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1.2 lievre 14:
1.6 ! lievre 15: <h1 align="center"><font color="#00006A">Computing Health
! 16: Expectancies using IMaCh</font></h1>
1.2 lievre 17:
1.6 ! lievre 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>Version
! 32: 0.7, February 2002</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>
1.2 lievre 56:
57: <hr>
1.6 ! lievre 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>
1.2 lievre 69: </ul>
1.6 ! lievre 70:
1.2 lievre 71: <hr>
72:
1.6 ! lievre 73: <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
1.2 lievre 74:
1.6 ! lievre 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
1.2 lievre 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
1.6 ! lievre 83: particular by the international <a href="http://euroreves/reves">REVES</a>
1.2 lievre 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
1.6 ! lievre 98: of the author who first described it).</p>
1.2 lievre 99:
1.6 ! lievre 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>
1.2 lievre 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>.
1.6 ! lievre 161: <br>
! 162: </p>
1.2 lievre 163:
1.6 ! lievre 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,
1.2 lievre 175: compared to other programs for the analysis of transition data
1.6 ! lievre 176: (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
1.2 lievre 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
1.5 lievre 184: the transitions (we can compute annual, quarterly or monthly
1.2 lievre 185: transitions), covariates in the model. It works on Windows or on
1.6 ! lievre 186: Unix.<br>
! 187: </p>
1.2 lievre 188:
189: <hr>
190:
1.6 ! lievre 191: <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
1.2 lievre 192: Methods for Analyzing Active Life Expectancy". <i>Journal of
1.6 ! lievre 193: Aging and Health</i>. Vol 10, No. 2. </p>
1.2 lievre 194:
195: <hr>
196:
1.6 ! lievre 197: <h2><a name="data"><font color="#00006A">On what kind of data can
! 198: it be used?</font></a></h2>
1.2 lievre 199:
1.6 ! lievre 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>
1.2 lievre 215:
216: <hr>
217:
1.6 ! lievre 218: <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
1.2 lievre 219:
1.6 ! lievre 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>
1.2 lievre 263: </ul>
264:
1.6 ! lievre 265: <p> </p>
1.2 lievre 266:
1.6 ! lievre 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>
1.2 lievre 270:
271: <hr>
272:
1.6 ! lievre 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>
1.2 lievre 275:
1.6 ! lievre 276: <h2><a name="biaspar"></a>#Imach version 0.7, February 2002,
! 277: INED-EUROREVES </h2>
1.2 lievre 278:
1.6 ! lievre 279: <p>This is a comment. Comments start with a '#'.</p>
1.2 lievre 280:
1.6 ! lievre 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>
1.2 lievre 301: </ul>
302:
1.6 ! lievre 303: <p> </p>
! 304:
! 305: <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
! 306: line</font></a></h4>
1.2 lievre 307:
1.6 ! lievre 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>
1.2 lievre 322: </ul>
323: </li>
1.6 ! lievre 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>
1.2 lievre 339: </ul>
340: </li>
1.6 ! lievre 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>
1.2 lievre 345: </ul>
346: </li>
347: </ul>
348:
1.6 ! lievre 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>
1.2 lievre 353:
1.6 ! lievre 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
1.2 lievre 366: product of the first and the second covariate (fields 2
1.6 ! lievre 367: and 3)</li>
! 368: <li>if <strong>model=V1+V1*age</strong> the model includes
! 369: the product covariate*age</li>
1.2 lievre 370: </ul>
371:
1.6 ! lievre 372: <h4><font color="#FF0000">Guess values for optimization</font><font
! 373: color="#00006A"> </font></h4>
! 374:
! 375: <p>You must write the initial guess values of the parameters for
! 376: optimization. The number of parameters, <em>N</em> depends on the
1.2 lievre 377: number of absorbing states and non-absorbing states and on the
378: number of covariates. <br>
379: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
380: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncov</em> . <br>
381: <br>
382: Thus in the simple case with 2 covariates (the model is log
383: (pij/pii) = aij + bij * age where intercept and age are the two
384: covariates), and 2 health degrees (1 for disability-free and 2
385: for disability) and 1 absorbing state (3), you must enter 8
386: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
387: start with zeros as in this example, but if you have a more
388: precise set (for example from an earlier run) you can enter it
389: and it will speed up them<br>
1.4 lievre 390: Each of the four lines starts with indices "ij": <b>ij
1.6 ! lievre 391: aij bij</b> </p>
! 392:
! 393: <blockquote>
! 394: <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
! 395: 12 -14.155633 0.110794
! 396: 13 -7.925360 0.032091
! 397: 21 -1.890135 -0.029473
! 398: 23 -6.234642 0.022315 </pre>
! 399: </blockquote>
! 400:
! 401: <p>or, to simplify: </p>
! 402:
! 403: <blockquote>
! 404: <pre>12 0.0 0.0
! 405: 13 0.0 0.0
! 406: 21 0.0 0.0
! 407: 23 0.0 0.0</pre>
! 408: </blockquote>
! 409:
! 410: <h4><font color="#FF0000">Guess values for computing variances</font></h4>
1.2 lievre 411:
1.6 ! lievre 412: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
! 413: used as an input to get the various output data files (Health
1.2 lievre 414: expectancies, stationary prevalence etc.) and figures without
1.6 ! lievre 415: rerunning the rather long maximisation phase (mle=0). </p>
1.2 lievre 416:
1.6 ! lievre 417: <p>The scales are small values for the evaluation of numerical
1.2 lievre 418: derivatives. These derivatives are used to compute the hessian
419: matrix of the parameters, that is the inverse of the covariance
420: matrix, and the variances of health expectancies. Each line
421: consists in indices "ij" followed by the initial scales
1.6 ! lievre 422: (zero to simplify) associated with aij and bij. </p>
1.2 lievre 423:
1.6 ! lievre 424: <ul>
! 425: <li>If mle=1 you can enter zeros:</li>
1.2 lievre 426: </ul>
427:
1.6 ! lievre 428: <blockquote>
! 429: <pre># Scales (for hessian or gradient estimation)
! 430: 12 0. 0.
