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1:  10: <html> 11: 12: <head> 13: <meta http-equiv="Content-Type" 14: content="text/html; charset=iso-8859-1"> 15: <meta name="GENERATOR" content="Microsoft FrontPage Express 2.0"> 16: <title></title> 17: </head> 18: 19: <body bgcolor="#FFFFFF"> 20: 21: <hr size="3" color="#EC5E5E"> 22: 23: <h1 align="center">Computing Health 24: Expectancies using IMaCh</h1> 25: 26: <h1 align="center">(a Maximum 27: Likelihood Computer Program using Interpolation of Markov Chains)</h1> 28: 29:   30: 31: <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"> 34: 35: <h3 align="center"><a href="http://www.ined.fr/">INED</a> and <a 37: href="http://euroreves.ined.fr">EUROREVES</a></h3> 38: 39: Version 40: 0.71a, March 2002 41: 42: <hr size="3" color="#EC5E5E"> 43: 44: Authors of the 45: program: <a href="http://sauvy.ined.fr/brouard">Nicolas Brouard</a>, senior researcher at the <a 48: href="http://www.ined.fr">Institut 49: National d'Etudes Démographiques</a> (INED, Paris) in the "Mortality, 51: Health and Epidemiology" Research Unit 52: 53: and Agnès 54: Lièvre 55: 56: 57: <h4>Contribution to the mathematics: C. R. 58: Heathcote (Australian 59: National University, Canberra).</h4> 60: 61: <h4>Contact: Agnès Lièvre (<a 62: href="mailto:lievre@ined.fr">lievre@ined.fr</a>) </h4> 64: 65: <hr> 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> 75: </ul> 76: 77: <hr> 78: 79: <h2><a name="intro">Introduction</a></h2> 80: 81: This program computes Healthy Life Expectancies from cross-longitudinal 82: data 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 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 Expansion 88: of morbidity. Most of the data collected today, in 89: particular by the international <a href="http://www.reves.org">REVES</a> 90: network on Health expectancy, and most HE indices based on these 91: data, are cross-sectional. 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 104: of the author who first described it). 105: 106: 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. 129: 130: 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. 135: 136: 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. 148: 149: The simplest model is the multinomial logistic model where pij 150: is the probability to be observed in state j at the second 151: wave conditional to be observed in state i at the first 152: wave. Therefore a simple model is: log(pij/pii)= aij + 153: bij*age+ cij*sex, where 'age' is age and 'sex' 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. hPijx is the 159: probability to be observed in state i at age x+h 160: conditional to the observed state i at age x. The 161: delay 'h' can be split into an exact number (nh*stepm) 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 hPx matrix is simply the matrix 165: product of nh*stepm elementary matrices and the 166: contribution of each individual to the likelihood is simply hPijx. 167: 168: 169: 170: The program presented in this manual is a quite general 171: program named IMaCh (for Interpolated 172: MArkov CHain), 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, 181: compared to other programs for the analysis of transition data 182: (For example: Proc Catmod of SAS®) is that the whole 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 190: the transitions (we can compute annual, quarterly or monthly 191: transitions), covariates in the model. It works on Windows or on 192: Unix. 193: 194: 195: <hr> 196: 197: (1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New 198: Methods for Analyzing Active Life Expectancy". Journal of 199: Aging and Health. Vol 10, No. 2. 200: 201: <hr> 202: 203: <h2><a name="data">On what kind of data can 204: it be used?</a></h2> 205: 206: 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. 221: 222: <hr> 223: 224: <h2><a name="datafile">The data file</a></h2> 225: 226: 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. 237: 238: 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: 240: 241: <ul> 242: <li>Index number: positive number (field 1) </li> 243: <li>First covariate positive number (field 2) </li> 244: <li>Second covariate positive number (field 3) </li> 245: <li><a name="Weight">Weight</a>: positive number 246: (field 4) . In most surveys individuals are weighted 247: according to the stratification of the sample.</li> 248: <li>Date of birth: coded as mm/yyyy. Missing dates are 249: coded as 99/9999 (field 5) </li> 250: <li>Date of death: coded as mm/yyyy. Missing dates are 251: coded as 99/9999 (field 6) </li> 252: <li>Date of first interview: coded as mm/yyyy. Missing 253: dates are coded as 99/9999 (field 7) </li> 254: <li>Status at first interview: positive number. 255: Missing values ar coded -1. (field 8) </li> 256: <li>Date of second interview: coded as mm/yyyy. 257: Missing dates are coded as 99/9999 (field 9) </li> 258: <li>Status at second interview positive 259: number. Missing values ar coded -1. (field 10) </li> 260: <li>Date of third interview: coded as mm/yyyy. Missing 261: dates are coded as 99/9999 (field 11) </li> 262: <li>Status at third interview positive 263: number. Missing values ar coded -1. (field 12) </li> 264: <li>Date of fourth interview: coded as mm/yyyy. 265: Missing dates are coded as 99/9999 (field 13) </li> 266: <li>Status at fourth interview positive 267: number. Missing values are coded -1. (field 14) </li> 268: <li>etc</li> 269: </ul> 270: 271:   272: 273: 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. 