 0. 0. 0.
! 469: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
! 470: </blockquote>
! 471:
! 472: <ul>
! 473: <li>If mle=0 you must enter a covariance matrix (usually
! 474: obtained from an earlier run).<br>
! 475: </li>
! 476: </ul>
! 477:
! 478: <h4><a name="biaspar-l"></a><font color="#FF0000">last
! 479: uncommented line</font></h4>
! 480:
! 481: <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
! 482:
! 483: <p>Once we obtained the estimated parameters, the program is able
! 484: to calculated stationary prevalence, transitions probabilities
! 485: and life expectancies at any age. Choice of age ranges is useful
! 486: for extrapolation. In our data file, ages varies from age 70 to
! 487: 102. Setting bage=50 and fage=100, makes the program computing
! 488: life expectancy from age bage to age fage. As we use a model, we
! 489: can compute life expectancy on a wider age range than the age
! 490: range from the data. But the model can be rather wrong on big
! 491: intervals.</p>
! 492:
! 493: <p>Similarly, it is possible to get extrapolated stationary
! 494: prevalence by age raning from agemin to agemax. </p>
! 495:
! 496: <ul>
! 497: <li><b>agemin=</b> Minimum age for calculation of the
! 498: stationary prevalence </li>
! 499: <li><b>agemax=</b> Maximum age for calculation of the
! 500: stationary prevalence </li>
! 501: <li><b>bage=</b> Minimum age for calculation of the health
! 502: expectancies </li>
! 503: <li><b>fage=</b> Maximum ages for calculation of the health
! 504: expectancies </li>
! 505: </ul>
! 506:
! 507: <hr>
! 508:
! 509: <h2><a name="running"></a><font color="#00006A">Running Imach
! 510: with this example</font></h2>
! 511:
! 512: <p>We assume that you entered your <a href="biaspar.txt">1st_example
! 513: parameter file</a> as explained <a href="#biaspar">above</a>. To
! 514: run the program you should click on the imach.exe icon and enter
! 515: the name of the parameter file which is for example <a
! 516: href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
! 517: (you also can click on the biaspar.txt icon located in <br>
! 518: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
! 519: the mouse on the imach window).<br>
! 520: </p>
! 521:
! 522: <p>The time to converge depends on the step unit that you used (1
! 523: month is cpu consuming), on the number of cases, and on the
! 524: number of variables.</p>
! 525:
! 526: <p>The program outputs many files. Most of them are files which
! 527: will be plotted for better understanding.</p>
! 528:
! 529: <hr>
! 530:
! 531: <h2><a name="output"><font color="#00006A">Output of the program
! 532: and graphs</font> </a></h2>
! 533:
! 534: <p>Once the optimization is finished, some graphics can be made
! 535: with a grapher. We use Gnuplot which is an interactive plotting
! 536: program copyrighted but freely distributed. Imach outputs the
! 537: source of a gnuplot file, named 'graph.gp', which can be directly
! 538: input into gnuplot.<br>
! 539: When the running is finished, the user should enter a caracter
! 540: for plotting and output editing. </p>
! 541:
! 542: <p>These caracters are:</p>
! 543:
! 544: <ul>
! 545: <li>'c' to start again the program from the beginning.</li>
! 546: <li>'g' to made graphics. The output graphs are in GIF format
! 547: and you have no control over which is produced. If you
! 548: want to modify the graphics or make another one, you
! 549: should modify the parameters in the file <b>graph.gp</b>
! 550: located in imach\bin. A gnuplot reference manual is
! 551: available <a
! 552: href="http://www.cs.dartmouth.edu/gnuplot/gnuplot.html">here</a>.
