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1.6 lievre 23: <h1 align="center"><font color="#00006A">Computing Health
24: Expectancies using IMaCh</font></h1>
1.2 lievre 25:
1.6 lievre 26: <h1 align="center"><font color="#00006A" size="5">(a Maximum
27: Likelihood Computer Program using Interpolation of Markov Chains)</font></h1>
28:
29: <p align="center"> </p>
30:
31: <p align="center"><a href="http://www.ined.fr/"><img
32: src="logo-ined.gif" border="0" width="151" height="76"></a><img
33: src="euroreves2.gif" width="151" height="75"></p>
34:
35: <h3 align="center"><a href="http://www.ined.fr/"><font
36: color="#00006A">INED</font></a><font color="#00006A"> and </font><a
37: href="http://euroreves.ined.fr"><font color="#00006A">EUROREVES</font></a></h3>
38:
39: <p align="center"><font color="#00006A" size="4"><strong>Version
1.12 ! brouard 40: 0.8, March 2002</strong></font></p>
1.6 lievre 41:
42: <hr size="3" color="#EC5E5E">
43:
44: <p align="center"><font color="#00006A"><strong>Authors of the
45: program: </strong></font><a href="http://sauvy.ined.fr/brouard"><font
46: color="#00006A"><strong>Nicolas Brouard</strong></font></a><font
47: color="#00006A"><strong>, senior researcher at the </strong></font><a
48: href="http://www.ined.fr"><font color="#00006A"><strong>Institut
49: National d'Etudes Démographiques</strong></font></a><font
50: color="#00006A"><strong> (INED, Paris) in the "Mortality,
51: Health and Epidemiology" Research Unit </strong></font></p>
52:
53: <p align="center"><font color="#00006A"><strong>and Agnès
54: Lièvre<br clear="left">
55: </strong></font></p>
56:
57: <h4><font color="#00006A">Contribution to the mathematics: C. R.
58: Heathcote </font><font color="#00006A" size="2">(Australian
59: National University, Canberra).</font></h4>
60:
61: <h4><font color="#00006A">Contact: Agnès Lièvre (</font><a
62: href="mailto:lievre@ined.fr"><font color="#00006A"><i>lievre@ined.fr</i></font></a><font
63: color="#00006A">) </font></h4>
1.2 lievre 64:
65: <hr>
1.6 lievre 66:
67: <ul>
68: <li><a href="#intro">Introduction</a> </li>
69: <li><a href="#data">On what kind of data can it be used?</a></li>
70: <li><a href="#datafile">The data file</a> </li>
71: <li><a href="#biaspar">The parameter file</a> </li>
72: <li><a href="#running">Running Imach</a> </li>
73: <li><a href="#output">Output files and graphs</a> </li>
74: <li><a href="#example">Exemple</a> </li>
1.2 lievre 75: </ul>
1.6 lievre 76:
1.2 lievre 77: <hr>
78:
1.6 lievre 79: <h2><a name="intro"><font color="#00006A">Introduction</font></a></h2>
1.2 lievre 80:
1.6 lievre 81: <p>This program computes <b>Healthy Life Expectancies</b> from <b>cross-longitudinal
82: data</b> using the methodology pioneered by Laditka and Wolf (1).
83: Within the family of Health Expectancies (HE), Disability-free
84: life expectancy (DFLE) is probably the most important index to
1.2 lievre 85: monitor. In low mortality countries, there is a fear that when
86: mortality declines, the increase in DFLE is not proportionate to
87: the increase in total Life expectancy. This case is called the <em>Expansion
88: of morbidity</em>. Most of the data collected today, in
1.7 brouard 89: particular by the international <a href="http://www.reves.org">REVES</a>
1.2 lievre 90: network on Health expectancy, and most HE indices based on these
91: data, are <em>cross-sectional</em>. It means that the information
92: collected comes from a single cross-sectional survey: people from
93: various ages (but mostly old people) are surveyed on their health
94: status at a single date. Proportion of people disabled at each
95: age, can then be measured at that date. This age-specific
96: prevalence curve is then used to distinguish, within the
97: stationary population (which, by definition, is the life table
98: estimated from the vital statistics on mortality at the same
99: date), the disable population from the disability-free
100: population. Life expectancy (LE) (or total population divided by
101: the yearly number of births or deaths of this stationary
102: population) is then decomposed into DFLE and DLE. This method of
103: computing HE is usually called the Sullivan method (from the name
1.6 lievre 104: of the author who first described it).</p>
1.2 lievre 105:
1.6 lievre 106: <p>Age-specific proportions of people disable are very difficult
107: to forecast because each proportion corresponds to historical
108: conditions of the cohort and it is the result of the historical
109: flows from entering disability and recovering in the past until
110: today. The age-specific intensities (or incidence rates) of
111: entering disability or recovering a good health, are reflecting
112: actual conditions and therefore can be used at each age to
113: forecast the future of this cohort. For example if a country is
114: improving its technology of prosthesis, the incidence of
115: recovering the ability to walk will be higher at each (old) age,
116: but the prevalence of disability will only slightly reflect an
117: improve because the prevalence is mostly affected by the history
118: of the cohort and not by recent period effects. To measure the
119: period improvement we have to simulate the future of a cohort of
120: new-borns entering or leaving at each age the disability state or
121: dying according to the incidence rates measured today on
122: different cohorts. The proportion of people disabled at each age
123: in this simulated cohort will be much lower (using the exemple of
124: an improvement) that the proportions observed at each age in a
125: cross-sectional survey. This new prevalence curve introduced in a
126: life table will give a much more actual and realistic HE level
127: than the Sullivan method which mostly measured the History of
128: health conditions in this country.</p>
129:
130: <p>Therefore, the main question is how to measure incidence rates
131: from cross-longitudinal surveys? This is the goal of the IMaCH
132: program. From your data and using IMaCH you can estimate period
133: HE and not only Sullivan's HE. Also the standard errors of the HE
134: are computed.</p>
135:
136: <p>A cross-longitudinal survey consists in a first survey
137: ("cross") where individuals from different ages are
138: interviewed on their health status or degree of disability. At
139: least a second wave of interviews ("longitudinal")
140: should measure each new individual health status. Health
141: expectancies are computed from the transitions observed between
142: waves and are computed for each degree of severity of disability
143: (number of life states). More degrees you consider, more time is
144: necessary to reach the Maximum Likelihood of the parameters
145: involved in the model. Considering only two states of disability
146: (disable and healthy) is generally enough but the computer
147: program works also with more health statuses.<br>
1.2 lievre 148: <br>
149: The simplest model is the multinomial logistic model where <i>pij</i>
150: is the probability to be observed in state <i>j</i> at the second
151: wave conditional to be observed in state <em>i</em> at the first
152: wave. Therefore a simple model is: log<em>(pij/pii)= aij +
153: bij*age+ cij*sex,</em> where '<i>age</i>' is age and '<i>sex</i>'
154: is a covariate. The advantage that this computer program claims,
155: comes from that if the delay between waves is not identical for
156: each individual, or if some individual missed an interview, the
157: information is not rounded or lost, but taken into account using
158: an interpolation or extrapolation. <i>hPijx</i> is the
159: probability to be observed in state <i>i</i> at age <i>x+h</i>
160: conditional to the observed state <i>i</i> at age <i>x</i>. The
161: delay '<i>h</i>' can be split into an exact number (<i>nh*stepm</i>)
162: of unobserved intermediate states. This elementary transition (by
163: month or quarter trimester, semester or year) is modeled as a
164: multinomial logistic. The <i>hPx</i> matrix is simply the matrix
165: product of <i>nh*stepm</i> elementary matrices and the
166: contribution of each individual to the likelihood is simply <i>hPijx</i>.