! 431: 13 0. 0.
! 432: 21 0. 0.
! 433: 23 0. 0. </pre>
! 434: </blockquote>
! 435:
! 436: <ul>
! 437: <li>If mle=0 you must enter a covariance matrix (usually
! 438: obtained from an earlier run).</li>
1.2 lievre 439: </ul>
440:
1.6 ! lievre 441: <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
! 442:
! 443: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
! 444: used as an input to get the various output data files (Health
1.5 lievre 445: expectancies, stationary prevalence etc.) and figures without
1.6 ! lievre 446: rerunning the rather long maximisation phase (mle=0). </p>
1.2 lievre 447:
1.6 ! lievre 448: <p>Each line starts with indices "ijk" followed by the
! 449: covariances between aij and bij: </p>
1.5 lievre 450:
1.6 ! lievre 451: <pre>
! 452: 121 Var(a12)
! 453: 122 Cov(b12,a12) Var(b12)
! 454: ...
! 455: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
1.2 lievre 456:
1.6 ! lievre 457: <ul>
! 458: <li>If mle=1 you can enter zeros. </li>
1.2 lievre 459: </ul>
460:
1.6 ! lievre 461: <blockquote>
! 462: <pre># Covariance matrix
! 463: 121 0.
! 464: 122 0. 0.
! 465: 131 0. 0. 0.
! 466: 132 0. 0. 0. 0.
! 467: 211 0. 0. 0. 0. 0.
! 468: 212 0. 0. 0. 0. 0. 0.
! 469: 231 0. 0. 0. 0. 0. 0. 0.
! 470: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
! 471: </blockquote>
! 472:
! 473: <ul>
! 474: <li>If mle=0 you must enter a covariance matrix (usually
! 475: obtained from an earlier run).<br>
! 476: </li>
1.2 lievre 477: </ul>
478:
1.6 ! lievre 479: <h4><font color="#FF0000">Age range for calculation of stationary
! 480: prevalences and health expectancies</font></h4>
1.2 lievre 481:
1.6 ! lievre 482: <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
1.2 lievre 483:
1.6 ! lievre 484: <p>Once we obtained the estimated parameters, the program is able
! 485: to calculated stationary prevalence, transitions probabilities
! 486: and life expectancies at any age. Choice of age range is useful
! 487: for extrapolation. In our data file, ages varies from age 70 to
! 488: 102. Setting bage=50 and fage=100, makes the program computing
! 489: life expectancy from age bage to age fage. As we use a model, we
! 490: can compute life expectancy on a wider age range than the age
! 491: range from the data. But the model can be rather wrong on big
! 492: intervals.</p>
! 493:
! 494: <p>Similarly, it is possible to get extrapolated stationary
! 495: prevalence by age ranging from agemin to agemax. </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>
1.2 lievre 506: </ul>
507:
1.6 ! lievre 508: <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
! 509: color="#FF0000"> the observed prevalence</font></h4>
1.4 lievre 510:
1.6 ! lievre 511: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
1.4 lievre 512:
1.6 ! lievre 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>
1.4 lievre 523: </ul>
524:
1.6 ! lievre 525: <h4><font color="#FF0000">Population- or status-based health
! 526: expectancies</font></h4>
1.5 lievre 527:
1.6 ! lievre 528: <pre>pop_based=0</pre>
1.5 lievre 529:
1.6 ! lievre 530: <p>The user has the possibility to choose between
! 531: population-based or status-based health expectancies. If
! 532: pop_based=0 then status-based health expectancies are computed
! 533: and if pop_based=1, the programme computes population-based
! 534: health expectancies. Health expectancies are weighted averages of
! 535: health expectancies respective of the initial state. For a
! 536: status-based index, the weights are the cross-sectional
! 537: prevalences observed between two dates, as <a href="#Computing">previously
! 538: explained</a>, whereas for a population-based index, the weights
! 539: are the stationary prevalences.</p>
1.5 lievre 540:
1.6 ! lievre 541: <h4><font color="#FF0000">Prevalence forecasting </font></h4>
1.5 lievre 542:
1.6 ! lievre 543: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
1.5 lievre 544:
1.6 ! lievre 545: <p>Prevalence and population projections are only available if
! 546: the interpolation unit is a month, i.e. stepm=1. The programme
! 547: estimates the prevalence in each state at a precise date
! 548: expressed in day/month/year. The programme computes one
! 549: forecasted prevalence a year from a starting date (1 january of
! 550: 1989 in this example) to a final date (1 january 1992). The