276: 277: <hr> 278: 279: <h2>Your first example parameter file<a 280: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> 281: 282: <h2><a name="biaspar"></a>#Imach version 0.71a, March 2002, 283: INED-EUROREVES </h2> 284: 285: This is a comment. Comments start with a '#'. 286: 287: <h4>First uncommented line</h4> 288: 289: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> 290: 291: <ul> 292: <li>title= 1st_example is title of the run. </li> 293: <li>datafile=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>lastobs= 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>firstpass=1 , lastpass=4 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> 307: </ul> 308: 309:   310: 311: <h4><a name="biaspar-2">Second uncommented 312: line</a></h4> 313: 314: <pre>ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 315: 316: <ul> 317: <li>ftol=1e-8 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>stepm=1 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> 328: </ul> 329: </li> 330: <li>ncov=2 Number of covariates in the datafile. </li> 331: <li>nlstate=2 Number of non-absorbing (alive) states. 332: Here we have two alive states: disability-free is coded 1 333: and disability is coded 2. </li> 334: <li>ndeath=1 Number of absorbing states. The absorbing 335: state death is coded 3. </li> 336: <li>maxwav=4 Number of waves in the datafile.</li> 337: <li><a name="mle">mle</a>=1 Option for the 338: Maximisation Likelihood Estimation. <ul> 339: <li>If mle=1 the program does the maximisation and 340: the calculation of health expectancies </li> 341: <li>If mle=0 the program only does the calculation of 342: the health expectancies. </li> 343: </ul> 344: </li> 345: <li>weight=0 Possibility to add weights. <ul> 346: <li>If weight=0 no weights are included </li> 347: <li>If weight=1 the maximisation integrates the 348: weights which are in field <a href="#Weight">4</a></li> 349: </ul> 350: </li> 351: </ul> 352: 353: <h4>Covariates</h4> 354: 355: Intercept and age are systematically included in the model. 356: Additional covariates can be included with the command: 357: 358: <pre>model=list of covariates</pre> 359: 360: <ul> 361: <li>if model=. then no covariates are 362: included</li> 363: <li>if model=V1 the model includes the first 364: covariate (field 2)</li> 365: <li>if model=V2 the model includes the 366: second covariate (field 3)</li> 367: <li>if model=V1+V2 the model includes the 368: first and the second covariate (fields 2 and 3)</li> 369: <li>if model=V1*V2 the model includes the 370: product of the first and the second covariate (fields 2 371: and 3)</li> 372: <li>if model=V1+V1*age the model includes 373: the product covariate*age</li> 374: </ul> 375: 376: In this example, we have two covariates in the data file 377: (fields 2 and 3). The number of covariates is defined with 378: statement ncov=2. If now you have 3 covariates in the datafile 379: (fields 2, 3 and 4), you have to set ncov=3. Then you can run the 380: programme with a new parametrisation taking into account the 381: third covariate. For example, model=V1+V3 estimates 382: a model with the first and third covariates. More complicated 383: models can be used, but it will takes more time to converge. With 384: a simple model (no covariates), the programme estimates 8 385: parameters. Adding covariates increases the number of parameters 386: : 12 for model=V1, 16 for model=V1+V1*age 387: and 20 for model=V1+V2+V3. 388: 389: <h4>Guess values for optimization </h4> 391: 392: You must write the initial guess values of the parameters for 393: optimization. The number of parameters, N depends on the 394: number of absorbing states and non-absorbing states and on the 395: number of covariates. 396: N is given by the formula N=(nlstate + 397: ndeath-1)*nlstate*ncov . 398: 399: Thus in the simple case with 2 covariates (the model is log 400: (pij/pii) = aij + bij * age where intercept and age are the two 401: covariates), and 2 health degrees (1 for disability-free and 2 402: for disability) and 1 absorbing state (3), you must enter 8 403: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can 404: start with zeros as in this example, but if you have a more 405: precise set (for example from an earlier run) you can enter it 406: and it will speed up them 407: Each of the four lines starts with indices "ij": ij 408: aij bij 409: 410: <blockquote> 411: <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age 412: 12 -14.155633 0.110794 413: 13 -7.925360 0.032091 414: 21 -1.890135 -0.029473 415: 23 -6.234642 0.022315 </pre> 416: </blockquote> 417: 418: or, to simplify (in most of cases it converges but there is no 419: warranty!): 420: 421: <blockquote> 422: <pre>12 0.0 0.0 423: 13 0.0 0.0 424: 21 0.0 0.0 425: 23 0.0 0.0</pre> 426: </blockquote> 427: 428: <h4>Guess values for computing variances</h4> 429: 430: This is an output if <a href="#mle">mle</a>=1. But it can be 431: used as an input to get the various output data files (Health 432: expectancies, stationary prevalence etc.) and figures without 433: rerunning the rather long maximisation phase (mle=0). 