1.6 lievre 167: <br>
168: </p>
1.2 lievre 169:
1.6 lievre 170: <p>The program presented in this manual is a quite general
171: program named <strong>IMaCh</strong> (for <strong>I</strong>nterpolated
172: <strong>MA</strong>rkov <strong>CH</strong>ain), designed to
173: analyse transition data from longitudinal surveys. The first step
174: is the parameters estimation of a transition probabilities model
175: between an initial status and a final status. From there, the
176: computer program produces some indicators such as observed and
177: stationary prevalence, life expectancies and their variances and
178: graphs. Our transition model consists in absorbing and
179: non-absorbing states with the possibility of return across the
180: non-absorbing states. The main advantage of this package,
1.2 lievre 181: compared to other programs for the analysis of transition data
1.6 lievre 182: (For example: Proc Catmod of SAS<sup>®</sup>) is that the whole
1.2 lievre 183: individual information is used even if an interview is missing, a
184: status or a date is unknown or when the delay between waves is
185: not identical for each individual. The program can be executed
186: according to parameters: selection of a sub-sample, number of
187: absorbing and non-absorbing states, number of waves taken in
188: account (the user inputs the first and the last interview), a
189: tolerance level for the maximization function, the periodicity of
1.5 lievre 190: the transitions (we can compute annual, quarterly or monthly
1.2 lievre 191: transitions), covariates in the model. It works on Windows or on
1.6 lievre 192: Unix.<br>
193: </p>
1.2 lievre 194:
195: <hr>
196:
1.6 lievre 197: <p>(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New
1.2 lievre 198: Methods for Analyzing Active Life Expectancy". <i>Journal of
1.6 lievre 199: Aging and Health</i>. Vol 10, No. 2. </p>
1.2 lievre 200:
201: <hr>
202:
1.6 lievre 203: <h2><a name="data"><font color="#00006A">On what kind of data can
204: it be used?</font></a></h2>
1.2 lievre 205:
1.6 lievre 206: <p>The minimum data required for a transition model is the
207: recording of a set of individuals interviewed at a first date and
208: interviewed again at least one another time. From the
209: observations of an individual, we obtain a follow-up over time of
210: the occurrence of a specific event. In this documentation, the
211: event is related to health status at older ages, but the program
212: can be applied on a lot of longitudinal studies in different
213: contexts. To build the data file explained into the next section,
214: you must have the month and year of each interview and the
215: corresponding health status. But in order to get age, date of
216: birth (month and year) is required (missing values is allowed for
217: month). Date of death (month and year) is an important
218: information also required if the individual is dead. Shorter
219: steps (i.e. a month) will more closely take into account the
220: survival time after the last interview.</p>
1.2 lievre 221:
222: <hr>
223:
1.6 lievre 224: <h2><a name="datafile"><font color="#00006A">The data file</font></a></h2>
1.2 lievre 225:
1.6 lievre 226: <p>In this example, 8,000 people have been interviewed in a
227: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990).
228: Some people missed 1, 2 or 3 interviews. Health statuses are
229: healthy (1) and disable (2). The survey is not a real one. It is
230: a simulation of the American Longitudinal Survey on Aging. The
231: disability state is defined if the individual missed one of four
232: ADL (Activity of daily living, like bathing, eating, walking).
233: Therefore, even is the individuals interviewed in the sample are
234: virtual, the information brought with this sample is close to the
235: situation of the United States. Sex is not recorded is this
236: sample.</p>
237:
238: <p>Each line of the data set (named <a href="data1.txt">data1.txt</a>
239: in this first example) is an individual record which fields are: </p>
240:
241: <ul>
242: <li><b>Index number</b>: positive number (field 1) </li>
243: <li><b>First covariate</b> positive number (field 2) </li>
244: <li><b>Second covariate</b> positive number (field 3) </li>
245: <li><a name="Weight"><b>Weight</b></a>: positive number
246: (field 4) . In most surveys individuals are weighted
247: according to the stratification of the sample.</li>
248: <li><b>Date of birth</b>: coded as mm/yyyy. Missing dates are
249: coded as 99/9999 (field 5) </li>
250: <li><b>Date of death</b>: coded as mm/yyyy. Missing dates are
251: coded as 99/9999 (field 6) </li>
252: <li><b>Date of first interview</b>: coded as mm/yyyy. Missing
253: dates are coded as 99/9999 (field 7) </li>
254: <li><b>Status at first interview</b>: positive number.
255: Missing values ar coded -1. (field 8) </li>
256: <li><b>Date of second interview</b>: coded as mm/yyyy.
257: Missing dates are coded as 99/9999 (field 9) </li>
258: <li><strong>Status at second interview</strong> positive
259: number. Missing values ar coded -1. (field 10) </li>
260: <li><b>Date of third interview</b>: coded as mm/yyyy. Missing
261: dates are coded as 99/9999 (field 11) </li>
262: <li><strong>Status at third interview</strong> positive
263: number. Missing values ar coded -1. (field 12) </li>
264: <li><b>Date of fourth interview</b>: coded as mm/yyyy.
265: Missing dates are coded as 99/9999 (field 13) </li>
266: <li><strong>Status at fourth interview</strong> positive
267: number. Missing values are coded -1. (field 14) </li>
268: <li>etc</li>
1.2 lievre 269: </ul>
270:
1.6 lievre 271: <p> </p>
1.2 lievre 272:
1.6 lievre 273: <p>If your longitudinal survey do not include information about
274: weights or covariates, you must fill the column with a number
275: (e.g. 1) because a missing field is not allowed.</p>
1.2 lievre 276:
277: <hr>
278:
1.6 lievre 279: <h2><font color="#00006A">Your first example parameter file</font><a
280: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2>
1.2 lievre 281:
1.12 ! brouard 282: <h2><a name="biaspar"></a>#Imach version 0.8, March 2002,
1.6 lievre 283: INED-EUROREVES </h2>
1.2 lievre 284:
1.6 lievre 285: <p>This is a comment. Comments start with a '#'.</p>
1.2 lievre 286:
1.6 lievre 287: <h4><font color="#FF0000">First uncommented line</font></h4>
288:
289: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre>
290:
291: <ul>
292: <li><b>title=</b> 1st_example is title of the run. </li>
293: <li><b>datafile=</b>data1.txt is the name of the data set.
294: Our example is a six years follow-up survey. It consists
295: in a baseline followed by 3 reinterviews. </li>
296: <li><b>lastobs=</b> 8600 the program is able to run on a
297: subsample where the last observation number is lastobs.
298: It can be set a bigger number than the real number of
299: observations (e.g. 100000). In this example, maximisation
300: will be done on the 8600 first records. </li>
301: <li><b>firstpass=1</b> , <b>lastpass=4 </b>In case of more
302: than two interviews in the survey, the program can be run
303: on selected transitions periods. firstpass=1 means the
304: first interview included in the calculation is the
305: baseline survey. lastpass=4 means that the information
306: brought by the 4th interview is taken into account.</li>
1.2 lievre 307: </ul>
308:
1.6 lievre 309: <p> </p>
310:
311: <h4><a name="biaspar-2"><font color="#FF0000">Second uncommented
312: line</font></a></h4>
1.2 lievre 313:
1.12 ! brouard 314: <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
1.6 lievre 315:
316: <ul>
317: <li><b>ftol=1e-8</b> Convergence tolerance on the function
318: value in the maximisation of the likelihood. Choosing a
319: correct value for ftol is difficult. 1e-8 is a correct
320: value for a 32 bits computer.</li>
321: <li><b>stepm=1</b> Time unit in months for interpolation.