! 551: statement mov_average allows to compute smoothed forecasted
! 552: prevalences with a five-age moving average centered at the
! 553: mid-age of the five-age period. </p>
1.5 lievre 554:
1.6 ! lievre 555: <ul>
! 556: <li><strong>starting-proj-date</strong>= starting date
! 557: (day/month/year) of forecasting</li>
! 558: <li><strong>final-proj-date= </strong>final date
! 559: (day/month/year) of forecasting</li>
! 560: <li><strong>mov_average</strong>= smoothing with a five-age
! 561: moving average centered at the mid-age of the five-age
! 562: period. The command<strong> mov_average</strong> takes
! 563: value 1 if the prevalences are smoothed and 0 otherwise.</li>
! 564: </ul>
1.5 lievre 565:
1.6 ! lievre 566: <h4><font color="#FF0000">Last uncommented line : Population
! 567: forecasting </font></h4>
1.5 lievre 568:
1.6 ! lievre 569: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
1.5 lievre 570:
1.6 ! lievre 571: <p>This command is available if the interpolation unit is a
! 572: month, i.e. stepm=1 and if popforecast=1. From a data file </p>
1.5 lievre 573:
1.6 ! lievre 574: <p>Structure of the data file <a href="pyram.txt"><b>pyram.txt</b></a><b>
! 575: : </b>age numbers</p>
1.5 lievre 576:
1.6 ! lievre 577: <p> </p>
1.5 lievre 578:
1.6 ! lievre 579: <hr>
1.5 lievre 580:
1.6 ! lievre 581: <h2><a name="running"></a><font color="#00006A">Running Imach
! 582: with this example</font></h2>
1.5 lievre 583:
1.6 ! lievre 584: <p>We assume that you entered your <a href="biaspar.imach">1st_example
! 585: parameter file</a> as explained <a href="#biaspar">above</a>. To
! 586: run the program you should click on the imach.exe icon and enter
! 587: the name of the parameter file which is for example <a
! 588: href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a>
! 589: (you also can click on the biaspar.txt icon located in <br>
! 590: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with
! 591: the mouse on the imach window).<br>
! 592: </p>
! 593:
! 594: <p>The time to converge depends on the step unit that you used (1
! 595: month is cpu consuming), on the number of cases, and on the
! 596: number of variables.</p>
1.5 lievre 597:
1.6 ! lievre 598: <p>The program outputs many files. Most of them are files which
! 599: will be plotted for better understanding.</p>
1.5 lievre 600:
1.6 ! lievre 601: <hr>
1.5 lievre 602:
1.6 ! lievre 603: <h2><a name="output"><font color="#00006A">Output of the program
! 604: and graphs</font> </a></h2>
1.5 lievre 605:
1.6 ! lievre 606: <p>Once the optimization is finished, some graphics can be made
! 607: with a grapher. We use Gnuplot which is an interactive plotting
! 608: program copyrighted but freely distributed. A gnuplot reference
! 609: manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
! 610: When the running is finished, the user should enter a caracter
! 611: for plotting and output editing. </p>
! 612:
! 613: <p>These caracters are:</p>
! 614:
! 615: <ul>
! 616: <li>'c' to start again the program from the beginning.</li>
! 617: <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
! 618: file to edit the output files and graphs. </li>
! 619: <li>'q' for exiting.</li>
! 620: </ul>
1.4 lievre 621:
1.6 ! lievre 622: <h5><font size="4"><strong>Results files </strong></font><br>
! 623: <br>
! 624: <font color="#EC5E5E" size="3"><strong>- </strong></font><a
! 625: name="Observed prevalence in each state"><font color="#EC5E5E"
! 626: size="3"><strong>Observed prevalence in each state</strong></font></a><font
! 627: color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
! 628: </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
! 629: </h5>
! 630:
! 631: <p>The first line is the title and displays each field of the
! 632: file. The first column is age. The fields 2 and 6 are the
! 633: proportion of individuals in states 1 and 2 respectively as
! 634: observed during the first exam. Others fields are the numbers of
! 635: people in states 1, 2 or more. The number of columns increases if
! 636: the number of states is higher than 2.<br>
! 637: The header of the file is </p>
! 638:
! 639: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
! 640: 70 1.00000 631 631 70 0.00000 0 631
! 641: 71 0.99681 625 627 71 0.00319 2 627
! 642: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
! 643:
! 644: <p>It means that at age 70, the prevalence in state 1 is 1.000
! 645: and in state 2 is 0.00 . At age 71 the number of individuals in
! 646: state 1 is 625 and in state 2 is 2, hence the total number of
! 647: people aged 71 is 625+2=627. <br>
! 648: </p>
! 649:
! 650: <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
! 651: covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.txt</b></a></h5>
! 652:
! 653: <p>This file contains all the maximisation results: </p>
! 654:
! 655: <pre> -2 log likelihood= 21660.918613445392
! 656: Estimated parameters: a12 = -12.290174 b12 = 0.092161
! 657: a13 = -9.155590 b13 = 0.046627
! 658: a21 = -2.629849 b21 = -0.022030
! 659: a23 = -7.958519 b23 = 0.042614
! 660: Covariance matrix: Var(a12) = 1.47453e-001
! 661: Var(b12) = 2.18676e-005
! 662: Var(a13) = 2.09715e-001
! 663: Var(b13) = 3.28937e-005
! 664: Var(a21) = 9.19832e-001
! 665: Var(b21) = 1.29229e-004
! 666: Var(a23) = 4.48405e-001
! 667: Var(b23) = 5.85631e-005
! 668: </pre>
! 669:
! 670: <p>By substitution of these parameters in the regression model,
! 671: we obtain the elementary transition probabilities:</p>
! 672:
! 673: <p><img src="pebiaspar1.gif" width="400" height="300"></p>
! 674:
! 675: <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
! 676: </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
! 677:
! 678: <p>Here are the transitions probabilities Pij(x, x+nh) where nh
! 679: is a multiple of 2 years. The first column is the starting age x
! 680: (from age 50 to 100), the second is age (x+nh) and the others are
! 681: the transition probabilities p11, p12, p13, p21, p22, p23. For
! 682: example, line 5 of the file is: </p>
! 683:
! 684: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
! 685:
! 686: <p>and this means: </p>
! 687:
! 688: <pre>p11(100,106)=0.02655
! 689: p12(100,106)=0.17622
! 690: p13(100,106)=0.79722
! 691: p21(100,106)=0.01809
! 692: p22(100,106)=0.13678
! 693: p22(100,106)=0.84513 </pre>
! 694:
! 695: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 696: name="Stationary prevalence in each state"><font color="#EC5E5E"
! 697: size="3"><b>Stationary prevalence in each state</b></font></a><b>:
! 698: </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
! 699:
! 700: <pre>#Prevalence
! 701: #Age 1-1 2-2
! 702:
! 703: #************
! 704: 70 0.90134 0.09866
! 705: 71 0.89177 0.10823
! 706: 72 0.88139 0.11861
! 707: 73 0.87015 0.12985 </pre>
1.4 lievre 708:
1.6 ! lievre 709: <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
1.3 lievre 710: 0.09866 in state 2. This stationary prevalence differs from
1.2 lievre 711: observed prevalence. Here is the point. The observed prevalence
712: at age 70 results from the incidence of disability, incidence of
713: recovery and mortality which occurred in the past of the cohort.
714: Stationary prevalence results from a simulation with actual
715: incidences and mortality (estimated from this cross-longitudinal
716: survey). It is the best predictive value of the prevalence in the
717: future if "nothing changes in the future". This is
718: exactly what demographers do with a Life table. Life expectancy
719: is the expected mean time to survive if observed mortality rates
720: (incidence of mortality) "remains constant" in the
1.6 ! lievre 721: future. </p>
1.2 lievre 722:
1.6 ! lievre 723: <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
! 724: stationary prevalence</b></font><b>: </b><a
! 725: href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
! 726:
! 727: <p>The stationary prevalence has to be compared with the observed
1.2 lievre 728: prevalence by age. But both are statistical estimates and
729: subjected to stochastic errors due to the size of the sample, the
730: design of the survey, and, for the stationary prevalence to the
731: model used and fitted. It is possible to compute the standard
1.6 ! lievre 732: deviation of the stationary prevalence at each age.</p>
! 733:
! 734: <h5><font color="#EC5E5E" size="3">-Observed and stationary
! 735: prevalence in state (2=disable) with the confident interval</font>:<b>
! 736: </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
! 737:
! 738: <p>This graph exhibits the stationary prevalence in state (2)
! 739: with the confidence interval in red. The green curve is the
! 740: observed prevalence (or proportion of individuals in state (2)).