434: 435: The scales are small values for the evaluation of numerical 436: derivatives. These derivatives are used to compute the hessian 437: matrix of the parameters, that is the inverse of the covariance 438: matrix, and the variances of health expectancies. Each line 439: consists in indices "ij" followed by the initial scales 440: (zero to simplify) associated with aij and bij. 441: 442: <ul> 443: <li>If mle=1 you can enter zeros:</li> 444: </ul> 445: 446: <blockquote> 447: <pre># Scales (for hessian or gradient estimation) 448: 12 0. 0. 449: 13 0. 0. 450: 21 0. 0. 451: 23 0. 0. </pre> 452: </blockquote> 453: 454: <ul> 455: <li>If mle=0 you must enter a covariance matrix (usually 456: obtained from an earlier run).</li> 457: </ul> 458: 459: <h4>Covariance matrix of parameters</h4> 460: 461: This is an output if <a href="#mle">mle</a>=1. But it can be 462: used as an input to get the various output data files (Health 463: expectancies, stationary prevalence etc.) and figures without 464: rerunning the rather long maximisation phase (mle=0). 465: 466: Each line starts with indices "ijk" followed by the 467: covariances between aij and bij: 468: 469: <pre> 470: 121 Var(a12) 471: 122 Cov(b12,a12) Var(b12) 472: ... 473: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> 474: 475: <ul> 476: <li>If mle=1 you can enter zeros. </li> 477: </ul> 478: 479: <blockquote> 480: <pre># Covariance matrix 481: 121 0. 482: 122 0. 0. 483: 131 0. 0. 0. 484: 132 0. 0. 0. 0. 485: 211 0. 0. 0. 0. 0. 486: 212 0. 0. 0. 0. 0. 0. 487: 231 0. 0. 0. 0. 0. 0. 0. 488: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> 489: </blockquote> 490: 491: <ul> 492: <li>If mle=0 you must enter a covariance matrix (usually 493: obtained from an earlier run). 494: </li> 495: </ul> 496: 497: <h4>Age range for calculation of stationary 498: prevalences and health expectancies</h4> 499: 500: <pre>agemin=70 agemax=100 bage=50 fage=100</pre> 501: 502: Once we obtained the estimated parameters, the program is able 503: to calculated stationary prevalence, transitions probabilities 504: and life expectancies at any age. Choice of age range is useful 505: for extrapolation. In our data file, ages varies from age 70 to 506: 102. It is possible to get extrapolated stationary prevalence by 507: age ranging from agemin to agemax. 508: 509: Setting bage=50 (begin age) and fage=100 (final age), makes 510: the program computing life expectancy from age 'bage' to age 511: 'fage'. As we use a model, we can interessingly compute life 512: expectancy on a wider age range than the age range from the data. 513: But the model can be rather wrong on much larger intervals. 514: Program is limited to around 120 for upper age! 515: 516: <ul> 517: <li>agemin= Minimum age for calculation of the 518: stationary prevalence </li> 519: <li>agemax= Maximum age for calculation of the 520: stationary prevalence </li> 521: <li>bage= Minimum age for calculation of the health 522: expectancies </li> 523: <li>fage= Maximum age for calculation of the health 524: expectancies </li> 525: </ul> 526: 527: <h4><a name="Computing">Computing</a> the observed prevalence</h4> 529: 530: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre> 531: 532: Statements 'begin-prev-date' and 'end-prev-date' allow to 533: select the period in which we calculate the observed prevalences 534: in each state. In this example, the prevalences are calculated on 535: data survey collected between 1 january 1984 and 1 june 1988. 536: 537: <ul> 538: <li>begin-prev-date= Starting date 539: (day/month/year)</li> 540: <li>end-prev-date= Final date 541: (day/month/year)</li> 542: </ul> 543: 544: <h4>Population- or status-based health 545: expectancies</h4> 546: 547: <pre>pop_based=0</pre> 548: 549: The program computes status-based health expectancies, i.e 550: health expectancies which depends on your initial health state. 551: If you are healthy your healthy life expectancy (e11) is higher 552: than if you were disabled (e21, with e11 > e21). 553: To compute a healthy life expectancy independant of the initial 554: status we have to weight e11 and e21 according to the probability 555: to be in each state at initial age or, with other word, according 556: to the proportion of people in each state. 557: We prefer computing a 'pure' period healthy life expectancy based 558: only on the transtion forces. Then the weights are simply the 559: stationnary prevalences or 'implied' prevalences at the initial 560: age. 561: Some other people would like to use the cross-sectional 562: prevalences (the "Sullivan prevalences") observed at 563: the initial age during a period of time <a href="#Computing">defined 564: just above</a>. 565: 566: <ul> 567: <li>popbased= 0 Health expectancies are 568: computed at each age from stationary prevalences 569: 'expected' at this initial age.</li> 570: <li>popbased= 1 Health expectancies are 571: computed at each age from cross-sectional 'observed' 572: prevalence at this initial age. As all the population is 573: not observed at the same exact date we define a short 574: period were the observed prevalence is computed.</li> 575: </ul> 576: 577: <h4>Prevalence forecasting ( Experimental)</h4> 578: 579: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre> 580: 581: Prevalence and population projections are only available if 582: the interpolation unit is a month, i.e. stepm=1 and if there are 583: no covariate. The programme estimates the prevalence in each 584: state at a precise date expressed in day/month/year. The 585: programme computes one forecasted prevalence a year from a 586: starting date (1 january of 1989 in this example) to a final date 587: (1 january 1992). The statement mov_average allows to compute 588: smoothed forecasted prevalences with a five-age moving average 589: centered at the mid-age of the five-age period. 