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! 8: <title>Computing Health Expectancies using IMaCh</title>
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! 16: <h1 align="center"><font color="#00006A">Computing Health
! 17: Expectancies using IMaCh</font></h1>
! 18:
! 19: <h1 align="center"><font color="#00006A" size="5">(a Maximum
! 20: Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
! 21:
! 22: <p align="center"> </p>
! 23:
! 24: <p align="center"><a href="http://www.ined.fr/"><img
! 25: src="logo-ined.gif" border="0" width="151" height="76"></a><img
! 26: src="euroreves2.gif" width="151" height="75"></p>
! 27:
! 28: <h3 align="center"><a href="http://www.ined.fr/"><font
! 29: color="#00006A">INED</font></a><font color="#00006A"> and </font><a
! 30: href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
! 31:
! 32: <p align="center"><font color="#00006A" size="4"><strong>Version
! 33: 0.71a, March 2002</strong></font></p>
! 34:
! 35: <hr size="3" color="#EC5E5E">
! 36:
! 37: <p align="center"><font color="#00006A"><strong>Authors of the
! 38: program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
! 39: color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
! 40: color="#00006A"><strong>, senior researcher at the </strong></font><a
! 41: href="http://www.ined.fr"><font color="#00006A"><strong>Institut
! 42: National d'Etudes Démographiques</strong></font></a><font
! 43: color="#00006A"><strong> (INED, Paris) in the "Mortality,
! 44: Health and Epidemiology" Research Unit </strong></font></p>
! 45:
! 46: <p align="center"><font color="#00006A"><strong>and Agnès
! 47: Lièvre<br clear="left">
! 48: </strong></font></p>
! 49:
! 50: <h4><font color="#00006A">Contribution to the mathematics: C. R.
! 51: Heathcote </font><font color="#00006A" size="2">(Australian
! 52: National University, Canberra).</font></h4>
! 53:
! 54: <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
! 55: href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
! 56: color="#00006A">) </font></h4>
! 57:
! 58: <hr>
! 59:
! 60: <ul>
! 61: <li><a href="#intro">Introduction</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> using the methodology pioneered by Laditka and Wolf (1).
! 76: Within the family of Health Expectancies (HE), Disability-free
! 77: life expectancy (DFLE) is probably the most important index to
! 78: monitor. In low mortality countries, there is a fear that when
! 79: mortality declines, the increase in DFLE is not proportionate to
! 80: the increase in total Life expectancy. This case is called the <em>Expansion
! 81: of morbidity</em>. Most of the data collected today, in
! 82: particular by the international <a href="http://www.reves.org">REVES</a>
! 83: network on Health expectancy, and most HE indices based on these
! 84: data, are <em>cross-sectional</em>. It means that the information
! 85: collected comes from a single cross-sectional survey: people from
! 86: various ages (but mostly old people) are surveyed on their health
! 87: status at a single date. Proportion of people disabled at each
! 88: age, can then be measured at that date. This age-specific
! 89: prevalence curve is then used to distinguish, within the
! 90: stationary population (which, by definition, is the life table
! 91: estimated from the vital statistics on mortality at the same
! 92: date), the disable population from the disability-free
! 93: population. Life expectancy (LE) (or total population divided by
! 94: the yearly number of births or deaths of this stationary
! 95: population) is then decomposed into DFLE and DLE. This method of
! 96: computing HE is usually called the Sullivan method (from the name
! 97: of the author who first described it).</p>
! 98:
! 99: <p>Age-specific proportions of people disable are very difficult
! 100: to forecast because each proportion corresponds to historical
! 101: conditions of the cohort and it is the result of the historical
! 102: flows from entering disability and recovering in the past until
! 103: today. The age-specific intensities (or incidence rates) of
! 104: entering disability or recovering a good health, are reflecting
! 105: actual conditions and therefore can be used at each age to
! 106: forecast the future of this cohort. For example if a country is
! 107: improving its technology of prosthesis, the incidence of
! 108: recovering the ability to walk will be higher at each (old) age,
! 109: but the prevalence of disability will only slightly reflect an
! 110: improve because the prevalence is mostly affected by the history
! 111: of the cohort and not by recent period effects. To measure the
! 112: period improvement we have to simulate the future of a cohort of
! 113: new-borns entering or leaving at each age the disability state or
! 114: dying according to the incidence rates measured today on
! 115: different cohorts. The proportion of people disabled at each age
! 116: in this simulated cohort will be much lower (using the exemple of
! 117: an improvement) that the proportions observed at each age in a
! 118: cross-sectional survey. This new prevalence curve introduced in a
! 119: life table will give a much more actual and realistic HE level
! 120: than the Sullivan method which mostly measured the History of
! 121: health conditions in this country.</p>
! 122:
! 123: <p>Therefore, the main question is how to measure incidence rates
! 124: from cross-longitudinal surveys? This is the goal of the IMaCH
! 125: program. From your data and using IMaCH you can estimate period
! 126: HE and not only Sullivan's HE. Also the standard errors of the HE
! 127: are computed.</p>
! 128:
! 129: <p>A cross-longitudinal survey consists in a first survey
! 130: ("cross") where individuals from different ages are
! 131: interviewed on their health status or degree of disability. At
! 132: least a second wave of interviews ("longitudinal")
! 133: should measure each new individual health status. Health
! 134: expectancies are computed from the transitions observed between
! 135: waves and are computed for each degree of severity of disability
! 136: (number of life states). More degrees you consider, more time is
! 137: necessary to reach the Maximum Likelihood of the parameters
! 138: involved in the model. Considering only two states of disability
! 139: (disable and healthy) is generally enough but the computer
! 140: program works also with more health statuses.<br>
! 141: <br>
! 142: The simplest model is the multinomial logistic model where <i>pij</i>
! 143: is the probability to be observed in state <i>j</i> at the second
! 144: wave conditional to be observed in state <em>i</em> at the first
! 145: wave. Therefore a simple model is: log<em>(pij/pii)= aij +
! 146: bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
! 147: is a covariate. The advantage that this computer program claims,
! 148: comes from that if the delay between waves is not identical for
! 149: each individual, or if some individual missed an interview, the
! 150: information is not rounded or lost, but taken into account using
! 151: an interpolation or extrapolation. <i>hPijx</i> is the
! 152: probability to be observed in state <i>i</i> at age <i>x+h</i>
! 153: conditional to the observed state <i>i</i> at age <i>x</i>. The
! 154: delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
! 155: of unobserved intermediate states. This elementary transition (by
! 156: month or quarter trimester, semester or year) is modeled as a
! 157: multinomial logistic. The <i>hPx</i> matrix is simply the matrix
! 158: product of <i>nh*stepm</i> elementary matrices and the
! 159: contribution of each individual to the likelihood is simply <i>hPijx</i>.