! 741: Without discussing the results (it is not the purpose here), we
! 742: observe that the green curve is rather below the stationary
! 743: prevalence. It suggests an increase of the disability prevalence
! 744: in the future.</p>
! 745:
! 746: <p><img src="vbiaspar21.gif" width="400" height="300"></p>
! 747:
! 748: <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
! 749: stationary prevalence of disability</b></font><b>: </b><a
! 750: href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
! 751: <img src="pbiaspar11.gif" width="400" height="300"> </h5>
1.2 lievre 752:
1.6 ! lievre 753: <p>This graph plots the conditional transition probabilities from
! 754: an initial state (1=healthy in red at the bottom, or 2=disable in
1.2 lievre 755: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
756: age <em>x+h. </em>Conditional means at the condition to be alive
757: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
758: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
759: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
760: prevalence of disability</em>. In order to get the stationary
761: prevalence at age 70 we should start the process at an earlier
762: age, i.e.50. If the disability state is defined by severe
763: disability criteria with only a few chance to recover, then the
764: incidence of recovery is low and the time to convergence is
1.6 ! lievre 765: probably longer. But we don't have experience yet.</p>
1.2 lievre 766:
1.6 ! lievre 767: <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
! 768: and initial health status</b></font><b>: </b><a
! 769: href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
! 770:
! 771: <pre># Health expectancies
! 772: # Age 1-1 1-2 2-1 2-2
! 773: 70 10.9226 3.0401 5.6488 6.2122
! 774: 71 10.4384 3.0461 5.2477 6.1599
! 775: 72 9.9667 3.0502 4.8663 6.1025
! 776: 73 9.5077 3.0524 4.5044 6.0401 </pre>
1.2 lievre 777:
1.6 ! lievre 778: <pre>For example 70 10.9226 3.0401 5.6488 6.2122 means:
! 779: e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122</pre>
1.2 lievre 780:
1.6 ! lievre 781: <pre><img src="expbiaspar21.gif" width="400" height="300"><img
! 782: src="expbiaspar11.gif" width="400" height="300"></pre>
1.2 lievre 783:
1.6 ! lievre 784: <p>For example, life expectancy of a healthy individual at age 70
! 785: is 10.92 in the healthy state and 3.04 in the disability state
1.3 lievre 786: (=13.96 years). If he was disable at age 70, his life expectancy
787: will be shorter, 5.64 in the healthy state and 6.21 in the
788: disability state (=11.85 years). The total life expectancy is a
789: weighted mean of both, 13.96 and 11.85; weight is the proportion
1.2 lievre 790: of people disabled at age 70. In order to get a pure period index
1.6 ! lievre 791: (i.e. based only on incidences) we use the <a
! 792: href="#Stationary prevalence in each state">computed or
! 793: stationary prevalence</a> at age 70 (i.e. computed from
! 794: incidences at earlier ages) instead of the <a
! 795: href="#Observed prevalence in each state">observed prevalence</a>
! 796: (for example at first exam) (<a href="#Health expectancies">see
! 797: below</a>).</p>
! 798:
! 799: <h5><font color="#EC5E5E" size="3"><b>- Variances of life
! 800: expectancies by age and initial health status</b></font><b>: </b><a
! 801: href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
! 802:
! 803: <p>For example, the covariances of life expectancies Cov(ei,ej)
! 804: at age 50 are (line 3) </p>
! 805:
! 806: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
! 807:
! 808: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
! 809: name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
! 810: expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
! 811: with standard errors in parentheses</b></font><b>: </b><a
! 812: href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
! 813:
! 814: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
! 815:
! 816: <pre>70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) </pre>
! 817:
! 818: <p>Thus, at age 70 the total life expectancy, e..=13.76years is
! 819: the weighted mean of e1.=13.96 and e2.=11.85 by the stationary
1.3 lievre 820: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
821: state 2, respectively (the sum is equal to one). e.1=10.40 is the
1.2 lievre 822: Disability-free life expectancy at age 70 (it is again a weighted
1.3 lievre 823: mean of e11 and e21). e.2=3.35 is also the life expectancy at age
1.6 ! lievre 824: 70 to be spent in the disability state.</p>
1.2 lievre 825:
1.6 ! lievre 826: <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
! 827: age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
! 828: </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
! 829:
! 830: <p>This figure represents the health expectancies and the total
! 831: life expectancy with the confident interval in dashed curve. </p>
! 832:
! 833: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
! 834:
! 835: <p>Standard deviations (obtained from the information matrix of
! 836: the model) of these quantities are very useful.