590: 591: <ul> 592: <li>starting-proj-date= starting date 593: (day/month/year) of forecasting</li> 594: <li>final-proj-date= final date 595: (day/month/year) of forecasting</li> 596: <li>mov_average= smoothing with a five-age 597: moving average centered at the mid-age of the five-age 598: period. The command mov_average takes 599: value 1 if the prevalences are smoothed and 0 otherwise.</li> 600: </ul> 601: 602: <h4>Last uncommented line : Population 603: forecasting </h4> 604: 605: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre> 606: 607: This command is available if the interpolation unit is a 608: month, i.e. stepm=1 and if popforecast=1. From a data file 609: including age and number of persons alive at the precise date 610: popfiledate, you can forecast the number of persons 611: in each state until date last-popfiledate. In this 612: example, the popfile <a href="pyram.txt">pyram.txt</a> 613: includes real data which are the Japanese population in 1989. 614: 615: <ul type="disc"> 616: <li class="MsoNormal" 617: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popforecast= 618: 0 Option for population forecasting. If 619: popforecast=1, the programme does the forecasting.</li> 620: <li class="MsoNormal" 621: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popfile= 622: name of the population file</li> 623: <li class="MsoNormal" 624: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popfiledate= 625: date of the population population</li> 626: <li class="MsoNormal" 627: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">last-popfiledate= 628: date of the last population projection </li> 629: </ul> 630: 631: <hr> 632: 633: <h2><a name="running"></a>Running Imach 634: with this example</h2> 635: 636: We assume that you entered your <a href="biaspar.imach">1st_example 637: parameter file</a> as explained <a href="#biaspar">above</a>. To 638: run the program you should click on the imach.exe icon and enter 639: the name of the parameter file which is for example <a 640: href="C:\usr\imach\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a> 641: (you also can click on the biaspar.txt icon located in 642: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> and put it with 643: the mouse on the imach window). 644: 645: 646: The time to converge depends on the step unit that you used (1 647: month is cpu consuming), on the number of cases, and on the 648: number of variables. 649: 650: The program outputs many files. Most of them are files which 651: will be plotted for better understanding. 652: 653: <hr> 654: 655: <h2><a name="output">Output of the program 656: and graphs </a></h2> 657: 658: Once the optimization is finished, some graphics can be made 659: with a grapher. We use Gnuplot which is an interactive plotting 660: program copyrighted but freely distributed. A gnuplot reference 661: manual is available <a href="http://www.gnuplot.info/">here</a>. 662: When the running is finished, the user should enter a caracter 663: for plotting and output editing. 664: 665: These caracters are: 666: 667: <ul> 668: <li>'c' to start again the program from the beginning.</li> 669: <li>'e' opens the <a href="biaspar.htm">biaspar.htm</a> 670: file to edit the output files and graphs. </li> 671: <li>'q' for exiting.</li> 672: </ul> 673: 674: <h5>Results files 675: 676: - <a 677: name="Observed prevalence in each state">Observed prevalence in each state</a> (and at first pass): 680: <a href="prbiaspar.txt">prbiaspar.txt</a> 681: </h5> 682: 683: The first line is the title and displays each field of the 684: file. The first column is age. The fields 2 and 6 are the 685: proportion of individuals in states 1 and 2 respectively as 686: observed during the first exam. Others fields are the numbers of 687: people in states 1, 2 or more. The number of columns increases if 688: the number of states is higher than 2. 689: The header of the file is 690: 691: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N 692: 70 1.00000 631 631 70 0.00000 0 631 693: 71 0.99681 625 627 71 0.00319 2 627 694: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> 695: 696: It means that at age 70, the prevalence in state 1 is 1.000 697: and in state 2 is 0.00 . At age 71 the number of individuals in 698: state 1 is 625 and in state 2 is 2, hence the total number of 699: people aged 71 is 625+2=627. 700: 701: 702: <h5>- Estimated parameters and 703: covariance matrix: <a href="rbiaspar.txt">rbiaspar.txt</a></h5> 704: 705: This file contains all the maximisation results: 706: 707: <pre> -2 log likelihood= 21660.918613445392 708: Estimated parameters: a12 = -12.290174 b12 = 0.092161 709: a13 = -9.155590 b13 = 0.046627 710: a21 = -2.629849 b21 = -0.022030 711: a23 = -7.958519 b23 = 0.042614 712: Covariance matrix: Var(a12) = 1.47453e-001 713: Var(b12) = 2.18676e-005 714: Var(a13) = 2.09715e-001 715: Var(b13) = 3.28937e-005 716: Var(a21) = 9.19832e-001 717: Var(b21) = 1.29229e-004 718: Var(a23) = 4.48405e-001 719: Var(b23) = 5.85631e-005 720: </pre> 721: 722: By substitution of these parameters in the regression model, 723: we obtain the elementary transition probabilities: 724: 725: <img