! 553: </li>
! 554: <li>'e' opens the <strong>index.htm</strong> file to edit the
! 555: output files and graphs. </li>
! 556: <li>'q' for exiting.</li>
! 557: </ul>
! 558:
! 559: <h5><font size="4"><strong>Results files </strong></font><br>
! 560: <br>
! 561: <font color="#EC5E5E" size="3"><strong>- </strong></font><a
! 562: name="Observed prevalence in each state"><font color="#EC5E5E"
! 563: size="3"><strong>Observed prevalence in each state</strong></font></a><font
! 564: color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
! 565: </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
! 566: </h5>
! 567:
! 568: <p>The first line is the title and displays each field of the
! 569: file. The first column is age. The fields 2 and 6 are the
! 570: proportion of individuals in states 1 and 2 respectively as
! 571: observed during the first exam. Others fields are the numbers of
! 572: people in states 1, 2 or more. The number of columns increases if
! 573: the number of states is higher than 2.<br>
! 574: The header of the file is </p>
! 575:
! 576: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
! 577: 70 1.00000 631 631 70 0.00000 0 631
! 578: 71 0.99681 625 627 71 0.00319 2 627
! 579: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
! 580:
! 581: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
! 582: 70 0.95721 604 631 70 0.04279 27 631</pre>
! 583:
! 584: <p>It means that at age 70, the prevalence in state 1 is 1.000
! 585: and in state 2 is 0.00 . At age 71 the number of individuals in
! 586: state 1 is 625 and in state 2 is 2, hence the total number of
! 587: people aged 71 is 625+2=627. <br>
! 588: </p>
! 589:
! 590: <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
! 591: covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
! 592:
! 593: <p>This file contains all the maximisation results: </p>
! 594:
! 595: <pre> Number of iterations=47
! 596: -2 log likelihood=46553.005854373667
! 597: Estimated parameters: a12 = -12.691743 b12 = 0.095819
! 598: a13 = -7.815392 b13 = 0.031851
! 599: a21 = -1.809895 b21 = -0.030470
! 600: a23 = -7.838248 b23 = 0.039490
! 601: Covariance matrix: Var(a12) = 1.03611e-001
! 602: Var(b12) = 1.51173e-005
! 603: Var(a13) = 1.08952e-001
! 604: Var(b13) = 1.68520e-005
! 605: Var(a21) = 4.82801e-001
! 606: Var(b21) = 6.86392e-005
! 607: Var(a23) = 2.27587e-001
! 608: Var(b23) = 3.04465e-005
! 609: </pre>
! 610:
! 611: <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
! 612: </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
! 613:
! 614: <p>Here are the transitions probabilities Pij(x, x+nh) where nh
! 615: is a multiple of 2 years. The first column is the starting age x
! 616: (from age 50 to 100), the second is age (x+nh) and the others are
! 617: the transition probabilities p11, p12, p13, p21, p22, p23. For
! 618: example, line 5 of the file is: </p>
! 619:
! 620: <pre> 100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460 </pre>
! 621:
! 622: <p>and this means: </p>
! 623:
! 624: <pre>p11(100,106)=0.03286
! 625: p12(100,106)=0.23512
! 626: p13(100,106)=0.73202
! 627: p21(100,106)=0.02330
! 628: p22(100,106)=0.19210
! 629: p22(100,106)=0.78460 </pre>
! 630:
! 631: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 632: name="Stationary prevalence in each state"><font color="#EC5E5E"
! 633: size="3"><b>Stationary prevalence in each state</b></font></a><b>:
! 634: </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
! 635:
! 636: <pre>#Age 1-1 2-2
! 637: 70 0.92274 0.07726
! 638: 71 0.91420 0.08580
! 639: 72 0.90481 0.09519
! 640: 73 0.89453 0.10547</pre>
! 641:
! 642: <p>At age 70 the stationary prevalence is 0.92274 in state 1 and
! 643: 0.07726 in state 2. This stationary prevalence differs from
! 644: observed prevalence. Here is the point. The observed prevalence
! 645: at age 70 results from the incidence of disability, incidence of
! 646: recovery and mortality which occurred in the past of the cohort.
! 647: Stationary prevalence results from a simulation with actual
! 648: incidences and mortality (estimated from this cross-longitudinal
! 649: survey). It is the best predictive value of the prevalence in the
! 650: future if "nothing changes in the future". This is
! 651: exactly what demographers do with a Life table. Life expectancy
! 652: is the expected mean time to survive if observed mortality rates
! 653: (incidence of mortality) "remains constant" in the
! 654: future. </p>
! 655:
! 656: <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
! 657: stationary prevalence</b></font><b>: </b><a
! 658: href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
! 659:
! 660: <p>The stationary prevalence has to be compared with the observed
! 661: prevalence by age. But both are statistical estimates and
! 662: subjected to stochastic errors due to the size of the sample, the
! 663: design of the survey, and, for the stationary prevalence to the
! 664: model used and fitted. It is possible to compute the standard
! 665: deviation of the stationary prevalence at each age.</p>
! 666:
! 667: <h6><font color="#EC5E5E" size="3">Observed and stationary
! 668: prevalence in state (2=disable) with the confident interval</font>:<b>
! 669: vbiaspar2.gif</b></h6>
! 670:
! 671: <p><br>
! 672: This graph exhibits the stationary prevalence in state (2) with
! 673: the confidence interval in red. The green curve is the observed
! 674: prevalence (or proportion of individuals in state (2)). Without
! 675: discussing the results (it is not the purpose here), we observe
! 676: that the green curve is rather below the stationary prevalence.