! 837: Cross-longitudinal surveys are costly and do not involve huge
! 838: samples, generally a few thousands; therefore it is very
! 839: important to have an idea of the standard deviation of our
! 840: estimates. It has been a big challenge to compute the Health
! 841: Expectancy standard deviations. Don't be confuse: life expectancy
! 842: is, as any expected value, the mean of a distribution; but here
! 843: we are not computing the standard deviation of the distribution,
! 844: but the standard deviation of the estimate of the mean.</p>
! 845:
! 846: <p>Our health expectancies estimates vary according to the sample
! 847: size (and the standard deviations give confidence intervals of
! 848: the estimate) but also according to the model fitted. Let us
! 849: explain it in more details.</p>
! 850:
! 851: <p>Choosing a model means ar least two kind of choices. First we
! 852: have to decide the number of disability states. Second we have to
! 853: design, within the logit model family, the model: variables,
! 854: covariables, confonding factors etc. to be included.</p>
! 855:
! 856: <p>More disability states we have, better is our demographical
! 857: approach of the disability process, but smaller are the number of
1.2 lievre 858: transitions between each state and higher is the noise in the
859: measurement. We do not have enough experiments of the various
860: models to summarize the advantages and disadvantages, but it is
861: important to say that even if we had huge and unbiased samples,
862: the total life expectancy computed from a cross-longitudinal
863: survey, varies with the number of states. If we define only two
864: states, alive or dead, we find the usual life expectancy where it
865: is assumed that at each age, people are at the same risk to die.
866: If we are differentiating the alive state into healthy and
867: disable, and as the mortality from the disability state is higher
868: than the mortality from the healthy state, we are introducing
869: heterogeneity in the risk of dying. The total mortality at each
870: age is the weighted mean of the mortality in each state by the
871: prevalence in each state. Therefore if the proportion of people
872: at each age and in each state is different from the stationary
873: equilibrium, there is no reason to find the same total mortality
874: at a particular age. Life expectancy, even if it is a very useful
875: tool, has a very strong hypothesis of homogeneity of the
876: population. Our main purpose is not to measure differential
877: mortality but to measure the expected time in a healthy or
878: disability state in order to maximise the former and minimize the
879: latter. But the differential in mortality complexifies the
1.6 ! lievre 880: measurement.</p>
1.2 lievre 881:
1.6 ! lievre 882: <p>Incidences of disability or recovery are not affected by the
! 883: number of states if these states are independant. But incidences
! 884: estimates are dependant on the specification of the model. More
! 885: covariates we added in the logit model better is the model, but
! 886: some covariates are not well measured, some are confounding
! 887: factors like in any statistical model. The procedure to "fit
! 888: the best model' is similar to logistic regression which itself is
! 889: similar to regression analysis. We haven't yet been sofar because
! 890: we also have a severe limitation which is the speed of the
! 891: convergence. On a Pentium III, 500 MHz, even the simplest model,
! 892: estimated by month on 8,000 people may take 4 hours to converge.
! 893: Also, the program is not yet a statistical package, which permits
! 894: a simple writing of the variables and the model to take into
! 895: account in the maximisation. The actual program allows only to
! 896: add simple variables like age+sex or age+sex+ age*sex but will
! 897: never be general enough. But what is to remember, is that
1.2 lievre 898: incidences or probability of change from one state to another is
1.6 ! lievre 899: affected by the variables specified into the model.</p>
1.2 lievre 900:
1.6 ! lievre 901: <p>Also, the age range of the people interviewed has a link with
! 902: the age range of the life expectancy which can be estimated by
1.2 lievre 903: extrapolation. If your sample ranges from age 70 to 95, you can
904: clearly estimate a life expectancy at age 70 and trust your
905: confidence interval which is mostly based on your sample size,
906: but if you want to estimate the life expectancy at age 50, you
907: should rely in your model, but fitting a logistic model on a age
1.6 ! lievre 908: range of 70-95 and estimating probabilties of transition out of
1.2 lievre 909: this age range, say at age 50 is very dangerous. At least you
910: should remember that the confidence interval given by the
911: standard deviation of the health expectancies, are under the
912: strong assumption that your model is the 'true model', which is
1.6 ! lievre 913: probably not the case.</p>
1.5 lievre 914:
1.6 ! lievre 915: <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
! 916: file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
1.2 lievre 917:
1.6 ! lievre 918: <p>This copy of the parameter file can be useful to re-run the