322: Examples:<ul>
323: <li>If stepm=1, the unit is a month </li>
324: <li>If stepm=4, the unit is a trimester</li>
325: <li>If stepm=12, the unit is a year </li>
326: <li>If stepm=24, the unit is two years</li>
327: <li>... </li>
1.2 lievre 328: </ul>
329: </li>
1.12 ! brouard 330: <li><b>ncovcol=2</b> Number of covariate columns in the datafile
! 331: which precede the date of birth. Here you can put variables that
! 332: won't necessary be used during the run. It is not the number of
! 333: covariates that will be specified by the model. The 'model'
! 334: syntax describe the covariates to take into account. </li>
1.6 lievre 335: <li><b>nlstate=2</b> Number of non-absorbing (alive) states.
336: Here we have two alive states: disability-free is coded 1
337: and disability is coded 2. </li>
338: <li><b>ndeath=1</b> Number of absorbing states. The absorbing
339: state death is coded 3. </li>
340: <li><b>maxwav=4</b> Number of waves in the datafile.</li>
341: <li><a name="mle"><b>mle</b></a><b>=1</b> Option for the
342: Maximisation Likelihood Estimation. <ul>
343: <li>If mle=1 the program does the maximisation and
344: the calculation of health expectancies </li>
345: <li>If mle=0 the program only does the calculation of
346: the health expectancies. </li>
1.2 lievre 347: </ul>
348: </li>
1.6 lievre 349: <li><b>weight=0</b> Possibility to add weights. <ul>
350: <li>If weight=0 no weights are included </li>
351: <li>If weight=1 the maximisation integrates the
352: weights which are in field <a href="#Weight">4</a></li>
1.2 lievre 353: </ul>
354: </li>
355: </ul>
356:
1.6 lievre 357: <h4><font color="#FF0000">Covariates</font></h4>
358:
359: <p>Intercept and age are systematically included in the model.
1.8 lievre 360: Additional covariates can be included with the command: </p>
1.2 lievre 361:
1.6 lievre 362: <pre>model=<em>list of covariates</em></pre>
363:
364: <ul>
365: <li>if<strong> model=. </strong>then no covariates are
366: included</li>
367: <li>if <strong>model=V1</strong> the model includes the first
368: covariate (field 2)</li>
369: <li>if <strong>model=V2 </strong>the model includes the
370: second covariate (field 3)</li>
371: <li>if <strong>model=V1+V2 </strong>the model includes the
372: first and the second covariate (fields 2 and 3)</li>
373: <li>if <strong>model=V1*V2 </strong>the model includes the
1.2 lievre 374: product of the first and the second covariate (fields 2
1.6 lievre 375: and 3)</li>
376: <li>if <strong>model=V1+V1*age</strong> the model includes
377: the product covariate*age</li>
1.2 lievre 378: </ul>
379:
1.8 lievre 380: <p>In this example, we have two covariates in the data file
1.12 ! brouard 381: (fields 2 and 3). The number of covariates included in the data file
! 382: between the id and the date of birth is ncovcol=2 (it was named ncov
! 383: in version prior to 0.8). If you have 3 covariates in the datafile
! 384: (fields 2, 3 and 4), you will set ncovcol=3. Then you can run the
1.8 lievre 385: programme with a new parametrisation taking into account the
386: third covariate. For example, <strong>model=V1+V3 </strong>estimates
387: a model with the first and third covariates. More complicated
388: models can be used, but it will takes more time to converge. With
389: a simple model (no covariates), the programme estimates 8
390: parameters. Adding covariates increases the number of parameters
391: : 12 for <strong>model=V1, </strong>16 for <strong>model=V1+V1*age
392: </strong>and 20 for <strong>model=V1+V2+V3.</strong></p>
393:
1.6 lievre 394: <h4><font color="#FF0000">Guess values for optimization</font><font
395: color="#00006A"> </font></h4>
396:
397: <p>You must write the initial guess values of the parameters for
398: optimization. The number of parameters, <em>N</em> depends on the
1.2 lievre 399: number of absorbing states and non-absorbing states and on the
400: number of covariates. <br>
401: <em>N</em> is given by the formula <em>N</em>=(<em>nlstate</em> +
1.12 ! brouard 402: <em>ndeath</em>-1)*<em>nlstate</em>*<em>ncovmodel</em> . <br>
1.2 lievre 403: <br>
404: Thus in the simple case with 2 covariates (the model is log
405: (pij/pii) = aij + bij * age where intercept and age are the two
406: covariates), and 2 health degrees (1 for disability-free and 2
407: for disability) and 1 absorbing state (3), you must enter 8
408: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
409: start with zeros as in this example, but if you have a more
410: precise set (for example from an earlier run) you can enter it
411: and it will speed up them<br>
1.4 lievre 412: Each of the four lines starts with indices "ij": <b>ij
1.6 lievre 413: aij bij</b> </p>
414:
415: <blockquote>
416: <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age
417: 12 -14.155633 0.110794
418: 13 -7.925360 0.032091
419: 21 -1.890135 -0.029473
420: 23 -6.234642 0.022315 </pre>
421: </blockquote>
422:
1.8 lievre 423: <p>or, to simplify (in most of cases it converges but there is no
424: warranty!): </p>
1.6 lievre 425:
426: <blockquote>
427: <pre>12 0.0 0.0
428: 13 0.0 0.0
429: 21 0.0 0.0
430: 23 0.0 0.0</pre>
431: </blockquote>
432:
1.9 brouard 433: <p> In order to speed up the convergence you can make a first run with
434: a large stepm i.e stepm=12 or 24 and then decrease the stepm until
435: stepm=1 month. If newstepm is the new shorter stepm and stepm can be
436: expressed as a multiple of newstepm, like newstepm=n stepm, then the
437: following approximation holds:
1.10 brouard 438: <pre>aij(stepm) = aij(n . stepm) - ln(n)
1.9 brouard 439: </pre> and
1.10 brouard 440: <pre>bij(stepm) = bij(n . stepm) .</pre>
441:
442: <p> For example if you already ran for a 6 months interval and
443: got:<br>
444: <pre># Parameters
445: 12 -13.390179 0.126133
446: 13 -7.493460 0.048069
447: 21 0.575975 -0.041322
448: 23 -4.748678 0.030626
449: </pre>
450: If you now want to get the monthly estimates, you can guess the aij by
451: substracting ln(6)= 1,7917<br> and running<br>
452: <pre>12 -15.18193847 0.126133
453: 13 -9.285219469 0.048069
454: 21 -1.215784469 -0.041322
455: 23 -6.540437469 0.030626
456: </pre>
457: and get<br>
458: <pre>12 -15.029768 0.124347
459: 13 -8.472981 0.036599
460: 21 -1.472527 -0.038394
461: 23 -6.553602 0.029856
462: </br>
463: which is closer to the results. The approximation is probably useful
464: only for very small intervals and we don't have enough experience to
465: know if you will speed up the convergence or not.