! 677: It suggests an increase of the disability prevalence in the
! 678: future.</p>
! 679:
! 680: <p><img src="vbiaspar2.gif" width="400" height="300"></p>
! 681:
! 682: <h6><font color="#EC5E5E" size="3"><b>Convergence to the
! 683: stationary prevalence of disability</b></font><b>: pbiaspar1.gif</b><br>
! 684: <img src="pbiaspar1.gif" width="400" height="300"> </h6>
! 685:
! 686: <p>This graph plots the conditional transition probabilities from
! 687: an initial state (1=healthy in red at the bottom, or 2=disable in
! 688: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
! 689: age <em>x+h. </em>Conditional means at the condition to be alive
! 690: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
! 691: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
! 692: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
! 693: prevalence of disability</em>. In order to get the stationary
! 694: prevalence at age 70 we should start the process at an earlier
! 695: age, i.e.50. If the disability state is defined by severe
! 696: disability criteria with only a few chance to recover, then the
! 697: incidence of recovery is low and the time to convergence is
! 698: probably longer. But we don't have experience yet.</p>
! 699:
! 700: <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
! 701: and initial health status</b></font><b>: </b><a
! 702: href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
! 703:
! 704: <pre># Health expectancies
! 705: # Age 1-1 1-2 2-1 2-2
! 706: 70 10.7297 2.7809 6.3440 5.9813
! 707: 71 10.3078 2.8233 5.9295 5.9959
! 708: 72 9.8927 2.8643 5.5305 6.0033
! 709: 73 9.4848 2.9036 5.1474 6.0035 </pre>
! 710:
! 711: <pre>For example 70 10.7297 2.7809 6.3440 5.9813 means:
! 712: e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813</pre>
! 713:
! 714: <pre><img src="exbiaspar1.gif" width="400" height="300"><img
! 715: src="exbiaspar2.gif" width="400" height="300"></pre>
! 716:
! 717: <p>For example, life expectancy of a healthy individual at age 70
! 718: is 10.73 in the healthy state and 2.78 in the disability state
! 719: (=13.51 years). If he was disable at age 70, his life expectancy
! 720: will be shorter, 6.34 in the healthy state and 5.98 in the
! 721: disability state (=12.32 years). The total life expectancy is a
! 722: weighted mean of both, 13.51 and 12.32; weight is the proportion
! 723: of people disabled at age 70. In order to get a pure period index
! 724: (i.e. based only on incidences) we use the <a
! 725: href="#Stationary prevalence in each state">computed or
! 726: stationary prevalence</a> at age 70 (i.e. computed from
! 727: incidences at earlier ages) instead of the <a
! 728: href="#Observed prevalence in each state">observed prevalence</a>
! 729: (for example at first exam) (<a href="#Health expectancies">see
! 730: below</a>).</p>
! 731:
! 732: <h5><font color="#EC5E5E" size="3"><b>- Variances of life
! 733: expectancies by age and initial health status</b></font><b>: </b><a
! 734: href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
! 735:
! 736: <p>For example, the covariances of life expectancies Cov(ei,ej)
! 737: at age 50 are (line 3) </p>
! 738:
! 739: <pre> Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183</pre>
! 740:
! 741: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 742: name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
! 743: expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
! 744: with standard errors in parentheses</b></font><b>: </b><a
! 745: href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
! 746:
! 747: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
! 748:
! 749: <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>
! 750:
! 751: <p>Thus, at age 70 the total life expectancy, e..=13.42 years is
! 752: the weighted mean of e1.=13.51 and e2.=12.32 by the stationary
! 753: prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in
! 754: state 2, respectively (the sum is equal to one). e.1=10.39 is the
! 755: Disability-free life expectancy at age 70 (it is again a weighted
! 756: mean of e11 and e21). e.2=3.03 is also the life expectancy at age
! 757: 70 to be spent in the disability state.</p>
! 758:
! 759: <h6><font color="#EC5E5E" size="3"><b>Total life expectancy by
! 760: age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
! 761: ebiaspar.gif</b></h6>
! 762:
! 763: <p>This figure represents the health expectancies and the total
! 764: life expectancy with the confident interval in dashed curve. </p>
! 765:
! 766: <pre> <img src="ebiaspar.gif" width="400" height="300"></pre>
! 767:
! 768: <p>Standard deviations (obtained from the information matrix of
! 769: the model) of these quantities are very useful.