! 160: <br>
! 161: </p>
! 162:
! 163: <p>The program presented in this manual is a quite general
! 164: program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
! 165: <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
! 166: analyse transition data from longitudinal surveys. The first step
! 167: is the parameters estimation of a transition probabilities model
! 168: between an initial status and a final status. From there, the
! 169: computer program produces some indicators such as observed and
! 170: stationary prevalence, life expectancies and their variances and
! 171: graphs. Our transition model consists in absorbing and
! 172: non-absorbing states with the possibility of return across the
! 173: non-absorbing states. The main advantage of this package,
! 174: compared to other programs for the analysis of transition data
! 175: (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
! 176: individual information is used even if an interview is missing, a
! 177: status or a date is unknown or when the delay between waves is
! 178: not identical for each individual. The program can be executed
! 179: according to parameters: selection of a sub-sample, number of
! 180: absorbing and non-absorbing states, number of waves taken in
! 181: account (the user inputs the first and the last interview), a
! 182: tolerance level for the maximization function, the periodicity of
! 183: the transitions (we can compute annual, quarterly or monthly
! 184: transitions), covariates in the model. It works on Windows or on
! 185: Unix.<br>
! 186: </p>
! 187:
! 188: <hr>
! 189:
! 190: <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
! 191: Methods for Analyzing Active Life Expectancy". <i>Journal of
! 192: Aging and Health</i>. Vol 10, No. 2. </p>
! 193:
! 194: <hr>
! 195:
! 196: <h2><a name="data"><font color="#00006A">On what kind of data can
! 197: it be used?</font></a></h2>
! 198:
! 199: <p>The minimum data required for a transition model is the
! 200: recording of a set of individuals interviewed at a first date and
! 201: interviewed again at least one another time. From the
! 202: observations of an individual, we obtain a follow-up over time of
! 203: the occurrence of a specific event. In this documentation, the
! 204: event is related to health status at older ages, but the program
! 205: can be applied on a lot of longitudinal studies in different
! 206: contexts. To build the data file explained into the next section,
! 207: you must have the month and year of each interview and the
! 208: corresponding health status. But in order to get age, date of
! 209: birth (month and year) is required (missing values is allowed for
! 210: month). Date of death (month and year) is an important
! 211: information also required if the individual is dead. Shorter
! 212: steps (i.e. a month) will more closely take into account the
! 213: survival time after the last interview.</p>
! 214:
! 215: <hr>
! 216:
! 217: <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
! 218:
! 219: <p>In this example, 8,000 people have been interviewed in a
! 220: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
! 221: Some people missed 1, 2 or 3 interviews. Health statuses are
! 222: healthy (1) and disable (2). The survey is not a real one. It is
! 223: a simulation of the American Longitudinal Survey on Aging. The
! 224: disability state is defined if the individual missed one of four
! 225: ADL (Activity of daily living, like bathing, eating, walking).
! 226: Therefore, even is the individuals interviewed in the sample are
! 227: virtual, the information brought with this sample is close to the
! 228: situation of the United States. Sex is not recorded is this
! 229: sample.</p>
! 230:
! 231: <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
! 232: in this first example) is an individual record which fields are: </p>
! 233:
! 234: <ul>
! 235: <li><b>Index number</b>: positive number (field 1) </li>
! 236: <li><b>First covariate</b> positive number (field 2) </li>
! 237: <li><b>Second covariate</b> positive number (field 3) </li>
! 238: <li><a name="Weight"><b>Weight</b></a>: positive number
! 239: (field 4) . In most surveys individuals are weighted
! 240: according to the stratification of the sample.</li>
! 241: <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
! 242: coded as 99/9999 (field 5) </li>
! 243: <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
! 244: coded as 99/9999 (field 6) </li>
! 245: <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
! 246: dates are coded as 99/9999 (field 7) </li>
! 247: <li><b>Status at first interview</b>: positive number.
! 248: Missing values ar coded -1. (field 8) </li>
! 249: <li><b>Date of second interview</b>: coded as mm/yyyy.
! 250: Missing dates are coded as 99/9999 (field 9) </li>
! 251: <li><strong>Status at second interview</strong> positive
! 252: number. Missing values ar coded -1. (field 10) </li>
! 253: <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
! 254: dates are coded as 99/9999 (field 11) </li>
! 255: <li><strong>Status at third interview</strong> positive
! 256: number. Missing values ar coded -1. (field 12) </li>
! 257: <li><b>Date of fourth interview</b>: coded as mm/yyyy.
! 258: Missing dates are coded as 99/9999 (field 13) </li>
! 259: <li><strong>Status at fourth interview</strong> positive
! 260: number. Missing values are coded -1. (field 14) </li>
! 261: <li>etc</li>
! 262: </ul>
! 263:
! 264: <p> </p>
! 265:
! 266: <p>If your longitudinal survey do not include information about
! 267: weights or covariates, you must fill the column with a number
! 268: (e.g. 1) because a missing field is not allowed.</p>
! 269:
! 270: <hr>
! 271:
! 272: <h2><font color="#00006A">Your first example parameter file</font><a
! 273: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
! 274:
! 275: <h2><a name="biaspar"></a>#Imach version 0.71a, March 2002,
! 276: INED-EUROREVES </h2>
! 277:
! 278: <p>This is a comment. Comments start with a '#'.</p>
! 279:
! 280: <h4><font color="#FF0000">First uncommented line</font></h4>
! 281:
! 282: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
! 283:
! 284: <ul>
! 285: <li><b>title=</b> 1st_example is title of the run. </li>
! 286: <li><b>datafile=</b>data1.txt is the name of the data set.