466: <pre> -ln(12)= -2.484
467: -ln(6/1)=-ln(6)= -1.791
468: -ln(3/1)=-ln(3)= -1.0986
469: -ln(12/6)=-ln(2)= -0.693
470: </pre>
471:
1.6 lievre 472: <h4><font color="#FF0000">Guess values for computing variances</font></h4>
1.2 lievre 473:
1.6 lievre 474: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
475: used as an input to get the various output data files (Health
1.2 lievre 476: expectancies, stationary prevalence etc.) and figures without
1.6 lievre 477: rerunning the rather long maximisation phase (mle=0). </p>
1.2 lievre 478:
1.6 lievre 479: <p>The scales are small values for the evaluation of numerical
1.2 lievre 480: derivatives. These derivatives are used to compute the hessian
481: matrix of the parameters, that is the inverse of the covariance
482: matrix, and the variances of health expectancies. Each line
483: consists in indices "ij" followed by the initial scales
1.6 lievre 484: (zero to simplify) associated with aij and bij. </p>
1.11 brouard 485: <ul> <li>If mle=1 you can enter zeros:</li>
486: <blockquote><pre># Scales (for hessian or gradient estimation)
1.6 lievre 487: 12 0. 0.
488: 13 0. 0.
489: 21 0. 0.
490: 23 0. 0. </pre>
491: </blockquote>
492: <li>If mle=0 you must enter a covariance matrix (usually
493: obtained from an earlier run).</li>
1.2 lievre 494: </ul>
495:
1.6 lievre 496: <h4><font color="#FF0000">Covariance matrix of parameters</font></h4>
497:
498: <p>This is an output if <a href="#mle">mle</a>=1. But it can be
499: used as an input to get the various output data files (Health
1.5 lievre 500: expectancies, stationary prevalence etc.) and figures without
1.11 brouard 501: rerunning the rather long maximisation phase (mle=0). <br>
502: Each line starts with indices "ijk" followed by the
503: covariances between aij and bij:<br>
1.6 lievre 504: <pre>
505: 121 Var(a12)
506: 122 Cov(b12,a12) Var(b12)
507: ...
508: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre>
509: <ul>
510: <li>If mle=1 you can enter zeros. </li>
511: <pre># Covariance matrix
512: 121 0.
513: 122 0. 0.
514: 131 0. 0. 0.
515: 132 0. 0. 0. 0.
516: 211 0. 0. 0. 0. 0.
517: 212 0. 0. 0. 0. 0. 0.
518: 231 0. 0. 0. 0. 0. 0. 0.
519: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre>
520: <li>If mle=0 you must enter a covariance matrix (usually
1.11 brouard 521: obtained from an earlier run). </li>
1.2 lievre 522: </ul>
523:
1.6 lievre 524: <h4><font color="#FF0000">Age range for calculation of stationary
525: prevalences and health expectancies</font></h4>
1.2 lievre 526:
1.6 lievre 527: <pre>agemin=70 agemax=100 bage=50 fage=100</pre>
1.2 lievre 528:
1.11 brouard 529: <br>Once we obtained the estimated parameters, the program is able
1.6 lievre 530: to calculated stationary prevalence, transitions probabilities
531: and life expectancies at any age. Choice of age range is useful
532: for extrapolation. In our data file, ages varies from age 70 to
1.8 lievre 533: 102. It is possible to get extrapolated stationary prevalence by
1.11 brouard 534: age ranging from agemin to agemax.
1.6 lievre 535:
1.11 brouard 536: <br>Setting bage=50 (begin age) and fage=100 (final age), makes
1.8 lievre 537: the program computing life expectancy from age 'bage' to age
538: 'fage'. As we use a model, we can interessingly compute life
539: expectancy on a wider age range than the age range from the data.
540: But the model can be rather wrong on much larger intervals.
1.11 brouard 541: Program is limited to around 120 for upper age!
1.6 lievre 542: <ul>
543: <li><b>agemin=</b> Minimum age for calculation of the
544: stationary prevalence </li>
545: <li><b>agemax=</b> Maximum age for calculation of the
546: stationary prevalence </li>
547: <li><b>bage=</b> Minimum age for calculation of the health
548: expectancies </li>
549: <li><b>fage=</b> Maximum age for calculation of the health
550: expectancies </li>
1.2 lievre 551: </ul>
552:
1.6 lievre 553: <h4><a name="Computing"><font color="#FF0000">Computing</font></a><font
554: color="#FF0000"> the observed prevalence</font></h4>
1.4 lievre 555:
1.6 lievre 556: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre>
1.4 lievre 557:
1.11 brouard 558: <br>Statements 'begin-prev-date' and 'end-prev-date' allow to
1.6 lievre 559: select the period in which we calculate the observed prevalences
560: in each state. In this example, the prevalences are calculated on
1.11 brouard 561: data survey collected between 1 january 1984 and 1 june 1988.
1.6 lievre 562: <ul>
563: <li><strong>begin-prev-date= </strong>Starting date
564: (day/month/year)</li>
565: <li><strong>end-prev-date= </strong>Final date
566: (day/month/year)</li>
1.4 lievre 567: </ul>
568:
1.6 lievre 569: <h4><font color="#FF0000">Population- or status-based health
570: expectancies</font></h4>
1.5 lievre 571:
1.6 lievre 572: <pre>pop_based=0</pre>
1.5 lievre 573:
1.8 lievre 574: <p>The program computes status-based health expectancies, i.e
575: health expectancies which depends on your initial health state.
576: If you are healthy your healthy life expectancy (e11) is higher
577: than if you were disabled (e21, with e11 > e21).<br>
578: To compute a healthy life expectancy independant of the initial
579: status we have to weight e11 and e21 according to the probability
580: to be in each state at initial age or, with other word, according
581: to the proportion of people in each state.<br>
582: We prefer computing a 'pure' period healthy life expectancy based
583: only on the transtion forces. Then the weights are simply the
584: stationnary prevalences or 'implied' prevalences at the initial
585: age.<br>
586: Some other people would like to use the cross-sectional
587: prevalences (the "Sullivan prevalences") observed at
588: the initial age during a period of time <a href="#Computing">defined
1.11 brouard 589: just above</a>. <br>
1.7 brouard 590:
591: <ul>
1.8 lievre 592: <li><strong>popbased= 0 </strong>Health expectancies are
593: computed at each age from stationary prevalences
594: 'expected' at this initial age.</li>
595: <li><strong>popbased= 1 </strong>Health expectancies are
596: computed at each age from cross-sectional 'observed'
597: prevalence at this initial age. As all the population is
598: not observed at the same exact date we define a short
599: period were the observed prevalence is computed.</li>
1.7 brouard 600: </ul>
601:
602: <h4><font color="#FF0000">Prevalence forecasting ( Experimental)</font></h4>
1.5 lievre 603:
1.6 lievre 604: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre>
1.5 lievre 605:
1.8 lievre 606: <p>Prevalence and population projections are only available if
607: the interpolation unit is a month, i.e. stepm=1 and if there are
608: no covariate. The programme estimates the prevalence in each
609: state at a precise date expressed in day/month/year. The
610: programme computes one forecasted prevalence a year from a
611: starting date (1 january of 1989 in this example) to a final date
612: (1 january 1992). The statement mov_average allows to compute
613: smoothed forecasted prevalences with a five-age moving average
1.11 brouard 614: centered at the mid-age of the five-age period. <br>
1.5 lievre 615:
1.6 lievre 616: <ul>
617: <li><strong>starting-proj-date</strong>= starting date
618: (day/month/year) of forecasting</li>
619: <li><strong>final-proj-date= </strong>final date
620: (day/month/year) of forecasting</li>
621: <li><strong>mov_average</strong>= smoothing with a five-age
622: moving average centered at the mid-age of the five-age
623: period. The command<strong> mov_average</strong> takes
624: value 1 if the prevalences are smoothed and 0 otherwise.</li>
625: </ul>
1.5 lievre 626:
1.6 lievre 627: <h4><font color="#FF0000">Last uncommented line : Population
628: forecasting </font></h4>
1.5 lievre 629:
1.6 lievre 630: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre>
1.5 lievre 631:
1.6 lievre 632: <p>This command is available if the interpolation unit is a
1.7 brouard 633: month, i.e. stepm=1 and if popforecast=1. From a data file
634: including age and number of persons alive at the precise date
635: ‘popfiledate’, you can forecast the number of persons
636: in each state until date ‘last-popfiledate’. In this
637: example, the popfile <a href="pyram.txt"><b>pyram.txt</b></a>
1.11 brouard 638: includes real data which are the Japanese population in 1989.<br>
1.7 brouard 639:
640: <ul type="disc">
641: <li class="MsoNormal"
642: 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=
643: 0 </b>Option for population forecasting. If
644: popforecast=1, the programme does the forecasting<b>.</b></li>
645: <li class="MsoNormal"
646: 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=
647: </b>name of the population file</li>
648: <li class="MsoNormal"
649: 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>
650: date of the population population</li>
651: <li class="MsoNormal"
652: 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>=
653: date of the last population projection </li>
654: </ul>
1.5 lievre 655:
1.6 lievre 656: <hr>
1.5 lievre 657:
1.6 lievre 658: <h2><a name="running"></a><font color="#00006A">Running Imach
659: with this example</font></h2>
1.5 lievre 660:
1.11 brouard 661: We assume that you typed in your <a href="biaspar.imach">1st_example
662: parameter file</a> as explained <a href="#biaspar">above</a>.