src="pebiaspar1.gif" width="400" height="300"> 726: 727: <h5>- Transition probabilities: 728: <a href="pijrbiaspar.txt">pijrbiaspar.txt</a></h5> 729: 730: Here are the transitions probabilities Pij(x, x+nh) where nh 731: is a multiple of 2 years. The first column is the starting age x 732: (from age 50 to 100), the second is age (x+nh) and the others are 733: the transition probabilities p11, p12, p13, p21, p22, p23. For 734: example, line 5 of the file is: 735: 736: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre> 737: 738: and this means: 739: 740: <pre>p11(100,106)=0.02655 741: p12(100,106)=0.17622 742: p13(100,106)=0.79722 743: p21(100,106)=0.01809 744: p22(100,106)=0.13678 745: p22(100,106)=0.84513 </pre> 746: 747: <h5>- <a 748: name="Stationary prevalence in each state">Stationary prevalence in each state</a>: 750: <a href="plrbiaspar.txt">plrbiaspar.txt</a></h5> 751: 752: <pre>#Prevalence 753: #Age 1-1 2-2 754: 755: #************ 756: 70 0.90134 0.09866 757: 71 0.89177 0.10823 758: 72 0.88139 0.11861 759: 73 0.87015 0.12985 </pre> 760: 761: At age 70 the stationary prevalence is 0.90134 in state 1 and 762: 0.09866 in state 2. This stationary prevalence differs from 763: observed prevalence. Here is the point. The observed prevalence 764: at age 70 results from the incidence of disability, incidence of 765: recovery and mortality which occurred in the past of the cohort. 766: Stationary prevalence results from a simulation with actual 767: incidences and mortality (estimated from this cross-longitudinal 768: survey). It is the best predictive value of the prevalence in the 769: future if "nothing changes in the future". This is 770: exactly what demographers do with a Life table. Life expectancy 771: is the expected mean time to survive if observed mortality rates 772: (incidence of mortality) "remains constant" in the 773: future. 774: 775: <h5>- Standard deviation of 776: stationary prevalence: <a 777: href="vplrbiaspar.txt">vplrbiaspar.txt</a></h5> 778: 779: The stationary prevalence has to be compared with the observed 780: prevalence by age. But both are statistical estimates and 781: subjected to stochastic errors due to the size of the sample, the 782: design of the survey, and, for the stationary prevalence to the 783: model used and fitted. It is possible to compute the standard 784: deviation of the stationary prevalence at each age. 785: 786: <h5>-Observed and stationary 787: prevalence in state (2=disable) with the confident interval: 788: <a href="vbiaspar21.htm">vbiaspar21.gif</a></h5> 789: 790: This graph exhibits the stationary prevalence in state (2) 791: with the confidence interval in red. The green curve is the 792: observed prevalence (or proportion of individuals in state (2)). 793: Without discussing the results (it is not the purpose here), we 794: observe that the green curve is rather below the stationary 795: prevalence. It suggests an increase of the disability prevalence 796: in the future. 797: 798: <img src="vbiaspar21.gif" width="400" height="300"> 799: 800: <h5>-Convergence to the 801: stationary prevalence of disability: <a 802: href="pbiaspar11.gif">pbiaspar11.gif</a> 803: <img src="pbiaspar11.gif" width="400" height="300"> </h5> 804: 805: This graph plots the conditional transition probabilities from 806: an initial state (1=healthy in red at the bottom, or 2=disable in 807: green on top) at age x to the final state 2=disable at 808: age x+h. Conditional means at the condition to be alive 809: at age x+h which is hP12x + hP22x. The 810: curves hP12x/(hP12x + hP22x) and hP22x/(hP12x 811: + hP22x) converge with h, to the stationary 812: prevalence of disability. In order to get the stationary 813: prevalence at age 70 we should start the process at an earlier 814: age, i.e.50. If the disability state is defined by severe 815: disability criteria with only a few chance to recover, then the 816: incidence of recovery is low and the time to convergence is 817: probably longer. But we don't have experience yet. 818: 819: <h5>- Life expectancies by age 820: and initial health status: <a 821: href="erbiaspar.txt">erbiaspar.txt</a></h5> 822: 823: <pre># Health expectancies 824: # Age 1-1 1-2 2-1 2-2 825: 70 10.9226 3.0401 5.6488 6.2122 826: 71 10.4384 3.0461 5.2477 6.1599 827: 72 9.9667 3.0502 4.8663 6.1025 828: 73 9.5077 3.0524 4.5044 6.0401 </pre> 829: 830: <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means: 831: e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre> 832: 833: <pre><img src="expbiaspar21.gif" width="400" height="300"><img 834: src="expbiaspar11.gif" width="400" height="300"></pre> 835: 836: For example, life expectancy of a healthy individual at age 70 837: is 10.42 in the healthy state and 3.04 in the disability state 838: (=13.46 years). If he was disable at age 70, his life expectancy 839: will be shorter, 5.64 in the healthy state and 5.71 in the 840: disability state (=11.35 years). The total life expectancy is a 841: weighted mean of both, 13.46 and 11.35; weight is the proportion 842: of people disabled at age 70. In order to get a pure period index 843: (i.e. based only on incidences) we use the <a 844: href="#Stationary prevalence in each state">computed or 845: stationary prevalence</a> at age 70 (i.e. computed from 846: incidences at earlier ages) instead of the <a 847: href="#Observed prevalence in each state">observed prevalence</a> 848: (for example at first exam) (<a href="#Health expectancies">see 849: below</a>). 