! 287: Our example is a six years follow-up survey. It consists
! 288: in a baseline followed by 3 reinterviews. </li>
! 289: <li><b>lastobs=</b> 8600 the program is able to run on a
! 290: subsample where the last observation number is lastobs.
! 291: It can be set a bigger number than the real number of
! 292: observations (e.g. 100000). In this example, maximisation
! 293: will be done on the 8600 first records. </li>
! 294: <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
! 295: than two interviews in the survey, the program can be run
! 296: on selected transitions periods. firstpass=1 means the
! 297: first interview included in the calculation is the
! 298: baseline survey. lastpass=4 means that the information
! 299: brought by the 4th interview is taken into account.</li>
! 300: </ul>
! 301:
! 302: <p> </p>
! 303:
! 304: <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
! 305: line</font></a></h4>
! 306:
! 307: <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
! 308:
! 309: <ul>
! 310: <li><b>ftol=1e-8</b> Convergence tolerance on the function
! 311: value in the maximisation of the likelihood. Choosing a
! 312: correct value for ftol is difficult. 1e-8 is a correct
! 313: value for a 32 bits computer.</li>
! 314: <li><b>stepm=1</b> Time unit in months for interpolation.
! 315: Examples:<ul>
! 316: <li>If stepm=1, the unit is a month </li>
! 317: <li>If stepm=4, the unit is a trimester</li>
! 318: <li>If stepm=12, the unit is a year </li>
! 319: <li>If stepm=24, the unit is two years</li>
! 320: <li>... </li>
! 321: </ul>
! 322: </li>
! 323: <li><b>ncov=2</b> Number of covariates in the datafile. The
! 324: intercept and the age parameter are counting for 2
! 325: covariates.</li>
! 326: <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
! 327: Here we have two alive states: disability-free is coded 1
! 328: and disability is coded 2. </li>
! 329: <li><b>ndeath=1</b> Number of absorbing states. The absorbing
! 330: state death is coded 3. </li>
! 331: <li><b>maxwav=4</b> Number of waves in the datafile.</li>
! 332: <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
! 333: Maximisation Likelihood Estimation. <ul>
! 334: <li>If mle=1 the program does the maximisation and
! 335: the calculation of health expectancies </li>
! 336: <li>If mle=0 the program only does the calculation of
! 337: the health expectancies. </li>
! 338: </ul>
! 339: </li>
! 340: <li><b>weight=0</b> Possibility to add weights. <ul>
! 341: <li>If weight=0 no weights are included </li>
! 342: <li>If weight=1 the maximisation integrates the
! 343: weights which are in field <a href="#Weight">4</a></li>
! 344: </ul>
! 345: </li>
! 346: </ul>
! 347:
! 348: <h4><font color="#FF0000">Covariates</font></h4>
! 349:
! 350: <p>Intercept and age are systematically included in the model.
! 351: Additional covariates (actually two) can be included with the command: </p>
! 352:
! 353: <pre>model=<em>list of covariates</em></pre>
! 354:
! 355: <ul>
! 356: <li>if<strong> model=. </strong>then no covariates are
! 357: included</li>
! 358: <li>if <strong>model=V1</strong> the model includes the first
! 359: covariate (field 2)</li>
! 360: <li>if <strong>model=V2 </strong>the model includes the
! 361: second covariate (field 3)</li>
! 362: <li>if <strong>model=V1+V2 </strong>the model includes the
! 363: first and the second covariate (fields 2 and 3)</li>
! 364: <li>if <strong>model=V1*V2 </strong>the model includes the
! 365: product of the first and the second covariate (fields 2
! 366: and 3)</li>
! 367: <li>if <strong>model=V1+V1*age</strong> the model includes
! 368: the product covariate*age</li>
! 369: </ul>
! 370:
! 371: <h4><font color="#FF0000">Guess values for optimization</font><font
! 372: color="#00006A"> </font></h4>
! 373:
! 374: <p>You must write the initial guess values of the parameters for
! 375: optimization. The number of parameters, <em>N</em> depends on the
! 376: number of absorbing states and non-absorbing states and on the
! 377: number of covariates. <br>
! 378: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
! 379: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br>
! 380: <br>
! 381: Thus in the simple case with 2 covariates (the model is log
! 382: (pij/pii) = aij + bij * age where intercept and age are the two
! 383: covariates), and 2 health degrees (1 for disability-free and 2
! 384: for disability) and 1 absorbing state (3), you must enter 8
! 385: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
! 386: start with zeros as in this example, but if you have a more
! 387: precise set (for example from an earlier run) you can enter it
! 388: and it will speed up them<br>
! 389: Each of the four lines starts with indices "ij": <b>ij
! 390: 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 (in most of cases it converges but there is no warranty!): </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 various 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 various 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><font color="#FF0000">Age range for calculation of stationary
! 479: prevalences and health expectancies</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 range is useful
! 486: for extrapolation. In our data file, ages varies from age 70 to
! 487: 102. It is possible to get extrapolated stationary
! 488: prevalence by age ranging from agemin to agemax. </p>
! 489:
! 490:
! 491: <p>Setting bage=50 (begin age) and fage=100 (final age), makes the program computing
! 492: life expectancy from age 'bage' to age 'fage'. As we use a model, we
! 493: can interessingly compute life expectancy on a wider age range than the age
! 494: range from the data. But the model can be rather wrong on much larger
! 495: intervals. Program is limited to around 120 for upper age!</p>
! 496:
! 497: <ul>
! 498: <li><b>agemin=</b> Minimum age for calculation of the
! 499: stationary prevalence </li>
! 500: <li><b>agemax=</b> Maximum age for calculation of the
! 501: stationary prevalence </li>
! 502: <li><b>bage=</b> Minimum age for calculation of the health
! 503: expectancies </li>