663: <br>To run the program you should either:
664: <ul> <li> click on the imach.exe icon and enter
1.6 lievre 665: the name of the parameter file which is for example <a
1.11 brouard 666: href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a>
667: <li> You also can locate the biaspar.imach icon in
668: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with
669: the mouse on the imach window).
670: <li> With latest version (0.7 and higher) if you setup windows in order to
671: understand ".imach" extension you can right click the
672: biaspar.imach icon and either edit with notepad the parameter file or
673: execute it with imach or whatever.
674: </ul>
1.6 lievre 675:
1.11 brouard 676: The time to converge depends on the step unit that you used (1
1.6 lievre 677: month is cpu consuming), on the number of cases, and on the
1.11 brouard 678: number of variables.
1.5 lievre 679:
1.11 brouard 680: <br>The program outputs many files. Most of them are files which
681: will be plotted for better understanding.
1.5 lievre 682:
1.6 lievre 683: <hr>
1.5 lievre 684:
1.6 lievre 685: <h2><a name="output"><font color="#00006A">Output of the program
686: and graphs</font> </a></h2>
1.5 lievre 687:
1.6 lievre 688: <p>Once the optimization is finished, some graphics can be made
689: with a grapher. We use Gnuplot which is an interactive plotting
690: program copyrighted but freely distributed. A gnuplot reference
691: manual is available <a href="http://www.gnuplot.info/">here</a>. <br>
692: When the running is finished, the user should enter a caracter
1.11 brouard 693: for plotting and output editing.
1.6 lievre 694:
1.11 brouard 695: <br>These caracters are:<br>
1.6 lievre 696:
697: <ul>
698: <li>'c' to start again the program from the beginning.</li>
699: <li>'e' opens the <a href="biaspar.htm"><strong>biaspar.htm</strong></a>
700: file to edit the output files and graphs. </li>
701: <li>'q' for exiting.</li>
702: </ul>
1.4 lievre 703:
1.6 lievre 704: <h5><font size="4"><strong>Results files </strong></font><br>
705: <br>
706: <font color="#EC5E5E" size="3"><strong>- </strong></font><a
707: name="Observed prevalence in each state"><font color="#EC5E5E"
708: size="3"><strong>Observed prevalence in each state</strong></font></a><font
709: color="#EC5E5E" size="3"><strong> (and at first pass)</strong></font><b>:
710: </b><a href="prbiaspar.txt"><b>prbiaspar.txt</b></a><br>
711: </h5>
712:
713: <p>The first line is the title and displays each field of the
714: file. The first column is age. The fields 2 and 6 are the
715: proportion of individuals in states 1 and 2 respectively as
716: observed during the first exam. Others fields are the numbers of
717: people in states 1, 2 or more. The number of columns increases if
718: the number of states is higher than 2.<br>
719: The header of the file is </p>
720:
721: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N
722: 70 1.00000 631 631 70 0.00000 0 631
723: 71 0.99681 625 627 71 0.00319 2 627
724: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre>
725:
726: <p>It means that at age 70, the prevalence in state 1 is 1.000
727: and in state 2 is 0.00 . At age 71 the number of individuals in
728: state 1 is 625 and in state 2 is 2, hence the total number of
729: people aged 71 is 625+2=627. <br>
730: </p>
731:
732: <h5><font color="#EC5E5E" size="3"><b>- Estimated parameters and
1.11 brouard 733: covariance matrix</b></font><b>: </b><a href="rbiaspar.txt"><b>rbiaspar.imach</b></a></h5>
1.6 lievre 734:
735: <p>This file contains all the maximisation results: </p>
736:
737: <pre> -2 log likelihood= 21660.918613445392
738: Estimated parameters: a12 = -12.290174 b12 = 0.092161
739: a13 = -9.155590 b13 = 0.046627
740: a21 = -2.629849 b21 = -0.022030
741: a23 = -7.958519 b23 = 0.042614
742: Covariance matrix: Var(a12) = 1.47453e-001
743: Var(b12) = 2.18676e-005
744: Var(a13) = 2.09715e-001
745: Var(b13) = 3.28937e-005
746: Var(a21) = 9.19832e-001
747: Var(b21) = 1.29229e-004
748: Var(a23) = 4.48405e-001
749: Var(b23) = 5.85631e-005
750: </pre>
751:
752: <p>By substitution of these parameters in the regression model,
753: we obtain the elementary transition probabilities:</p>
754:
755: <p><img src="pebiaspar1.gif" width="400" height="300"></p>
756:
757: <h5><font color="#EC5E5E" size="3"><b>- Transition probabilities</b></font><b>:
758: </b><a href="pijrbiaspar.txt"><b>pijrbiaspar.txt</b></a></h5>
759:
760: <p>Here are the transitions probabilities Pij(x, x+nh) where nh
761: is a multiple of 2 years. The first column is the starting age x
762: (from age 50 to 100), the second is age (x+nh) and the others are
763: the transition probabilities p11, p12, p13, p21, p22, p23. For
764: example, line 5 of the file is: </p>
765:
766: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre>
767:
768: <p>and this means: </p>
769:
770: <pre>p11(100,106)=0.02655
771: p12(100,106)=0.17622
772: p13(100,106)=0.79722
773: p21(100,106)=0.01809
774: p22(100,106)=0.13678
775: p22(100,106)=0.84513 </pre>
776:
777: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
778: name="Stationary prevalence in each state"><font color="#EC5E5E"
779: size="3"><b>Stationary prevalence in each state</b></font></a><b>:
780: </b><a href="plrbiaspar.txt"><b>plrbiaspar.txt</b></a></h5>
781:
782: <pre>#Prevalence
783: #Age 1-1 2-2
784:
785: #************
786: 70 0.90134 0.09866
787: 71 0.89177 0.10823
788: 72 0.88139 0.11861
789: 73 0.87015 0.12985 </pre>
1.4 lievre 790:
1.6 lievre 791: <p>At age 70 the stationary prevalence is 0.90134 in state 1 and
1.3 lievre 792: 0.09866 in state 2. This stationary prevalence differs from
1.2 lievre 793: observed prevalence. Here is the point. The observed prevalence
794: at age 70 results from the incidence of disability, incidence of
795: recovery and mortality which occurred in the past of the cohort.