! 770: Cross-longitudinal surveys are costly and do not involve huge
! 771: samples, generally a few thousands; therefore it is very
! 772: important to have an idea of the standard deviation of our
! 773: estimates. It has been a big challenge to compute the Health
! 774: Expectancy standard deviations. Don't be confuse: life expectancy
! 775: is, as any expected value, the mean of a distribution; but here
! 776: we are not computing the standard deviation of the distribution,
! 777: but the standard deviation of the estimate of the mean.</p>
! 778:
! 779: <p>Our health expectancies estimates vary according to the sample
! 780: size (and the standard deviations give confidence intervals of
! 781: the estimate) but also according to the model fitted. Let us
! 782: explain it in more details.</p>
! 783:
! 784: <p>Choosing a model means ar least two kind of choices. First we
! 785: have to decide the number of disability states. Second we have to
! 786: design, within the logit model family, the model: variables,
! 787: covariables, confonding factors etc. to be included.</p>
! 788:
! 789: <p>More disability states we have, better is our demographical
! 790: approach of the disability process, but smaller are the number of
! 791: transitions between each state and higher is the noise in the
! 792: measurement. We do not have enough experiments of the various
! 793: models to summarize the advantages and disadvantages, but it is
! 794: important to say that even if we had huge and unbiased samples,
! 795: the total life expectancy computed from a cross-longitudinal
! 796: survey, varies with the number of states. If we define only two
! 797: states, alive or dead, we find the usual life expectancy where it
! 798: is assumed that at each age, people are at the same risk to die.
! 799: If we are differentiating the alive state into healthy and
! 800: disable, and as the mortality from the disability state is higher
! 801: than the mortality from the healthy state, we are introducing
! 802: heterogeneity in the risk of dying. The total mortality at each
! 803: age is the weighted mean of the mortality in each state by the
! 804: prevalence in each state. Therefore if the proportion of people
! 805: at each age and in each state is different from the stationary
! 806: equilibrium, there is no reason to find the same total mortality
! 807: at a particular age. Life expectancy, even if it is a very useful
! 808: tool, has a very strong hypothesis of homogeneity of the
! 809: population. Our main purpose is not to measure differential
! 810: mortality but to measure the expected time in a healthy or
! 811: disability state in order to maximise the former and minimize the
! 812: latter. But the differential in mortality complexifies the
! 813: measurement.</p>
! 814:
! 815: <p>Incidences of disability or recovery are not affected by the
! 816: number of states if these states are independant. But incidences
! 817: estimates are dependant on the specification of the model. More
! 818: covariates we added in the logit model better is the model, but
! 819: some covariates are not well measured, some are confounding
! 820: factors like in any statistical model. The procedure to "fit
! 821: the best model' is similar to logistic regression which itself is
! 822: similar to regression analysis. We haven't yet been sofar because
! 823: we also have a severe limitation which is the speed of the
! 824: convergence. On a Pentium III, 500 MHz, even the simplest model,
! 825: estimated by month on 8,000 people may take 4 hours to converge.