! 504: <li><b>fage=</b> Maximum age for calculation of the health
! 505: expectancies </li>
! 506: </ul>
! 507:
! 508: <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
! 509: color="#FF0000"> the observed prevalence</font></h4>
! 510:
! 511: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
! 512:
! 513: <p>Statements 'begin-prev-date' and 'end-prev-date' allow to
! 514: select the period in which we calculate the observed prevalences
! 515: in each state. In this example, the prevalences are calculated on
! 516: data survey collected between 1 january 1984 and 1 june 1988. </p>
! 517:
! 518: <ul>
! 519: <li><strong>begin-prev-date= </strong>Starting date
! 520: (day/month/year)</li>
! 521: <li><strong>end-prev-date= </strong>Final date
! 522: (day/month/year)</li>
! 523: </ul>
! 524:
! 525: <h4><font color="#FF0000">Population- or status-based health
! 526: expectancies</font></h4>
! 527:
! 528: <pre>pop_based=0</pre>
! 529:
! 530: <p>The program computes status-based health expectancies, i.e health
! 531: expectancies which depends on your initial health state. If you are
! 532: healthy your healthy life expectancy (e11) is higher than if you were
! 533: disabled (e21, with e11 > e21).<br>
! 534: To compute a healthy life expectancy independant of the initial status
! 535: we have to weight e11 and e21 according to the probability to be in
! 536: each state at initial age or, with other word, according to the
! 537: proportion of people in each state.<br>
! 538:
! 539: We prefer computing a 'pure' period healthy life expectancy based only
! 540: on the transtion forces. Then the weights are simply the stationnary
! 541: prevalences or 'implied' prevalences at the initial age.<br>
! 542:
! 543: Some other people would like to use the cross-sectional prevalences
! 544: (the "Sullivan prevalences") observed at the initial age during a
! 545: period of time <a href="#Computing">defined just above</a>.
! 546:
! 547: <ul>
! 548: <li><strong>popbased= 0 </strong> Health expectancies are computed
! 549: at each age from stationary prevalences 'expected' at this initial age.</li>
! 550: <li><strong>popbased= 1 </strong> Health expectancies are computed
! 551: at each age from cross-sectional 'observed' prevalence at this
! 552: initial age. As all the population is not observed at the same exact date we
! 553: define a short period were the observed prevalence is computed.</li>
! 554: </ul>
! 555:
! 556: </p>
! 557:
! 558: <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
! 559:
! 560: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
! 561:
! 562: <p>Prevalence and population projections are only available if the
! 563: interpolation unit is a month, i.e. stepm=1 and if there are no
! 564: covariate. The programme estimates the prevalence in each state at a
! 565: precise date expressed in day/month/year. The programme computes one
! 566: forecasted prevalence a year from a starting date (1 january of 1989
! 567: in this example) to a final date (1 january 1992). The statement
! 568: mov_average allows to compute smoothed forecasted prevalences with a
! 569: five-age moving average centered at the mid-age of the five-age
! 570: period. </p>
! 571:
! 572: <ul>
! 573: <li><strong>starting-proj-date</strong>= starting date
! 574: (day/month/year) of forecasting</li>
! 575: <li><strong>final-proj-date= </strong>final date
! 576: (day/month/year) of forecasting</li>
! 577: <li><strong>mov_average</strong>= smoothing with a five-age
! 578: moving average centered at the mid-age of the five-age
! 579: period. The command<strong> mov_average</strong> takes
! 580: value 1 if the prevalences are smoothed and 0 otherwise.</li>
! 581: </ul>
! 582:
! 583: <h4><font color="#FF0000">Last uncommented line : Population
! 584: forecasting </font></h4>
! 585:
! 586: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
! 587:
! 588: <p>This command is available if the interpolation unit is a
! 589: month, i.e. stepm=1 and if popforecast=1. From a data file
! 590: including age and number of persons alive at the precise date
! 591: ‘popfiledate’, you can forecast the number of persons
! 592: in each state until date ‘last-popfiledate’. In this
! 593: example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
! 594: includes real data which are the Japanese population in 1989.</p>
! 595:
! 596: <ul type="disc">
! 597: <li class="MsoNormal"
! 598: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popforecast=
! 599: 0 </b>Option for population forecasting. If
! 600: popforecast=1, the programme does the forecasting<b>.</b></li>
! 601: <li class="MsoNormal"
! 602: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfile=
! 603: </b>name of the population file</li>
! 604: <li class="MsoNormal"
! 605: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>popfiledate=</b>
! 606: date of the population population</li>
! 607: <li class="MsoNormal"
! 608: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt"><b>last-popfiledate</b>=
! 609: date of the last population projection </li>
! 610: </ul>
! 611:
! 612: <hr>
! 613:
! 614: <h2><a name="running"></a><font color="#00006A">Running Imach
! 615: with this example</font></h2>
! 616:
! 617: <p>We assume that you entered your <a href="biaspar.imach">1st_example
! 618: parameter file</a> as explained <a href="#biaspar">above</a>. To
! 619: run the program you should click on the imach.exe icon and enter
! 620: the name of the parameter file which is for example <a
! 621: href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
! 622: (you also can click on the biaspar.txt icon located in <br>
! 623: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
! 624: the mouse on the imach window).<br>
! 625: </p>
! 626:
! 627: <p>The time to converge depends on the step unit that you used (1
! 628: month is cpu consuming), on the number of cases, and on the
! 629: number of variables.</p>
! 630:
! 631: <p>The program outputs many files. Most of them are files which
! 632: will be plotted for better understanding.</p>
! 633:
! 634: <hr>
! 635:
! 636: <h2><a name="output"><font color="#00006A">Output of the program
