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1: <html> 2: 3: <head> 4: <meta http-equiv="Content-Type" 5: content="text/html; charset=iso-8859-1"> 6: <meta name="ProgId" content="Word.Document"> 7: <meta name="Originator" content="Microsoft Word 9"> 8: <meta name="GENERATOR" content="Microsoft FrontPage Express 2.0"> 9: <title>Computing Health Expectancies using IMaCh</title> 10: <link rel="File-List" href="./imach_fichiers/filelist.xml"> 11: <link rel="Edit-Time-Data" href="./imach_fichiers/editdata.mso"> 12:  20:  38:  43: <style> 44:  386: </style> 387:  390:  394:  395: </head> 396: 397: <body bgcolor="#FFFFFF" link="#0000FF" vlink="#0000FF" lang="FR" 398: style="tab-interval:35.4pt"> 399: 400: <hr size="3" noshade color="#EC5E5E"> 401: 402: <h1 align="center" style="text-align:center">Computing Health 404: Expectancies using IMaCh<o:p></o:p></h1> 405: 406: <h1 align="center" style="text-align:center">(a Maximum 408: Likelihood Computer Program using Interpolation of Markov Chains)<o:p></o:p></h1> 409: 410:  <o:p></o:p> 412: 413: <a 414: href="http://www.ined.fr/"><img src="logo-ined.gif" border="0" 415: width="151" height="76" id="_x0000_i1026"></a><img 416: src="euroreves2.gif" width="151" height="75" id="_x0000_i1027"> 417: 418: <h3 align="center" style="text-align:center"><a 419: href="http://www.ined.fr/">INED</a> and <a 420: href="http://euroreves.ined.fr">EUROREVES<o:p></o:p></a></h3> 423: 424: Version 0.7, 425: February 2002<o:p></o:p> 426: 427: <hr size="3" noshade color="#EC5E5E"> 428: 429: Authors of 430: the program: <a href="http://sauvy.ined.fr/brouard">Nicolas 432: Brouard</a>, senior researcher at the <a 433: href="http://www.ined.fr">Institut National d'Etudes 434: D�mographiques</a> (INED, Paris) in the 436: "Mortality, Health and Epidemiology" Research Unit <o:p></o:p> 437: 438: and Agn�s 439: Li�vre 441: <o:p></o:p> 442: 443: <h4>Contribution to the mathematics: C. R. Heathcote (Australian 445: National University, Canberra).<o:p></o:p></h4> 446: 447: <h4>Contact: Agn�s Li�vre (<a href="mailto:lievre@ined.fr">lievre@ined.fr</a>) 448: </h4> 449: 450: <hr> 451: 454: <ul type="disc"> 455: <li class="MsoNormal" 456: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 457: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 458: href="#intro">Introduction</a> <o:p></o:p></li> 459: <li class="MsoNormal" 460: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 461: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 462: href="#data">On what kind of data can it be used?<o:p></o:p></a></li> 463: <li class="MsoNormal" 464: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 465: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 466: href="#datafile">The data file</a> <o:p></o:p></li> 467: <li class="MsoNormal" 468: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 469: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 470: href="#biaspar">The parameter file</a> <o:p></o:p></li> 471: <li class="MsoNormal" 472: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 473: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 474: href="#running">Running Imach</a> <o:p></o:p></li> 475: <li class="MsoNormal" 476: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 477: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 478: href="#output">Output files and graphs</a> <o:p></o:p></li> 479: <li class="MsoNormal" 480: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 481: mso-list:l17 level1 lfo3;tab-stops:list 36.0pt"><a 482: href="#example">Exemple</a> </li> 483: </ul> 484: 485: <hr> 486: 487: <h2><a name="intro">Introduction<o:p></o:p></a></h2> 489: 490: This program computes Healthy 491: Life Expectancies from cross-longitudinal data using 492: the methodology pioneered by Laditka and Wolf (1). Within the 493: family of Health Expectancies (HE), Disability-free life 494: expectancy (DFLE) is probably the most important index to 495: monitor. In low mortality countries, there is a fear that when 496: mortality declines, the increase in DFLE is not proportionate to 497: the increase in total Life expectancy. This case is called the Expansion 498: of morbidity. Most of the data collected today, in 499: particular by the international <a href="http://euroreves/reves">REVES</a> 500: network on Health expectancy, and most HE indices based on these 501: data, are cross-sectional. It means that the information 502: collected comes from a single cross-sectional survey: people from 503: various ages (but mostly old people) are surveyed on their health 504: status at a single date. Proportion of people disabled at each 505: age, can then be measured at that date. This age-specific 506: prevalence curve is then used to distinguish, within the 507: stationary population (which, by definition, is the life table 508: estimated from the vital statistics on mortality at the same 509: date), the disable population from the disability-free 510: population. Life expectancy (LE) (or total population divided by 511: the yearly number of births or deaths of this stationary 512: population) is then decomposed into DFLE and DLE. This method of 513: computing HE is usually called the Sullivan method (from the name 514: of the author who first described it).