796: Stationary prevalence results from a simulation with actual
797: incidences and mortality (estimated from this cross-longitudinal
798: survey). It is the best predictive value of the prevalence in the
799: future if "nothing changes in the future". This is
800: exactly what demographers do with a Life table. Life expectancy
801: is the expected mean time to survive if observed mortality rates
802: (incidence of mortality) "remains constant" in the
1.6 lievre 803: future. </p>
1.2 lievre 804:
1.6 lievre 805: <h5><font color="#EC5E5E" size="3"><b>- Standard deviation of
806: stationary prevalence</b></font><b>: </b><a
807: href="vplrbiaspar.txt"><b>vplrbiaspar.txt</b></a></h5>
808:
809: <p>The stationary prevalence has to be compared with the observed
1.2 lievre 810: prevalence by age. But both are statistical estimates and
811: subjected to stochastic errors due to the size of the sample, the
812: design of the survey, and, for the stationary prevalence to the
813: model used and fitted. It is possible to compute the standard
1.6 lievre 814: deviation of the stationary prevalence at each age.</p>
815:
816: <h5><font color="#EC5E5E" size="3">-Observed and stationary
817: prevalence in state (2=disable) with the confident interval</font>:<b>
818: </b><a href="vbiaspar21.htm"><b>vbiaspar21.gif</b></a></h5>
819:
820: <p>This graph exhibits the stationary prevalence in state (2)
821: with the confidence interval in red. The green curve is the
822: observed prevalence (or proportion of individuals in state (2)).
823: Without discussing the results (it is not the purpose here), we
824: observe that the green curve is rather below the stationary
825: prevalence. It suggests an increase of the disability prevalence
826: in the future.</p>
827:
828: <p><img src="vbiaspar21.gif" width="400" height="300"></p>
829:
830: <h5><font color="#EC5E5E" size="3"><b>-Convergence to the
831: stationary prevalence of disability</b></font><b>: </b><a
832: href="pbiaspar11.gif"><b>pbiaspar11.gif</b></a><br>
833: <img src="pbiaspar11.gif" width="400" height="300"> </h5>
1.2 lievre 834:
1.6 lievre 835: <p>This graph plots the conditional transition probabilities from
836: an initial state (1=healthy in red at the bottom, or 2=disable in
1.2 lievre 837: green on top) at age <em>x </em>to the final state 2=disable<em> </em>at
838: age <em>x+h. </em>Conditional means at the condition to be alive
839: at age <em>x+h </em>which is <i>hP12x</i> + <em>hP22x</em>. The
840: curves <i>hP12x/(hP12x</i> + <em>hP22x) </em>and <i>hP22x/(hP12x</i>
841: + <em>hP22x) </em>converge with <em>h, </em>to the <em>stationary
842: prevalence of disability</em>. In order to get the stationary
843: prevalence at age 70 we should start the process at an earlier
844: age, i.e.50. If the disability state is defined by severe
845: disability criteria with only a few chance to recover, then the
846: incidence of recovery is low and the time to convergence is
1.6 lievre 847: probably longer. But we don't have experience yet.</p>
1.2 lievre 848:
1.6 lievre 849: <h5><font color="#EC5E5E" size="3"><b>- Life expectancies by age
850: and initial health status</b></font><b>: </b><a
851: href="erbiaspar.txt"><b>erbiaspar.txt</b></a></h5>
852:
853: <pre># Health expectancies
854: # Age 1-1 1-2 2-1 2-2
855: 70 10.9226 3.0401 5.6488 6.2122
856: 71 10.4384 3.0461 5.2477 6.1599
857: 72 9.9667 3.0502 4.8663 6.1025
858: 73 9.5077 3.0524 4.5044 6.0401 </pre>
1.2 lievre 859:
1.7 brouard 860: <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means:
861: e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre>
1.2 lievre 862:
1.6 lievre 863: <pre><img src="expbiaspar21.gif" width="400" height="300"><img
864: src="expbiaspar11.gif" width="400" height="300"></pre>
1.2 lievre 865:
1.6 lievre 866: <p>For example, life expectancy of a healthy individual at age 70
1.7 brouard 867: is 10.42 in the healthy state and 3.04 in the disability state
868: (=13.46 years). If he was disable at age 70, his life expectancy
869: will be shorter, 5.64 in the healthy state and 5.71 in the
870: disability state (=11.35 years). The total life expectancy is a
871: weighted mean of both, 13.46 and 11.35; weight is the proportion
1.2 lievre 872: of people disabled at age 70. In order to get a pure period index
1.6 lievre 873: (i.e. based only on incidences) we use the <a
874: href="#Stationary prevalence in each state">computed or
875: stationary prevalence</a> at age 70 (i.e. computed from
876: incidences at earlier ages) instead of the <a
877: href="#Observed prevalence in each state">observed prevalence</a>
878: (for example at first exam) (<a href="#Health expectancies">see
879: below</a>).</p>
880:
881: <h5><font color="#EC5E5E" size="3"><b>- Variances of life
882: expectancies by age and initial health status</b></font><b>: </b><a
883: href="vrbiaspar.txt"><b>vrbiaspar.txt</b></a></h5>
884:
885: <p>For example, the covariances of life expectancies Cov(ei,ej)
886: at age 50 are (line 3) </p>
887:
888: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre>
889:
890: <h5><font color="#EC5E5E" size="3"><b>- </b></font><a
891: name="Health expectancies"><font color="#EC5E5E" size="3"><b>Health
892: expectancies</b></font></a><font color="#EC5E5E" size="3"><b>
893: with standard errors in parentheses</b></font><b>: </b><a
894: href="trbiaspar.txt"><font face="Courier New"><b>trbiaspar.txt</b></font></a></h5>
895:
896: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre>
897:
1.7 brouard 898: <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre>
1.6 lievre 899:
1.7 brouard 900: <p>Thus, at age 70 the total life expectancy, e..=13.26 years is
901: the weighted mean of e1.=13.46 and e2.=11.35 by the stationary
1.3 lievre 902: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in
1.7 brouard 903: state 2, respectively (the sum is equal to one). e.1=9.95 is the
1.2 lievre 904: Disability-free life expectancy at age 70 (it is again a weighted
1.7 brouard 905: mean of e11 and e21). e.2=3.30 is also the life expectancy at age
1.6 lievre 906: 70 to be spent in the disability state.</p>
1.2 lievre 907:
1.6 lievre 908: <h5><font color="#EC5E5E" size="3"><b>-Total life expectancy by
909: age and health expectancies in states (1=healthy) and (2=disable)</b></font><b>:
910: </b><a href="ebiaspar1.gif"><b>ebiaspar1.gif</b></a></h5>
911:
912: <p>This figure represents the health expectancies and the total
913: life expectancy with the confident interval in dashed curve. </p>
914:
915: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre>
916:
917: <p>Standard deviations (obtained from the information matrix of
918: the model) of these quantities are very useful.