! 637: and graphs</font> </a></h2>
! 638:
! 639: <p>Once the optimization is finished, some graphics can be made
! 640: with a grapher. We use Gnuplot which is an interactive plotting
! 641: program copyrighted but freely distributed. A gnuplot reference
! 642: manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
! 643: When the running is finished, the user should enter a caracter
! 644: for plotting and output editing. </p>
! 645:
! 646: <p>These caracters are:</p>
! 647:
! 648: <ul>
! 649: <li>'c' to start again the program from the beginning.</li>
! 650: <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
! 651: file to edit the output files and graphs. </li>
! 652: <li>'q' for exiting.</li>
! 653: </ul>
! 654:
! 655: <h5><font size="4"><strong>Results files </strong></font><br>
! 656: <br>
! 657: <font color="#EC5E5E" size="3"><strong>- </strong></font><a
! 658: name="Observed prevalence in each state"><font color="#EC5E5E"
! 659: size="3"><strong>Observed prevalence in each state</strong></font></a><font
! 660: color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
! 661: </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
! 662: </h5>
! 663:
! 664: <p>The first line is the title and displays each field of the
! 665: file. The first column is age. The fields 2 and 6 are the
! 666: proportion of individuals in states 1 and 2 respectively as
! 667: observed during the first exam. Others fields are the numbers of
! 668: people in states 1, 2 or more. The number of columns increases if
! 669: the number of states is higher than 2.<br>
! 670: The header of the file is </p>
! 671:
! 672: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
! 673: 70 1.00000 631 631 70 0.00000 0 631
! 674: 71 0.99681 625 627 71 0.00319 2 627
! 675: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
! 676:
! 677: <p>It means that at age 70, the prevalence in state 1 is 1.000
! 678: and in state 2 is 0.00 . At age 71 the number of individuals in
! 679: state 1 is 625 and in state 2 is 2, hence the total number of
! 680: people aged 71 is 625+2=627. <br>
! 681: </p>
! 682:
! 683: <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
! 684: covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
! 685:
! 686: <p>This file contains all the maximisation results: </p>
! 687:
! 688: <pre> -2 log likelihood= 21660.918613445392
! 689: Estimated parameters: a12 = -12.290174 b12 = 0.092161
! 690: a13 = -9.155590 b13 = 0.046627
! 691: a21 = -2.629849 b21 = -0.022030
! 692: a23 = -7.958519 b23 = 0.042614
! 693: Covariance matrix: Var(a12) = 1.47453e-001
! 694: Var(b12) = 2.18676e-005
! 695: Var(a13) = 2.09715e-001
! 696: Var(b13) = 3.28937e-005
! 697: Var(a21) = 9.19832e-001
! 698: Var(b21) = 1.29229e-004
! 699: Var(a23) = 4.48405e-001
! 700: Var(b23) = 5.85631e-005
! 701: </pre>
! 702:
! 703: <p>By substitution of these parameters in the regression model,
! 704: we obtain the elementary transition probabilities:</p>
! 705:
! 706: <p><img src="pebiaspar1.gif" width="400" height="300"></p>
! 707:
! 708: <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
! 709: </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
! 710:
! 711: <p>Here are the transitions probabilities Pij(x, x+nh) where nh
! 712: is a multiple of 2 years. The first column is the starting age x
! 713: (from age 50 to 100), the second is age (x+nh) and the others are
! 714: the transition probabilities p11, p12, p13, p21, p22, p23. For
! 715: example, line 5 of the file is: </p>
! 716:
! 717: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
! 718:
! 719: <p>and this means: </p>
! 720:
! 721: <pre>p11(100,106)=0.02655
! 722: p12(100,106)=0.17622
! 723: p13(100,106)=0.79722
! 724: p21(100,106)=0.01809
! 725: p22(100,106)=0.13678
! 726: p22(100,106)=0.84513 </pre>
! 727:
! 728: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 729: name="Stationary prevalence in each state"><font color="#EC5E5E"
! 730: size="3"><b>Stationary prevalence in each state</b></font></a><b>:
! 731: </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
! 732:
! 733: <pre>#Prevalence
! 734: #Age 1-1 2-2
! 735:
! 736: #************
! 737: 70 0.90134 0.09866
! 738: 71 0.89177 0.10823
! 739: 72 0.88139 0.11861
! 740: 73 0.87015 0.12985 </pre>
! 741:
! 742: <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
! 743: 0.09866 in state 2. This stationary prevalence differs from
! 744: observed prevalence. Here is the point. The observed prevalence
! 745: at age 70 results from the incidence of disability, incidence of
! 746: recovery and mortality which occurred in the past of the cohort.
! 747: Stationary prevalence results from a simulation with actual
! 748: incidences and mortality (estimated from this cross-longitudinal
! 749: survey). It is the best predictive value of the prevalence in the
! 750: future if "nothing changes in the future". This is
! 751: exactly what demographers do with a Life table. Life expectancy
! 752: is the expected mean time to survive if observed mortality rates
! 753: (incidence of mortality) "remains constant" in the
! 754: future. </p>
! 755:
! 756: <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
! 757: stationary prevalence</b></font><b>: </b><a
! 758: href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
! 759:
! 760: <p>The stationary prevalence has to be compared with the observed
! 761: prevalence by age. But both are statistical estimates and
! 762: subjected to stochastic errors due to the size of the sample, the
! 763: design of the survey, and, for the stationary prevalence to the
! 764: model used and fitted. It is possible to compute the standard
! 765: deviation of the stationary prevalence at each age.</p>
! 766:
! 767: <h5><font color="#EC5E5E" size="3">-Observed and stationary
! 768: prevalence in state (2=disable) with the confident interval</font>:<b>
! 769: </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
! 770:
! 771: <p>This graph exhibits the stationary prevalence in state (2)
! 772: with the confidence interval in red. The green curve is the
! 773: observed prevalence (or proportion of individuals in state (2)).