850: 851: <h5>- Variances of life 852: expectancies by age and initial health status: <a 853: href="vrbiaspar.txt">vrbiaspar.txt</a></h5> 854: 855: For example, the covariances of life expectancies Cov(ei,ej) 856: at age 50 are (line 3) 857: 858: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre> 859: 860: <h5>- <a 861: name="Health expectancies">Health 862: expectancies</a> 863: with standard errors in parentheses: <a 864: href="trbiaspar.txt">trbiaspar.txt</a></h5> 865: 866: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> 867: 868: <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre> 869: 870: Thus, at age 70 the total life expectancy, e..=13.26 years is 871: the weighted mean of e1.=13.46 and e2.=11.35 by the stationary 872: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in 873: state 2, respectively (the sum is equal to one). e.1=9.95 is the 874: Disability-free life expectancy at age 70 (it is again a weighted 875: mean of e11 and e21). e.2=3.30 is also the life expectancy at age 876: 70 to be spent in the disability state. 877: 878: <h5>-Total life expectancy by 879: age and health expectancies in states (1=healthy) and (2=disable): 880: <a href="ebiaspar1.gif">ebiaspar1.gif</a></h5> 881: 882: This figure represents the health expectancies and the total 883: life expectancy with the confident interval in dashed curve. 884: 885: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre> 886: 887: Standard deviations (obtained from the information matrix of 888: the model) of these quantities are very useful. 889: Cross-longitudinal surveys are costly and do not involve huge 890: samples, generally a few thousands; therefore it is very 891: important to have an idea of the standard deviation of our 892: estimates. It has been a big challenge to compute the Health 893: Expectancy standard deviations. Don't be confuse: life expectancy 894: is, as any expected value, the mean of a distribution; but here 895: we are not computing the standard deviation of the distribution, 896: but the standard deviation of the estimate of the mean. 897: 898: Our health expectancies estimates vary according to the sample 899: size (and the standard deviations give confidence intervals of 900: the estimate) but also according to the model fitted. Let us 901: explain it in more details. 902: 903: Choosing a model means ar least two kind of choices. First we 904: have to decide the number of disability states. Second we have to 905: design, within the logit model family, the model: variables, 906: covariables, confonding factors etc. to be included. 907: 908: More disability states we have, better is our demographical 909: approach of the disability process, but smaller are the number of 910: transitions between each state and higher is the noise in the 911: measurement. We do not have enough experiments of the various 912: models to summarize the advantages and disadvantages, but it is 913: important to say that even if we had huge and unbiased samples, 914: the total life expectancy computed from a cross-longitudinal 915: survey, varies with the number of states. If we define only two 916: states, alive or dead, we find the usual life expectancy where it 917: is assumed that at each age, people are at the same risk to die. 918: If we are differentiating the alive state into healthy and 919: disable, and as the mortality from the disability state is higher 920: than the mortality from the healthy state, we are introducing 921: heterogeneity in the risk of dying. The total mortality at each 922: age is the weighted mean of the mortality in each state by the 923: prevalence in each state. Therefore if the proportion of people 924: at each age and in each state is different from the stationary 925: equilibrium, there is no reason to find the same total mortality 926: at a particular age. Life expectancy, even if it is a very useful 927: tool, has a very strong hypothesis of homogeneity of the 928: population. Our main purpose is not to measure differential 929: mortality but to measure the expected time in a healthy or 930: disability state in order to maximise the former and minimize the 931: latter. But the differential in mortality complexifies the 932: measurement. 933: 934: Incidences of disability or recovery are not affected by the 935: number of states if these states are independant. But incidences 936: estimates are dependant on the specification of the model. More 937: covariates we added in the logit model better is the model, but 938: some covariates are not well measured, some are confounding 939: factors like in any statistical model. The procedure to "fit 940: the best model' is similar to logistic regression which itself is 941: similar to regression analysis. We haven't yet been sofar because 942: we also have a severe limitation which is the speed of the 943: convergence. On a Pentium III, 500 MHz, even the simplest model, 944: estimated by month on 8,000 people may take 4 hours to converge. 945: Also, the program is not yet a statistical package, which permits 946: a simple writing of the variables and the model to take into 947: account in the maximisation. The actual program allows only to 948: add simple variables like age+sex or age+sex+ age*sex but will 949: never be general enough. But what is to remember, is that 950: incidences or probability of change from one state to another is 951: affected by the variables specified into the model. 