919: Cross-longitudinal surveys are costly and do not involve huge
920: samples, generally a few thousands; therefore it is very
921: important to have an idea of the standard deviation of our
922: estimates. It has been a big challenge to compute the Health
923: Expectancy standard deviations. Don't be confuse: life expectancy
924: is, as any expected value, the mean of a distribution; but here
925: we are not computing the standard deviation of the distribution,
926: but the standard deviation of the estimate of the mean.</p>
927:
928: <p>Our health expectancies estimates vary according to the sample
929: size (and the standard deviations give confidence intervals of
930: the estimate) but also according to the model fitted. Let us
931: explain it in more details.</p>
932:
933: <p>Choosing a model means ar least two kind of choices. First we
934: have to decide the number of disability states. Second we have to
935: design, within the logit model family, the model: variables,
936: covariables, confonding factors etc. to be included.</p>
937:
938: <p>More disability states we have, better is our demographical
939: approach of the disability process, but smaller are the number of
1.2 lievre 940: transitions between each state and higher is the noise in the
941: measurement. We do not have enough experiments of the various
942: models to summarize the advantages and disadvantages, but it is
943: important to say that even if we had huge and unbiased samples,
944: the total life expectancy computed from a cross-longitudinal
945: survey, varies with the number of states. If we define only two
946: states, alive or dead, we find the usual life expectancy where it
947: is assumed that at each age, people are at the same risk to die.
948: If we are differentiating the alive state into healthy and
949: disable, and as the mortality from the disability state is higher
950: than the mortality from the healthy state, we are introducing
951: heterogeneity in the risk of dying. The total mortality at each
952: age is the weighted mean of the mortality in each state by the
953: prevalence in each state. Therefore if the proportion of people
954: at each age and in each state is different from the stationary
955: equilibrium, there is no reason to find the same total mortality
956: at a particular age. Life expectancy, even if it is a very useful
957: tool, has a very strong hypothesis of homogeneity of the
958: population. Our main purpose is not to measure differential
959: mortality but to measure the expected time in a healthy or
960: disability state in order to maximise the former and minimize the
961: latter. But the differential in mortality complexifies the
1.6 lievre 962: measurement.</p>
1.2 lievre 963:
1.6 lievre 964: <p>Incidences of disability or recovery are not affected by the
965: number of states if these states are independant. But incidences
966: estimates are dependant on the specification of the model. More
967: covariates we added in the logit model better is the model, but
968: some covariates are not well measured, some are confounding
969: factors like in any statistical model. The procedure to "fit
970: the best model' is similar to logistic regression which itself is
971: similar to regression analysis. We haven't yet been sofar because
972: we also have a severe limitation which is the speed of the
973: convergence. On a Pentium III, 500 MHz, even the simplest model,
974: estimated by month on 8,000 people may take 4 hours to converge.
975: Also, the program is not yet a statistical package, which permits
976: a simple writing of the variables and the model to take into
977: account in the maximisation. The actual program allows only to
978: add simple variables like age+sex or age+sex+ age*sex but will
979: never be general enough. But what is to remember, is that
1.2 lievre 980: incidences or probability of change from one state to another is
1.6 lievre 981: affected by the variables specified into the model.</p>
1.2 lievre 982:
1.6 lievre 983: <p>Also, the age range of the people interviewed has a link with
984: the age range of the life expectancy which can be estimated by
1.2 lievre 985: extrapolation. If your sample ranges from age 70 to 95, you can
986: clearly estimate a life expectancy at age 70 and trust your
987: confidence interval which is mostly based on your sample size,
988: but if you want to estimate the life expectancy at age 50, you
989: should rely in your model, but fitting a logistic model on a age
1.6 lievre 990: range of 70-95 and estimating probabilties of transition out of
1.2 lievre 991: this age range, say at age 50 is very dangerous. At least you
992: should remember that the confidence interval given by the
993: standard deviation of the health expectancies, are under the
994: strong assumption that your model is the 'true model', which is
1.6 lievre 995: probably not the case.</p>
1.5 lievre 996:
1.6 lievre 997: <h5><font color="#EC5E5E" size="3"><b>- Copy of the parameter
998: file</b></font><b>: </b><a href="orbiaspar.txt"><b>orbiaspar.txt</b></a></h5>
1.2 lievre 999:
1.6 lievre 1000: <p>This copy of the parameter file can be useful to re-run the
1001: program while saving the old output files. </p>
1.2 lievre 1002:
1.6 lievre 1003: <h5><font color="#EC5E5E" size="3"><b>- Prevalence forecasting</b></font><b>:
1004: </b><a href="frbiaspar.txt"><b>frbiaspar.txt</b></a></h5>
1.2 lievre 1005:
1.7 brouard 1006: <p
1007: 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,
1008: we have estimated the observed prevalence between 1/1/1984 and
1009: 1/6/1988. The mean date of interview (weighed average of the
1010: interviews performed between1/1/1984 and 1/6/1988) is estimated
1011: to be 13/9/1985, as written on the top on the file. Then we
1012: forecast the probability to be in each state. </p>
1013:
1014: <p
1015: 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,
1016: at date 1/1/1989 : </p>
1017:
1018: <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3
1019: # Forecasting at date 1/1/1989
1020: 73 0.807 0.078 0.115</pre>
1021:
1022: <p
1023: 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
1024: the minimum age is 70 on the 13/9/1985, the youngest forecasted
1025: age is 73. This means that at age a person aged 70 at 13/9/1989
1026: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
1027: Similarly, the probability to be in state 2 is 0.078 and the
1028: probability to die is 0.115. Then, on the 1/1/1989, the
1029: prevalence of disability at age 73 is estimated to be 0.088.</p>
1.4 lievre 1030:
1.6 lievre 1031: <h5><font color="#EC5E5E" size="3"><b>- Population forecasting</b></font><b>:
1032: </b><a href="poprbiaspar.txt"><b>poprbiaspar.txt</b></a></h5>
1.4 lievre 1033:
1.6 lievre 1034: <pre># Age P.1 P.2 P.3 [Population]
1035: # Forecasting at date 1/1/1989
1036: 75 572685.22 83798.08
1037: 74 621296.51 79767.99
1038: 73 645857.70 69320.60 </pre>
1.4 lievre 1039:
1.6 lievre 1040: <pre># Forecasting at date 1/1/19909
1041: 76 442986.68 92721.14 120775.48
1042: 75 487781.02 91367.97 121915.51
1043: 74 512892.07 85003.47 117282.76 </pre>
1.4 lievre 1044:
1.7 brouard 1045: <p>From the population file, we estimate the number of people in
1046: each state. At age 73, 645857 persons are in state 1 and 69320
1047: are in state 2. One year latter, 512892 are still in state 1,
1048: 85003 are in state 2 and 117282 died before 1/1/1990.</p>
1049:
1.6 lievre 1050: <hr>
1.4 lievre 1051:
1.8 lievre 1052: <h2><a name="example"></a><font color="#00006A">Trying an example</font></h2>
1.5 lievre 1053:
1.6 lievre 1054: <p>Since you know how to run the program, it is time to test it
1055: on your own computer. Try for example on a parameter file named <a
1.11 brouard 1056: href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of <font
1057: size="2" face="Courier New">mypar.imach</font> included in the
1.6 lievre 1058: subdirectory of imach, <font size="2" face="Courier New">mytry</font>.