! 774: Without discussing the results (it is not the purpose here), we
! 775: observe that the green curve is rather below the stationary
! 776: prevalence. It suggests an increase of the disability prevalence
! 777: in the future.</p>
! 778:
! 779: <p><img src="vbiaspar21.gif" width="400" height="300"></p>
! 780:
! 781: <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
! 782: stationary prevalence of disability</b></font><b>: </b><a
! 783: href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
! 784: <img src="pbiaspar11.gif" width="400" height="300"> </h5>
! 785:
! 786: <p>This graph plots the conditional transition probabilities from
! 787: an initial state (1=healthy in red at the bottom, or 2=disable in
! 788: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
! 789: age <em>x+h. </em>Conditional means at the condition to be alive
! 790: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
! 791: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
! 792: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
! 793: prevalence of disability</em>. In order to get the stationary
! 794: prevalence at age 70 we should start the process at an earlier
! 795: age, i.e.50. If the disability state is defined by severe
! 796: disability criteria with only a few chance to recover, then the
! 797: incidence of recovery is low and the time to convergence is
! 798: probably longer. But we don't have experience yet.</p>
! 799:
! 800: <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
! 801: and initial health status</b></font><b>: </b><a
! 802: href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
! 803:
! 804: <pre># Health expectancies
! 805: # Age 1-1 1-2 2-1 2-2
! 806: 70 10.9226 3.0401 5.6488 6.2122
! 807: 71 10.4384 3.0461 5.2477 6.1599
! 808: 72 9.9667 3.0502 4.8663 6.1025
! 809: 73 9.5077 3.0524 4.5044 6.0401 </pre>
! 810:
! 811: <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
! 812: e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
! 813:
! 814: <pre><img src="expbiaspar21.gif" width="400" height="300"><img
! 815: src="expbiaspar11.gif" width="400" height="300"></pre>
! 816:
! 817: <p>For example, life expectancy of a healthy individual at age 70
! 818: is 10.42 in the healthy state and 3.04 in the disability state
! 819: (=13.46 years). If he was disable at age 70, his life expectancy
! 820: will be shorter, 5.64 in the healthy state and 5.71 in the
! 821: disability state (=11.35 years). The total life expectancy is a
! 822: weighted mean of both, 13.46 and 11.35; weight is the proportion
! 823: of people disabled at age 70. In order to get a pure period index
! 824: (i.e. based only on incidences) we use the <a
! 825: href="#Stationary prevalence in each state">computed or
! 826: stationary prevalence</a> at age 70 (i.e. computed from
! 827: incidences at earlier ages) instead of the <a
! 828: href="#Observed prevalence in each state">observed prevalence</a>
! 829: (for example at first exam) (<a href="#Health expectancies">see
! 830: below</a>).</p>
! 831:
! 832: <h5><font color="#EC5E5E" size="3"><b>- Variances of life
! 833: expectancies by age and initial health status</b></font><b>: </b><a
! 834: href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
! 835:
! 836: <p>For example, the covariances of life expectancies Cov(ei,ej)
! 837: at age 50 are (line 3) </p>
! 838:
! 839: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
! 840:
! 841: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 842: name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
! 843: expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
! 844: with standard errors in parentheses</b></font><b>: </b><a
! 845: href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
! 846:
! 847: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
! 848:
! 849: <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
! 850:
! 851: <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
! 852: the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
! 853: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
! 854: state 2, respectively (the sum is equal to one). e.1=9.95 is the
! 855: Disability-free life expectancy at age 70 (it is again a weighted
! 856: mean of e11 and e21). e.2=3.30 is also the life expectancy at age
! 857: 70 to be spent in the disability state.</p>
! 858:
! 859: <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
! 860: age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
! 861: </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
! 862:
! 863: <p>This figure represents the health expectancies and the total
! 864: life expectancy with the confident interval in dashed curve. </p>
! 865:
! 866: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
! 867:
! 868: <p>Standard deviations (obtained from the information matrix of
! 869: the model) of these quantities are very useful.
! 870: Cross-longitudinal surveys are costly and do not involve huge
! 871: samples, generally a few thousands; therefore it is very
! 872: important to have an idea of the standard deviation of our
! 873: estimates. It has been a big challenge to compute the Health
! 874: Expectancy standard deviations. Don't be confuse: life expectancy
! 875: is, as any expected value, the mean of a distribution; but here
! 876: we are not computing the standard deviation of the distribution,
! 877: but the standard deviation of the estimate of the mean.</p>
! 878:
! 879: <p>Our health expectancies estimates vary according to the sample
! 880: size (and the standard deviations give confidence intervals of
! 881: the estimate) but also according to the model fitted. Let us
! 882: explain it in more details.</p>
! 883:
! 884: <p>Choosing a model means ar least two kind of choices. First we
! 885: have to decide the number of disability states. Second we have to
! 886: design, within the logit model family, the model: variables,
! 887: covariables, confonding factors etc. to be included.</p>
! 888:
! 889: <p>More disability states we have, better is our demographical
! 890: approach of the disability process, but smaller are the number of
! 891: transitions between each state and higher is the noise in the
! 892: measurement. We do not have enough experiments of the various
! 893: models to summarize the advantages and disadvantages, but it is
! 894: important to say that even if we had huge and unbiased samples,
! 895: the total life expectancy computed from a cross-longitudinal
! 896: survey, varies with the number of states. If we define only two
! 897: states, alive or dead, we find the usual life expectancy where it
! 898: is assumed that at each age, people are at the same risk to die.
! 899: If we are differentiating the alive state into healthy and
! 900: disable, and as the mortality from the disability state is higher
! 901: than the mortality from the healthy state, we are introducing
! 902: heterogeneity in the risk of dying. The total mortality at each
! 903: age is the weighted mean of the mortality in each state by the
! 904: prevalence in each state. Therefore if the proportion of people
! 905: at each age and in each state is different from the stationary
! 906: equilibrium, there is no reason to find the same total mortality
! 907: at a particular age. Life expectancy, even if it is a very useful
! 908: tool, has a very strong hypothesis of homogeneity of the
! 909: population. Our main purpose is not to measure differential
! 910: mortality but to measure the expected time in a healthy or
! 911: disability state in order to maximise the former and minimize the
! 912: latter. But the differential in mortality complexifies the
! 913: measurement.</p>
! 914:
! 915: <p>Incidences of disability or recovery are not affected by the
! 916: number of states if these states are independant. But incidences
! 917: estimates are dependant on the specification of the model. More
! 918: covariates we added in the logit model better is the model, but
! 919: some covariates are not well measured, some are confounding
! 920: factors like in any statistical model. The procedure to "fit
! 921: the best model' is similar to logistic regression which itself is
! 922: similar to regression analysis. We haven't yet been sofar because
! 923: we also have a severe limitation which is the speed of the
! 924: convergence. On a Pentium III, 500 MHz, even the simplest model,
! 925: estimated by month on 8,000 people may take 4 hours to converge.