! 826: Also, the program is not yet a statistical package, which permits
! 827: a simple writing of the variables and the model to take into
! 828: account in the maximisation. The actual program allows only to
! 829: add simple variables without covariations, like age+sex but
! 830: without age+sex+ age*sex . This can be done from the source code
! 831: (you have to change three lines in the source code) but will
! 832: never be general enough. But what is to remember, is that
! 833: incidences or probability of change from one state to another is
! 834: affected by the variables specified into the model.</p>
! 835:
! 836: <p>Also, the age range of the people interviewed has a link with
! 837: the age range of the life expectancy which can be estimated by
! 838: extrapolation. If your sample ranges from age 70 to 95, you can
! 839: clearly estimate a life expectancy at age 70 and trust your
! 840: confidence interval which is mostly based on your sample size,
! 841: but if you want to estimate the life expectancy at age 50, you
! 842: should rely in your model, but fitting a logistic model on a age
! 843: range of 70-95 and estimating probabilties of transition out of
! 844: this age range, say at age 50 is very dangerous. At least you
! 845: should remember that the confidence interval given by the
! 846: standard deviation of the health expectancies, are under the
! 847: strong assumption that your model is the 'true model', which is
! 848: probably not the case.</p>
! 849:
! 850: <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
! 851: file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
! 852:
! 853: <p>This copy of the parameter file can be useful to re-run the
! 854: program while saving the old output files. </p>
! 855:
! 856: <hr>
! 857:
! 858: <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
! 859:
! 860: <p>Since you know how to run the program, it is time to test it
! 861: on your own computer. Try for example on a parameter file named <a
! 862: href="file://../mytry/imachpar.txt">imachpar.txt</a> which is a
! 863: copy of <font size="2" face="Courier New">mypar.txt</font>
! 864: included in the subdirectory of imach, <font size="2"
! 865: face="Courier New">mytry</font>. Edit it to change the name of
! 866: the data file to <font size="2" face="Courier New">..\data\mydata.txt</font>
! 867: if you don't want to copy it on the same directory. The file <font
! 868: face="Courier New">mydata.txt</font> is a smaller file of 3,000
! 869: people but still with 4 waves. </p>
! 870:
! 871: <p>Click on the imach.exe icon to open a window. Answer to the
! 872: question:'<strong>Enter the parameter file name:'</strong></p>
! 873:
! 874: <table border="1">
! 875: <tr>
! 876: <td width="100%"><strong>IMACH, Version 0.63</strong><p><strong>Enter
! 877: the parameter file name: ..\mytry\imachpar.txt</strong></p>
! 878: </td>
! 879: </tr>
! 880: </table>
! 881:
! 882: <p>Most of the data files or image files generated, will use the
! 883: 'imachpar' string into their name. The running time is about 2-3
! 884: minutes on a Pentium III. If the execution worked correctly, the
! 885: outputs files are created in the current directory, and should be
! 886: the same as the mypar files initially included in the directory <font
! 887: size="2" face="Courier New">mytry</font>.</p>
! 888:
! 889: <ul>
! 890: <li><pre><u>Output on the screen</u> The output screen looks like <a
! 891: href="imachrun.LOG">this Log file</a>
! 892: #
! 893:
! 894: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
! 895: ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
! 896: </li>
! 897: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
! 898:
! 899: Warning, no any valid information for:126 line=126
! 900: Warning, no any valid information for:2307 line=2307
! 901: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
! 902: <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
! 903: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
! 904: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
! 905: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
! 906: </li>
! 907: </ul>
! 908:
! 909: <p> </p>
! 910:
! 911: <ul>
! 912: <li>Maximisation with the Powell algorithm. 8 directions are
! 913: given corresponding to the 8 parameters. this can be
! 914: rather long to get convergence.<br>
! 915: <font size="1" face="Courier New"><br>
! 916: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
! 917: 0.000000000000 3<br>
! 918: 0.000000000000 4 0.000000000000 5 0.000000000000 6
! 919: 0.000000000000 7 <br>
! 920: 0.000000000000 8 0.000000000000<br>
! 921: 1..........2.................3..........4.................5.........<br>
! 922: 6................7........8...............<br>
! 923: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
! 924: <br>
! 925: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
! 926: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
! 927: 8 0.051272038506<br>
! 928: 1..............2...........3..............4...........<br>
! 929: 5..........6................7...........8.........<br>
! 930: #Number of iterations = 23, -2 Log likelihood =
! 931: 6744.954042573691<br>
! 932: # Parameters<br>
! 933: 12 -12.966061 0.135117 <br>
! 934: 13 -7.401109 0.067831 <br>
! 935: 21 -0.672648 -0.006627 <br>
! 936: 23 -5.051297 0.051271 </font><br>
! 937: </li>
! 938: <li><pre><font size="2">Calculation of the hessian matrix. Wait...