<o:p></o:p> 515: 516: Age-specific proportions of people 517: disable are very difficult to forecast because each proportion 518: corresponds to historical conditions of the cohort and it is the 519: result of the historical flows from entering disability and 520: recovering in the past until today. The age-specific intensities 521: (or incidence rates) of entering disability or recovering a good 522: health, are reflecting actual conditions and therefore can be 523: used at each age to forecast the future of this cohort. For 524: example if a country is improving its technology of prosthesis, 525: the incidence of recovering the ability to walk will be higher at 526: each (old) age, but the prevalence of disability will only 527: slightly reflect an improve because the prevalence is mostly 528: affected by the history of the cohort and not by recent period 529: effects. To measure the period improvement we have to simulate 530: the future of a cohort of new-borns entering or leaving at each 531: age the disability state or dying according to the incidence 532: rates measured today on different cohorts. The proportion of 533: people disabled at each age in this simulated cohort will be much 534: lower (using the example of an improvement) that the proportions 535: observed at each age in a cross-sectional survey. This new 536: prevalence curve introduced in a life table will give a much more 537: actual and realistic HE level than the Sullivan method which 538: mostly measured the History of health conditions in this country.<o:p></o:p> 539: 540: Therefore, the main question is how 541: to measure incidence rates from cross-longitudinal surveys? This 542: is the goal of the IMaCH program. From your data and using IMaCH 543: you can estimate period HE and not only Sullivan's HE. Also the 544: standard errors of the HE are computed.<o:p></o:p> 545: 546: A cross-longitudinal survey 547: consists in a first survey ("cross") where individuals 548: from different ages are interviewed on their health status or 549: degree of disability. At least a second wave of interviews 550: ("longitudinal") should measure each new individual 551: health status. Health expectancies are computed from the 552: transitions observed between waves and are computed for each 553: degree of severity of disability (number of life states). More 554: degrees you consider, more time is necessary to reach the Maximum 555: Likelihood of the parameters involved in the model. Considering 556: only two states of disability (disable and healthy) is generally 557: enough but the computer program works also with more health 558: statuses.        560: 561: The simplest model is the multinomial logistic model where pij 562: is the probability to be observed in state j at the second 563: wave conditional to be observed in state i at the first 564: wave. Therefore a simple model is: log(pij/pii)= aij + 565: bij*age+ cij*sex, where 'age' is age and 'sex' 566: is a covariate. The advantage that this computer program claims, 567: comes from that if the delay between waves is not identical for 568: each individual, or if some individual missed an interview, the 569: information is not rounded or lost, but taken into account using 570: an interpolation or extrapolation. hPijx is the 571: probability to be observed in state i at age x+h 572: conditional to the observed state i at age x. The 573: delay 'h' can be split into an exact number (nh*stepm) 574: of unobserved intermediate states. This elementary transition (by 575: month or quarter trimester, semester or year) is modeled as a 576: multinomial logistic. The hPx matrix is simply the matrix 577: product of nh*stepm elementary matrices and the 578: contribution of each individual to the likelihood is simply hPijx. 579: <o:p></o:p> 580: 581: The program presented in this 582: manual is a quite general program named IMaCh 583: (for Interpolated MArkov CHain), 584: designed to analyse transition data from longitudinal surveys. 585: The first step is the parameters estimation of a transition 586: probabilities model between an initial status and a final status. 