952: 953: Also, the age range of the people interviewed has a link with 954: the age range of the life expectancy which can be estimated by 955: extrapolation. If your sample ranges from age 70 to 95, you can 956: clearly estimate a life expectancy at age 70 and trust your 957: confidence interval which is mostly based on your sample size, 958: but if you want to estimate the life expectancy at age 50, you 959: should rely in your model, but fitting a logistic model on a age 960: range of 70-95 and estimating probabilties of transition out of 961: this age range, say at age 50 is very dangerous. At least you 962: should remember that the confidence interval given by the 963: standard deviation of the health expectancies, are under the 964: strong assumption that your model is the 'true model', which is 965: probably not the case. 966: 967: <h5>- Copy of the parameter 968: file: <a href="orbiaspar.txt">orbiaspar.txt</a></h5> 969: 970: This copy of the parameter file can be useful to re-run the 971: program while saving the old output files. 972: 973: <h5>- Prevalence forecasting: 974: <a href="frbiaspar.txt">frbiaspar.txt</a></h5> 975: 976: First, 978: we have estimated the observed prevalence between 1/1/1984 and 979: 1/6/1988. The mean date of interview (weighed average of the 980: interviews performed between1/1/1984 and 1/6/1988) is estimated 981: to be 13/9/1985, as written on the top on the file. Then we 982: forecast the probability to be in each state. 983: 984: Example, 986: at date 1/1/1989 : 987: 988: <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3 989: # Forecasting at date 1/1/1989 990: 73 0.807 0.078 0.115</pre> 991: 992: Since 994: the minimum age is 70 on the 13/9/1985, the youngest forecasted 995: age is 73. This means that at age a person aged 70 at 13/9/1989 996: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989. 997: Similarly, the probability to be in state 2 is 0.078 and the 998: probability to die is 0.115. Then, on the 1/1/1989, the 999: prevalence of disability at age 73 is estimated to be 0.088. 1000: 1001: <h5>- Population forecasting: 1002: <a href="poprbiaspar.txt">poprbiaspar.txt</a></h5> 1003: 1004: <pre># Age P.1 P.2 P.3 [Population] 1005: # Forecasting at date 1/1/1989 1006: 75 572685.22 83798.08 1007: 74 621296.51 79767.99 1008: 73 645857.70 69320.60 </pre> 1009: 1010: <pre># Forecasting at date 1/1/19909 1011: 76 442986.68 92721.14 120775.48 1012: 75 487781.02 91367.97 121915.51 1013: 74 512892.07 85003.47 117282.76 </pre> 1014: 1015: From the population file, we estimate the number of people in 1016: each state. At age 73, 645857 persons are in state 1 and 69320 1017: are in state 2. One year latter, 512892 are still in state 1, 1018: 85003 are in state 2 and 117282 died before 1/1/1990. 1019: 1020: <hr> 1021: 1022: <h2><a name="example"></a>Trying an example</h2> 1023: 1024: Since you know how to run the program, it is time to test it 1025: on your own computer. Try for example on a parameter file named <a 1026: href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of mypar.txt included in the 1028: subdirectory of imach, mytry. 1029: Edit it to change the name of the data file to ..\data\mydata.txt if you don't want to 1031: copy it on the same directory. The file mydata.txt 1032: is a smaller file of 3,000 people but still with 4 waves. 1033: 1034: Click on the imach.exe icon to open a window. Answer to the 1035: question:'Enter the parameter file name:' 1036: 1037: <table border="1"> 1038: <tr> 1039: <td width="100%">IMACH, Version 0.71Enter 1040: the parameter file name: ..\mytry\imachpar.txt 1041: </td> 1042: </tr> 1043: </table> 1044: 1045: Most of the data files or image files generated, will use the 1046: 'imachpar' string into their name. The running time is about 2-3 1047: minutes on a Pentium III. If the execution worked correctly, the 1048: outputs files are created in the current directory, and should be 1049: the same as the mypar files initially included in the directory mytry. 1051: 1052: <ul> 1053: <li><pre>Output on the screen The output screen looks like <a 1054: href="imachrun.LOG">this Log file</a> 1055: # 1056: 1057: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 1058: ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 1059: </li> 1060: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 1061: 1062: Warning, no any valid information for:126 line=126 1063: Warning, no any valid information for:2307 line=2307 1064: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 1065: These lines give some warnings on the data file and also some raw statistics on frequencies of transitions. 1066: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 1067: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 1068: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> 1069: </li> 1070: </ul> 1071: 1072:   1073: 1074: <ul> 1075: <li>Maximisation with the Powell algorithm. 8 directions are 1076: given corresponding to the 8 parameters. this can be 1077: rather long to get convergence. 1078: 1079: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 1080: 0.000000000000 3 1081: 0.000000000000 4 0.000000000000 5 0.000000000000 6 1082: 0.000000000000 7 1083: 0.000000000000 8 0.000000000000 1084: 1..........2.................3..........4.................5......... 