1059: Edit it to change the name of the data file to <font size="2"
1060: face="Courier New">..\data\mydata.txt</font> if you don't want to
1061: copy it on the same directory. The file <font face="Courier New">mydata.txt</font>
1062: is a smaller file of 3,000 people but still with 4 waves. </p>
1.5 lievre 1063:
1.6 lievre 1064: <p>Click on the imach.exe icon to open a window. Answer to the
1065: question:'<strong>Enter the parameter file name:'</strong></p>
1.5 lievre 1066:
1.6 lievre 1067: <table border="1">
1.2 lievre 1068: <tr>
1.12 ! brouard 1069: <td width="100%"><strong>IMACH, Version 0.8</strong><p><strong>Enter
1.11 brouard 1070: the parameter file name: ..\mytry\imachpar.imach</strong></p>
1.2 lievre 1071: </td>
1072: </tr>
1073: </table>
1074:
1.6 lievre 1075: <p>Most of the data files or image files generated, will use the
1.2 lievre 1076: 'imachpar' string into their name. The running time is about 2-3
1077: minutes on a Pentium III. If the execution worked correctly, the
1078: outputs files are created in the current directory, and should be
1.6 lievre 1079: the same as the mypar files initially included in the directory <font
1080: size="2" face="Courier New">mytry</font>.</p>
1.5 lievre 1081:
1.6 lievre 1082: <ul>
1083: <li><pre><u>Output on the screen</u> The output screen looks like <a
1084: href="imachrun.LOG">this Log file</a>
1085: #
1.5 lievre 1086:
1.6 lievre 1087: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3
1.12 ! brouard 1088: ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre>
1.6 lievre 1089: </li>
1090: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
1.5 lievre 1091:
1.6 lievre 1092: Warning, no any valid information for:126 line=126
1093: Warning, no any valid information for:2307 line=2307
1094: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
1095: <font face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</font>
1096: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
1097: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
1098: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre>
1099: </li>
1100: </ul>
1.2 lievre 1101:
1.6 lievre 1102: <p> </p>
1.2 lievre 1103:
1.6 lievre 1104: <ul>
1105: <li>Maximisation with the Powell algorithm. 8 directions are
1106: given corresponding to the 8 parameters. this can be
1107: rather long to get convergence.<br>
1108: <font size="1" face="Courier New"><br>
1.2 lievre 1109: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2
1110: 0.000000000000 3<br>
1111: 0.000000000000 4 0.000000000000 5 0.000000000000 6
1112: 0.000000000000 7 <br>
1113: 0.000000000000 8 0.000000000000<br>
1114: 1..........2.................3..........4.................5.........<br>
1115: 6................7........8...............<br>
1116: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283
1117: <br>
1118: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 <br>
1119: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 <br>
1120: 8 0.051272038506<br>
1121: 1..............2...........3..............4...........<br>
1122: 5..........6................7...........8.........<br>
1123: #Number of iterations = 23, -2 Log likelihood =
1124: 6744.954042573691<br>
1125: # Parameters<br>
1126: 12 -12.966061 0.135117 <br>
1127: 13 -7.401109 0.067831 <br>
1128: 21 -0.672648 -0.006627 <br>
1.6 lievre 1129: 23 -5.051297 0.051271 </font><br>
1130: </li>
1131: <li><pre><font size="2">Calculation of the hessian matrix. Wait...
1132: 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
1133:
1134: Inverting the hessian to get the covariance matrix. Wait...
1135:
1136: #Hessian matrix#
1137: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
1138: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
1139: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
1140: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
1141: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
1142: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
1143: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
1144: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
1145: # Scales
1146: 12 1.00000e-004 1.00000e-006
1147: 13 1.00000e-004 1.00000e-006
1148: 21 1.00000e-003 1.00000e-005
1149: 23 1.00000e-004 1.00000e-005
1150: # Covariance
1151: 1 5.90661e-001
1152: 2 -7.26732e-003 8.98810e-005
1153: 3 8.80177e-002 -1.12706e-003 5.15824e-001
1154: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
1155: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
1156: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
1157: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
1158: 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
1159: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
1160:
1161:
1162: agemin=70 agemax=100 bage=50 fage=100
1163: Computing prevalence limit: result on file 'plrmypar.txt'
1164: Computing pij: result on file 'pijrmypar.txt'
1165: Computing Health Expectancies: result on file 'ermypar.txt'
1166: Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
1167: Computing Total LEs with variances: file 'trmypar.txt'
1168: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
1169: End of Imach
1170: </font></pre>
1171: </li>
1.2 lievre 1172: </ul>
1173:
1.6 lievre 1174: <p><font size="3">Once the running is finished, the program
1175: requires a caracter:</font></p>
1.2 lievre 1176:
1.6 lievre 1177: <table border="1">
1.2 lievre 1178: <tr>
1.6 lievre 1179: <td width="100%"><strong>Type e to edit output files, c
1180: to start again, and q for exiting:</strong></td>
1.2 lievre 1181: </tr>
1182: </table>
1183:
1.6 lievre 1184: <p><font size="3">First you should enter <strong>e </strong>to
1185: edit the master file mypar.htm. </font></p>
1186:
1187: <ul>
1188: <li><u>Outputs files</u> <br>
1.3 lievre 1189: <br>
1.6 lievre 1190: - Observed prevalence in each state: <a
1191: href="..\mytry\prmypar.txt">pmypar.txt</a> <br>
1192: - Estimated parameters and the covariance matrix: <a
1.11 brouard 1193: href="..\mytry\rmypar.txt">rmypar.imach</a> <br>
1.6 lievre 1194: - Stationary prevalence in each state: <a
1195: href="..\mytry\plrmypar.txt">plrmypar.txt</a> <br>
1196: - Transition probabilities: <a
1197: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> <br>
1198: - Copy of the parameter file: <a
1199: href="..\mytry\ormypar.txt">ormypar.txt</a> <br>
1200: - Life expectancies by age and initial health status: <a
1201: href="..\mytry\ermypar.txt">ermypar.txt</a> <br>
1.2 lievre 1202: - Variances of life expectancies by age and initial
1.6 lievre 1203: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a>
1.2 lievre 1204: <br>
1.6 lievre 1205: - Health expectancies with their variances: <a
1206: href="..\mytry\trmypar.txt">trmypar.txt</a> <br>
1207: - Standard deviation of stationary prevalence: <a
1208: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a><br>
1209: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a>
1.2 lievre 1210: <br>
1.6 lievre 1211: - Population forecasting (if popforecast=1): <a
1212: href="poprmypar.txt">poprmypar.txt</a> <br>
1213: </li>
1214: <li><u>Graphs</u> <br>
1.2 lievre 1215: <br>
1.11 brouard 1216: -<a href="../mytry/pemypar1.gif">One-step transition probabilities</a><br>
1217: -<a href="../mytry/pmypar11.gif">Convergence to the stationary prevalence</a><br>
1218: -<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> <br>
1219: -<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> <br>
1220: -<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> <br>
1221: -<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> <br>
1222: -<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li>
1.2 lievre 1223: </ul>
1224:
1.6 lievre 1225: <p>This software have been partly granted by <a
1226: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted
1.2 lievre 1227: action from the European Union. It will be copyrighted
1228: identically to a GNU software product, i.e. program and software
1229: can be distributed freely for non commercial use. Sources are not
1230: widely distributed today. You can get them by asking us with a
1.6 lievre 1231: simple justification (name, email, institute) <a
1232: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a
1233: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .</p>
1234:
1.12 ! brouard 1235: <p>Latest version (0.8 of March 2002) can be accessed at <a
1.8 lievre 1236: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a><br>
1.6 lievre 1237: </p>
1.2 lievre 1238: </body>
1239: </html>
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