! 926: Also, the program is not yet a statistical package, which permits
! 927: a simple writing of the variables and the model to take into
! 928: account in the maximisation. The actual program allows only to
! 929: add simple variables like age+sex or age+sex+ age*sex but will
! 930: never be general enough. But what is to remember, is that
! 931: incidences or probability of change from one state to another is
! 932: affected by the variables specified into the model.</p>
! 933:
! 934: <p>Also, the age range of the people interviewed has a link with
! 935: the age range of the life expectancy which can be estimated by
! 936: extrapolation. If your sample ranges from age 70 to 95, you can
! 937: clearly estimate a life expectancy at age 70 and trust your
! 938: confidence interval which is mostly based on your sample size,
! 939: but if you want to estimate the life expectancy at age 50, you
! 940: should rely in your model, but fitting a logistic model on a age
! 941: range of 70-95 and estimating probabilties of transition out of
! 942: this age range, say at age 50 is very dangerous. At least you
! 943: should remember that the confidence interval given by the
! 944: standard deviation of the health expectancies, are under the
! 945: strong assumption that your model is the 'true model', which is
! 946: probably not the case.</p>
! 947:
! 948: <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
! 949: file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
! 950:
! 951: <p>This copy of the parameter file can be useful to re-run the
! 952: program while saving the old output files. </p>
! 953:
! 954: <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
! 955: </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
! 956:
! 957: <p
! 958: style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">First,
! 959: we have estimated the observed prevalence between 1/1/1984 and
! 960: 1/6/1988. The mean date of interview (weighed average of the
! 961: interviews performed between1/1/1984 and 1/6/1988) is estimated
! 962: to be 13/9/1985, as written on the top on the file. Then we
! 963: forecast the probability to be in each state. </p>
! 964:
! 965: <p
! 966: style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Example,
! 967: at date 1/1/1989 : </p>
! 968:
! 969: <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
! 970: # Forecasting at date 1/1/1989
! 971: 73 0.807 0.078 0.115</pre>
! 972:
! 973: <p
! 974: style="TEXT-ALIGN: justify; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">Since
! 975: the minimum age is 70 on the 13/9/1985, the youngest forecasted
! 976: age is 73. This means that at age a person aged 70 at 13/9/1989
! 977: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
! 978: Similarly, the probability to be in state 2 is 0.078 and the
! 979: probability to die is 0.115. Then, on the 1/1/1989, the
! 980: prevalence of disability at age 73 is estimated to be 0.088.</p>
! 981:
! 982: <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
! 983: </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
! 984:
! 985: <pre># Age P.1 P.2 P.3 [Population]
! 986: # Forecasting at date 1/1/1989
! 987: 75 572685.22 83798.08
! 988: 74 621296.51 79767.99
! 989: 73 645857.70 69320.60 </pre>
! 990:
! 991: <pre># Forecasting at date 1/1/19909
! 992: 76 442986.68 92721.14 120775.48
! 993: 75 487781.02 91367.97 121915.51
! 994: 74 512892.07 85003.47 117282.76 </pre>
! 995:
! 996: <p>From the population file, we estimate the number of people in
! 997: each state. At age 73, 645857 persons are in state 1 and 69320
! 998: are in state 2. One year latter, 512892 are still in state 1,
! 999: 85003 are in state 2 and 117282 died before 1/1/1990.</p>
! 1000:
! 1001: <hr>
! 1002:
! 1003: <h2><a name="example"> </a><font color="#00006A">Trying an example</font></a></h2>
! 1004:
! 1005: <p>Since you know how to run the program, it is time to test it
! 1006: on your own computer. Try for example on a parameter file named <a
! 1007: href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
! 1008: size="2" face="Courier New">mypar.txt</font> included in the
! 1009: subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
! 1010: Edit it to change the name of the data file to <font size="2"
! 1011: face="Courier New">..\data\mydata.txt</font> if you don't want to
! 1012: copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
! 1013: is a smaller file of 3,000 people but still with 4 waves. </p>
! 1014:
! 1015: <p>Click on the imach.exe icon to open a window. Answer to the
! 1016: question:'<strong>Enter the parameter file name:'</strong></p>
! 1017:
! 1018: <table border="1">
! 1019: <tr>
! 1020: <td width="100%"><strong>IMACH, Version 0.71</strong><p><strong>Enter
! 1021: the parameter file name: ..\mytry\imachpar.txt</strong></p>
! 1022: </td>
! 1023: </tr>
! 1024: </table>
! 1025:
! 1026: <p>Most of the data files or image files generated, will use the
! 1027: 'imachpar' string into their name. The running time is about 2-3
! 1028: minutes on a Pentium III. If the execution worked correctly, the
! 1029: outputs files are created in the current directory, and should be
! 1030: the same as the mypar files initially included in the directory <font
! 1031: size="2" face="Courier New">mytry</font>.</p>
! 1032:
! 1033: <ul>
! 1034: <li><pre><u>Output on the screen</u> The output screen looks like <a
! 1035: href="imachrun.LOG">this Log file</a>
! 1036: #
! 1037:
! 1038: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
! 1039: ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
! 1040: </li>
! 1041: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
! 1042:
! 1043: Warning, no any valid information for:126 line=126
! 1044: Warning, no any valid information for:2307 line=2307
! 1045: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
! 1046: <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
! 1047: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
! 1048: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
! 1049: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
! 1050: </li>
! 1051: </ul>
! 1052:
! 1053: <p> </p>
! 1054:
! 1055: <ul>
! 1056: <li>Maximisation with the Powell algorithm. 8 directions are
! 1057: given corresponding to the 8 parameters. this can be
! 1058: rather long to get convergence.<br>
! 1059: <font size="1" face="Courier New"><br>
! 1060: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
! 1061: 0.000000000000 3<br>
! 1062: 0.000000000000 4 0.000000000000 5 0.000000000000 6
! 1063: 0.000000000000 7 <br>
! 1064: 0.000000000000 8 0.000000000000<br>
! 1065: 1..........2.................3..........4.................5.........<br>
! 1066: 6................7........8...............<br>
! 1067: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
! 1068: <br>
! 1069: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
! 1070: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
! 1071: 8 0.051272038506<br>
! 1072: 1..............2...........3..............4...........<br>
! 1073: 5..........6................7...........8.........<br>
! 1074: #Number of iterations = 23, -2 Log likelihood =
! 1075: 6744.954042573691<br>
! 1076: # Parameters<br>
! 1077: 12 -12.966061 0.135117 <br>
! 1078: 13 -7.401109 0.067831 <br>
! 1079: 21 -0.672648 -0.006627 <br>
! 1080: 23 -5.051297 0.051271 </font><br>
! 1081: </li>
! 1082: <li><pre><font size="2">Calculation of the hessian matrix. Wait...