! 919: program while saving the old output files. </p>
1.2 lievre 920:
1.6 ! lievre 921: <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
! 922: </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
1.2 lievre 923:
1.6 ! lievre 924: <p>On a d'abord estimé la date moyenne des interviaew. ie
! 925: 13/9/1995. This file contains </p>
1.4 lievre 926:
1.6 ! lievre 927: <p>Example, at date 1/1/1989 : </p>
1.4 lievre 928:
1.6 ! lievre 929: <p>73 0.807 0.078 0.115 </p>
1.4 lievre 930:
1.6 ! lievre 931: <p>This means that at age 73, the probability for a person age 70
! 932: at 13/9/1989 to be in state 1 is 0.807, in state 2 is 0.078 and
! 933: to die is 0.115 at 1/1/1989.</p>
1.4 lievre 934:
1.6 ! lievre 935: <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
! 936: </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
1.4 lievre 937:
1.6 ! lievre 938: <pre># Age P.1 P.2 P.3 [Population]
! 939: # Forecasting at date 1/1/1989
! 940: 75 572685.22 83798.08
! 941: 74 621296.51 79767.99
! 942: 73 645857.70 69320.60 </pre>
1.4 lievre 943:
1.6 ! lievre 944: <pre># Forecasting at date 1/1/19909
! 945: 76 442986.68 92721.14 120775.48
! 946: 75 487781.02 91367.97 121915.51
! 947: 74 512892.07 85003.47 117282.76 </pre>
1.4 lievre 948:
1.6 ! lievre 949: <hr>
1.4 lievre 950:
1.6 ! lievre 951: <h2><a name="example" </a><font color="#00006A">Trying an example</font></a></h2>
1.5 lievre 952:
1.6 ! lievre 953: <p>Since you know how to run the program, it is time to test it
! 954: on your own computer. Try for example on a parameter file named <a
! 955: href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of <font
! 956: size="2" face="Courier New">mypar.txt</font> included in the
! 957: subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
! 958: Edit it to change the name of the data file to <font size="2"
! 959: face="Courier New">..\data\mydata.txt</font> if you don't want to
! 960: copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
! 961: is a smaller file of 3,000 people but still with 4 waves. </p>
1.5 lievre 962:
1.6 ! lievre 963: <p>Click on the imach.exe icon to open a window. Answer to the
! 964: question:'<strong>Enter the parameter file name:'</strong></p>
1.5 lievre 965:
1.6 ! lievre 966: <table border="1">
1.2 lievre 967: <tr>
1.6 ! lievre 968: <td width="100%"><strong>IMACH, Version 0.7</strong><p><strong>Enter
! 969: the parameter file name: ..\mytry\imachpar.txt</strong></p>
1.2 lievre 970: </td>
971: </tr>
972: </table>
973:
1.6 ! lievre 974: <p>Most of the data files or image files generated, will use the
1.2 lievre 975: 'imachpar' string into their name. The running time is about 2-3
976: minutes on a Pentium III. If the execution worked correctly, the
977: outputs files are created in the current directory, and should be
1.6 ! lievre 978: the same as the mypar files initially included in the directory <font
! 979: size="2" face="Courier New">mytry</font>.</p>
1.5 lievre 980:
1.6 ! lievre 981: <ul>
! 982: <li><pre><u>Output on the screen</u> The output screen looks like <a
! 983: href="imachrun.LOG">this Log file</a>
! 984: #
1.5 lievre 985:
1.6 ! lievre 986: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
! 987: ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
! 988: </li>
! 989: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
1.5 lievre 990:
1.6 ! lievre 991: Warning, no any valid information for:126 line=126
! 992: Warning, no any valid information for:2307 line=2307
! 993: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
! 994: <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
! 995: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
! 996: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
! 997: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
! 998: </li>
! 999: </ul>
1.2 lievre 1000:
1.6 ! lievre 1001: <p> </p>
1.2 lievre 1002:
1.6 ! lievre 1003: <ul>
! 1004: <li>Maximisation with the Powell algorithm. 8 directions are
! 1005: given corresponding to the 8 parameters. this can be
! 1006: rather long to get convergence.<br>
! 1007: <font size="1" face="Courier New"><br>
1.2 lievre 1008: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
1009: 0.000000000000 3<br>
1010: 0.000000000000 4 0.000000000000 5 0.000000000000 6
1011: 0.000000000000 7 <br>
1012: 0.000000000000 8 0.000000000000<br>
1013: 1..........2.................3..........4.................5.........<br>
1014: 6................7........8...............<br>
1015: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
1016: <br>
1017: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
1018: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
1019: 8 0.051272038506<br>
1020: 1..............2...........3..............4...........<br>
1021: 5..........6................7...........8.........<br>
1022: #Number of iterations = 23, -2 Log likelihood =
1023: 6744.954042573691<br>
1024: # Parameters<br>
1025: 12 -12.966061 0.135117 <br>
1026: 13 -7.401109 0.067831 <br>
1027: 21 -0.672648 -0.006627 <br>
1.6 ! lievre 1028: 23 -5.051297 0.051271 </font><br>
! 1029: </li>
! 1030: <li><pre><font size="2">Calculation of the hessian matrix. Wait...
! 1031: 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
! 1032:
! 1033: Inverting the hessian to get the covariance matrix. Wait...