! 939: 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
! 940:
! 941: Inverting the hessian to get the covariance matrix. Wait...
! 942:
! 943: #Hessian matrix#
! 944: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
! 945: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
! 946: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
! 947: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
! 948: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
! 949: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
! 950: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
! 951: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
! 952: # Scales
! 953: 12 1.00000e-004 1.00000e-006
! 954: 13 1.00000e-004 1.00000e-006
! 955: 21 1.00000e-003 1.00000e-005
! 956: 23 1.00000e-004 1.00000e-005
! 957: # Covariance
! 958: 1 5.90661e-001
! 959: 2 -7.26732e-003 8.98810e-005
! 960: 3 8.80177e-002 -1.12706e-003 5.15824e-001
! 961: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
! 962: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
! 963: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
! 964: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
! 965: 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
! 966: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
! 967:
! 968:
! 969: agemin=70 agemax=100 bage=50 fage=100
! 970: Computing prevalence limit: result on file 'plrmypar.txt'
! 971: Computing pij: result on file 'pijrmypar.txt'
! 972: Computing Health Expectancies: result on file 'ermypar.txt'
! 973: Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
! 974: Computing Total LEs with variances: file 'trmypar.txt'
! 975: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
! 976: End of Imach
! 977: </font></pre>
! 978: </li>
! 979: </ul>
! 980:
! 981: <p><font size="3">Once the running is finished, the program
! 982: requires a caracter:</font></p>
! 983:
! 984: <table border="1">
! 985: <tr>
! 986: <td width="100%"><strong>Type g for plotting (available
! 987: if mle=1), e to edit output files, c to start again,</strong><p><strong>and
! 988: q for exiting:</strong></p>
! 989: </td>
! 990: </tr>
! 991: </table>
! 992:
! 993: <p><font size="3">First you should enter <strong>g</strong> to
! 994: make the figures and then you can edit all the results by typing <strong>e</strong>.
! 995: </font></p>
! 996:
! 997: <ul>
! 998: <li><u>Outputs files</u> <br>
! 999: - index.htm, this file is the master file on which you
! 1000: should click first.<br>
! 1001: - Observed prevalence in each state: <a
! 1002: href="..\mytry\prmypar.txt">mypar.txt</a> <br>
! 1003: - Estimated parameters and the covariance matrix: <a
! 1004: href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
! 1005: - Stationary prevalence in each state: <a
! 1006: href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
! 1007: - Transition probabilities: <a
! 1008: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
! 1009: - Copy of the parameter file: <a
! 1010: href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
! 1011: - Life expectancies by age and initial health status: <a
! 1012: href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
! 1013: - Variances of life expectancies by age and initial
! 1014: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
! 1015: <br>
! 1016: - Health expectancies with their variances: <a
! 1017: href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
! 1018: - Standard deviation of stationary prevalence: <a
! 1019: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> <br>
! 1020: <br>
! 1021: </li>
! 1022: <li><u>Graphs</u> <br>
! 1023: <br>
! 1024: -<a href="..\mytry\vmypar1.gif">Observed and stationary
! 1025: prevalence in state (1) with the confident interval</a> <br>
! 1026: -<a href="..\mytry\vmypar2.gif">Observed and stationary
! 1027: prevalence in state (2) with the confident interval</a> <br>
! 1028: -<a href="..\mytry\exmypar1.gif">Health life expectancies
! 1029: by age and initial health state (1)</a> <br>
! 1030: -<a href="..\mytry\exmypar2.gif">Health life expectancies
! 1031: by age and initial health state (2)</a> <br>
! 1032: -<a href="..\mytry\emypar.gif">Total life expectancy by
! 1033: age and health expectancies in states (1) and (2).</a> </li>
! 1034: </ul>
! 1035:
! 1036: <p>This software have been partly granted by <a
! 1037: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
! 1038: action from the European Union. It will be copyrighted
! 1039: identically to a GNU software product, i.e. program and software
! 1040: can be distributed freely for non commercial use. Sources are not
! 1041: widely distributed today. You can get them by asking us with a
! 1042: simple justification (name, email, institute) <a
! 1043: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
! 1044: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
! 1045:
! 1046: <p>Latest version (0.63 of 16 march 2000) can be accessed at <a
! 1047: href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
! 1048: </p>
! 1049: </body>
! 1050: </html>
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