! 1083: 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
! 1084:
! 1085: Inverting the hessian to get the covariance matrix. Wait...
! 1086:
! 1087: #Hessian matrix#
! 1088: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
! 1089: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
! 1090: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
! 1091: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
! 1092: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
! 1093: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
! 1094: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
! 1095: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
! 1096: # Scales
! 1097: 12 1.00000e-004 1.00000e-006
! 1098: 13 1.00000e-004 1.00000e-006
! 1099: 21 1.00000e-003 1.00000e-005
! 1100: 23 1.00000e-004 1.00000e-005
! 1101: # Covariance
! 1102: 1 5.90661e-001
! 1103: 2 -7.26732e-003 8.98810e-005
! 1104: 3 8.80177e-002 -1.12706e-003 5.15824e-001
! 1105: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
! 1106: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
! 1107: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
! 1108: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
! 1109: 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
! 1110: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
! 1111:
! 1112:
! 1113: agemin=70 agemax=100 bage=50 fage=100
! 1114: Computing prevalence limit: result on file 'plrmypar.txt'
! 1115: Computing pij: result on file 'pijrmypar.txt'
! 1116: Computing Health Expectancies: result on file 'ermypar.txt'
! 1117: Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
! 1118: Computing Total LEs with variances: file 'trmypar.txt'
! 1119: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
! 1120: End of Imach
! 1121: </font></pre>
! 1122: </li>
! 1123: </ul>
! 1124:
! 1125: <p><font size="3">Once the running is finished, the program
! 1126: requires a caracter:</font></p>
! 1127:
! 1128: <table border="1">
! 1129: <tr>
! 1130: <td width="100%"><strong>Type e to edit output files, c
! 1131: to start again, and q for exiting:</strong></td>
! 1132: </tr>
! 1133: </table>
! 1134:
! 1135: <p><font size="3">First you should enter <strong>e </strong>to
! 1136: edit the master file mypar.htm. </font></p>
! 1137:
! 1138: <ul>
! 1139: <li><u>Outputs files</u> <br>
! 1140: <br>
! 1141: - Observed prevalence in each state: <a
! 1142: href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
! 1143: - Estimated parameters and the covariance matrix: <a
! 1144: href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
! 1145: - Stationary prevalence in each state: <a
! 1146: href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
! 1147: - Transition probabilities: <a
! 1148: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
! 1149: - Copy of the parameter file: <a
! 1150: href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
! 1151: - Life expectancies by age and initial health status: <a
! 1152: href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
! 1153: - Variances of life expectancies by age and initial
! 1154: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
! 1155: <br>
! 1156: - Health expectancies with their variances: <a
! 1157: href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
! 1158: - Standard deviation of stationary prevalence: <a
! 1159: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
! 1160: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
! 1161: <br>
! 1162: - Population forecasting (if popforecast=1): <a
! 1163: href="poprmypar.txt">poprmypar.txt</a> <br>
! 1164: </li>
! 1165: <li><u>Graphs</u> <br>
! 1166: <br>
! 1167: -<a href="../mytry/pemypar1.gif">One-step transition
! 1168: probabilities</a><br>
! 1169: -<a href="../mytry/pmypar11.gif">Convergence to the
! 1170: stationary prevalence</a><br>
! 1171: -<a href="..\mytry\vmypar11.gif">Observed and stationary
! 1172: prevalence in state (1) with the confident interval</a> <br>
! 1173: -<a href="..\mytry\vmypar21.gif">Observed and stationary
! 1174: prevalence in state (2) with the confident interval</a> <br>
! 1175: -<a href="..\mytry\expmypar11.gif">Health life
! 1176: expectancies by age and initial health state (1)</a> <br>
! 1177: -<a href="..\mytry\expmypar21.gif">Health life
! 1178: expectancies by age and initial health state (2)</a> <br>
! 1179: -<a href="..\mytry\emypar1.gif">Total life expectancy by
! 1180: age and health expectancies in states (1) and (2).</a> </li>
! 1181: </ul>
! 1182:
! 1183: <p>This software have been partly granted by <a
! 1184: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
! 1185: action from the European Union. It will be copyrighted
! 1186: identically to a GNU software product, i.e. program and software
! 1187: can be distributed freely for non commercial use. Sources are not
! 1188: widely distributed today. You can get them by asking us with a
! 1189: simple justification (name, email, institute) <a
! 1190: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
! 1191: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
! 1192:
! 1193: <p>Latest version (0.71 of February 2002) can be accessed at <a
! 1194: href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
! 1195: </p>
! 1196: </body>
! 1197: </html>
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