! 1034:
! 1035: #Hessian matrix#
! 1036: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
! 1037: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
! 1038: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
! 1039: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
! 1040: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
! 1041: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
! 1042: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
! 1043: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
! 1044: # Scales
! 1045: 12 1.00000e-004 1.00000e-006
! 1046: 13 1.00000e-004 1.00000e-006
! 1047: 21 1.00000e-003 1.00000e-005
! 1048: 23 1.00000e-004 1.00000e-005
! 1049: # Covariance
! 1050: 1 5.90661e-001
! 1051: 2 -7.26732e-003 8.98810e-005
! 1052: 3 8.80177e-002 -1.12706e-003 5.15824e-001
! 1053: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
! 1054: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
! 1055: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
! 1056: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
! 1057: 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
! 1058: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
! 1059:
! 1060:
! 1061: agemin=70 agemax=100 bage=50 fage=100
! 1062: Computing prevalence limit: result on file 'plrmypar.txt'
! 1063: Computing pij: result on file 'pijrmypar.txt'
! 1064: Computing Health Expectancies: result on file 'ermypar.txt'
! 1065: Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
! 1066: Computing Total LEs with variances: file 'trmypar.txt'
! 1067: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
! 1068: End of Imach
! 1069: </font></pre>
! 1070: </li>
1.2 lievre 1071: </ul>
1072:
1.6 ! lievre 1073: <p><font size="3">Once the running is finished, the program
! 1074: requires a caracter:</font></p>
1.2 lievre 1075:
1.6 ! lievre 1076: <table border="1">
1.2 lievre 1077: <tr>
1.6 ! lievre 1078: <td width="100%"><strong>Type e to edit output files, c
! 1079: to start again, and q for exiting:</strong></td>
1.2 lievre 1080: </tr>
1081: </table>
1082:
1.6 ! lievre 1083: <p><font size="3">First you should enter <strong>e </strong>to
! 1084: edit the master file mypar.htm. </font></p>
! 1085:
! 1086: <ul>
! 1087: <li><u>Outputs files</u> <br>
1.3 lievre 1088: <br>
1.6 ! lievre 1089: - Observed prevalence in each state: <a
! 1090: href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
! 1091: - Estimated parameters and the covariance matrix: <a
! 1092: href="..\mytry\rmypar.txt">rmypar.txt</a> <br>
! 1093: - Stationary prevalence in each state: <a
! 1094: href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
! 1095: - Transition probabilities: <a
! 1096: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
! 1097: - Copy of the parameter file: <a
! 1098: href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
! 1099: - Life expectancies by age and initial health status: <a
! 1100: href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
1.2 lievre 1101: - Variances of life expectancies by age and initial
1.6 ! lievre 1102: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
1.2 lievre 1103: <br>
1.6 ! lievre 1104: - Health expectancies with their variances: <a
! 1105: href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
! 1106: - Standard deviation of stationary prevalence: <a
! 1107: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
! 1108: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
1.2 lievre 1109: <br>
1.6 ! lievre 1110: - Population forecasting (if popforecast=1): <a
! 1111: href="poprmypar.txt">poprmypar.txt</a> <br>
! 1112: </li>
! 1113: <li><u>Graphs</u> <br>
1.2 lievre 1114: <br>
1.6 ! lievre 1115: -<a href="../mytry/pemypar1.gif">One-step transition
! 1116: probabilities</a><br>
! 1117: -<a href="../mytry/pmypar11.gif">Convergence to the
! 1118: stationary prevalence</a><br>
! 1119: -<a href="..\mytry\vmypar11.gif">Observed and stationary
! 1120: prevalence in state (1) with the confident interval</a> <br>
! 1121: -<a href="..\mytry\vmypar21.gif">Observed and stationary
! 1122: prevalence in state (2) with the confident interval</a> <br>
! 1123: -<a href="..\mytry\expmypar11.gif">Health life
! 1124: expectancies by age and initial health state (1)</a> <br>
! 1125: -<a href="..\mytry\expmypar21.gif">Health life
! 1126: expectancies by age and initial health state (2)</a> <br>
! 1127: -<a href="..\mytry\emypar1.gif">Total life expectancy by
! 1128: age and health expectancies in states (1) and (2).</a> </li>
1.2 lievre 1129: </ul>
1130:
1.6 ! lievre 1131: <p>This software have been partly granted by <a
! 1132: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
1.2 lievre 1133: action from the European Union. It will be copyrighted
1134: identically to a GNU software product, i.e. program and software
1135: can be distributed freely for non commercial use. Sources are not
1136: widely distributed today. You can get them by asking us with a
1.6 ! lievre 1137: simple justification (name, email, institute) <a
! 1138: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
! 1139: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
! 1140:
! 1141: <p>Latest version (0.7 of February 2002) can be accessed at <a
! 1142: href="http://euroeves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
! 1143: </p>
1.2 lievre 1144: </body>
1145: </html>
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