1085: 6................7........8............... 1086: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 1087: 1088: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 1089: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 1090: 8 0.051272038506 1091: 1..............2...........3..............4........... 1092: 5..........6................7...........8......... 1093: #Number of iterations = 23, -2 Log likelihood = 1094: 6744.954042573691 1095: # Parameters 1096: 12 -12.966061 0.135117 1097: 13 -7.401109 0.067831 1098: 21 -0.672648 -0.006627 1099: 23 -5.051297 0.051271 1100: </li> 1101: <li><pre>Calculation of the hessian matrix. Wait... 1102: 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 1103: 1104: Inverting the hessian to get the covariance matrix. Wait... 1105: 1106: #Hessian matrix# 1107: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 1108: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 1109: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 1110: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 1111: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 1112: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 1113: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 1114: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 1115: # Scales 1116: 12 1.00000e-004 1.00000e-006 1117: 13 1.00000e-004 1.00000e-006 1118: 21 1.00000e-003 1.00000e-005 1119: 23 1.00000e-004 1.00000e-005 1120: # Covariance 1121: 1 5.90661e-001 1122: 2 -7.26732e-003 8.98810e-005 1123: 3 8.80177e-002 -1.12706e-003 5.15824e-001 1124: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 1125: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 1126: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 1127: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 1128: 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 1129: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). 1130: 1131: 1132: agemin=70 agemax=100 bage=50 fage=100 1133: Computing prevalence limit: result on file 'plrmypar.txt' 1134: Computing pij: result on file 'pijrmypar.txt' 1135: Computing Health Expectancies: result on file 'ermypar.txt' 1136: Computing Variance-covariance of DFLEs: file 'vrmypar.txt' 1137: Computing Total LEs with variances: file 'trmypar.txt' 1138: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' 1139: End of Imach 1140: </pre> 1141: </li> 1142: </ul> 1143: 1144: Once the running is finished, the program 1145: requires a caracter: 1146: 1147: <table border="1"> 1148: <tr> 1149: <td width="100%">Type e to edit output files, c 1150: to start again, and q for exiting:</td> 1151: </tr> 1152: </table> 1153: 1154: First you should enter e to 1155: edit the master file mypar.htm. 1156: 1157: <ul> 1158: <li>Outputs files 1159: 1160: - Observed prevalence in each state: <a 1161: href="..\mytry\prmypar.txt">pmypar.txt</a> 1162: - Estimated parameters and the covariance matrix: <a 1163: href="..\mytry\rmypar.txt">rmypar.txt</a> 1164: - Stationary prevalence in each state: <a 1165: href="..\mytry\plrmypar.txt">plrmypar.txt</a> 1166: - Transition probabilities: <a 1167: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> 1168: - Copy of the parameter file: <a 1169: href="..\mytry\ormypar.txt">ormypar.txt</a> 1170: - Life expectancies by age and initial health status: <a 1171: href="..\mytry\ermypar.txt">ermypar.txt</a> 1172: - Variances of life expectancies by age and initial 1173: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> 1174: 1175: - Health expectancies with their variances: <a 1176: href="..\mytry\trmypar.txt">trmypar.txt</a> 1177: - Standard deviation of stationary prevalence: <a 1178: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> 1179: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a> 1180: 1181: - Population forecasting (if popforecast=1): <a 1182: href="poprmypar.txt">poprmypar.txt</a> 1183: </li> 1184: <li>Graphs 1185: 1186: -<a href="../mytry/pemypar1.gif">One-step transition 1187: probabilities</a> 1188: -<a href="../mytry/pmypar11.gif">Convergence to the 1189: stationary prevalence</a> 1190: -<a href="..\mytry\vmypar11.gif">Observed and stationary 1191: prevalence in state (1) with the confident interval</a> 1192: -<a href="..\mytry\vmypar21.gif">Observed and stationary 1193: prevalence in state (2) with the confident interval</a> 1194: -<a href="..\mytry\expmypar11.gif">Health life 1195: expectancies by age and initial health state (1)</a> 1196: -<a href="..\mytry\expmypar21.gif">Health life 1197: expectancies by age and initial health state (2)</a> 1198: -<a href="..\mytry\emypar1.gif">Total life expectancy by 1199: age and health expectancies in states (1) and (2).</a> </li> 1200: </ul> 1201: 1202: This software have been partly granted by <a 1203: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted 1204: action from the European Union. It will be copyrighted 1205: identically to a GNU software product, i.e. program and software 1206: can be distributed freely for non commercial use. Sources are not 1207: widely distributed today. You can get them by asking us with a 1208: simple justification (name, email, institute) <a 1209: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a 1210: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> . 1211: 1212: Latest version (0.71a of March 2002) can be accessed at <a 1213: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a> 1214: 1215: </body> 1216: </html>