587: From there, the computer program produces some indicators such as 588: observed and stationary prevalence, life expectancies and their 589: variances and graphs. Our transition model consists in absorbing 590: and non-absorbing states with the possibility of return across 591: the non-absorbing states. The main advantage of this package, 592: compared to other programs for the analysis of transition data 593: (For example: Proc Catmod of SAS(r)) is that the whole 594: individual information is used even if an interview is missing, a 595: status or a date is unknown or when the delay between waves is 596: not identical for each individual. The program can be executed 597: according to parameters: selection of a sub-sample, number of 598: absorbing and non-absorbing states, number of waves taken in 599: account (the user inputs the first and the last interview), a 600: tolerance level for the maximization function, the periodicity of 601: the transitions (we can compute annual, quarterly or monthly 602: transitions), covariates in the model. It works on Windows or on 603: Unix.<o:p></o:p> 604: 605: <hr> 606: 607: (1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New 608: Methods for Analyzing Active Life Expectancy". Journal of 609: Aging and Health. Vol 10, No. 2. 610: 611: <hr> 612: 613: <h2><a name="data">On what kind of data can it be used?<o:p></o:p></a></h2> 614: 615: The minimum data required for a 616: transition model is the recording of a set of individuals 617: interviewed at a first date and interviewed again at least one 618: another time. From the observations of an individual, we obtain a 619: follow-up over time of the occurrence of a specific event. In 620: this documentation, the event is related to health status at 621: older ages, but the program can be applied on a lot of 622: longitudinal studies in different contexts. To build the data 623: file explained into the next section, you must have the month and 624: year of each interview and the corresponding health status. But 625: in order to get age, date of birth (month and year) is required 626: (missing values is allowed for month). Date of death (month and 627: year) is an important information also required if the individual 628: is dead. Shorter steps (i.e. a month) will more closely take into 629: account the survival time after the last interview.<o:p></o:p> 630: 631: <hr> 632: 633: <h2><a name="datafile">The data file<o:p></o:p></a></h2> 635: 636: In this example, 8,000 people have 637: been interviewed in a cross-longitudinal survey of 4 waves (1984, 638: 1986, 1988, 1990). Some people missed 1, 2 or 3 interviews. 639: Health statuses are healthy (1) and disable (2). The survey is 640: not a real one. It is a simulation of the American Longitudinal 641: Survey on Aging. The disability state is defined if the 642: individual missed one of four ADL (Activity of daily living, like 643: bathing, eating, walking). Therefore, even is the individuals 644: interviewed in the sample are virtual, the information brought 645: with this sample is close to the situation of the United States. 646: Sex is not recorded is this sample.<o:p></o:p> 647: 648: Each line of the data set (named <a href="data1.txt">data1.txt</a> 650: in this first example) is an individual record which fields are: <o:p></o:p> 651: 652: <ul type="disc"> 653: <li class="MsoNormal" 654: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 655: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Index 656: number: positive number (field 1) <o:p></o:p></li> 657: <li class="MsoNormal" 658: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 659: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">First 660: covariate positive number (field 2) <o:p></o:p></li> 661: <li class="MsoNormal" 662: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 663: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Second 664: covariate positive number (field 3) <o:p></o:p></li> 665: <li class="MsoNormal" 666: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 667: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt"><a 668: name="Weight">Weight</a>: positive number (field 670: 4) . In most surveys individuals are weighted according 671: to the stratification of the sample.<o:p></o:p></li> 672: <li class="MsoNormal" 673: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 674: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 675: of birth: coded as mm/yyyy. Missing dates are coded 676: as 99/9999 (field 5) <o:p></o:p></li> 677: <li class="MsoNormal" 678: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 679: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 680: of death: coded as mm/yyyy. Missing dates are coded 681: as 99/9999 (field 6) <o:p></o:p></li> 682: <li class="MsoNormal" 683: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 684: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 685: of first interview: coded as mm/yyyy. Missing dates 686: are coded as 99/9999 (field 7) <o:p></o:p></li> 687: <li class="MsoNormal" 688: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 689: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Status 690: at first interview: positive number. Missing values 691: ar coded -1. (field 8) <o:p></o:p></li> 692: <li class="MsoNormal" 693: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 694: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 695: of second interview: coded as mm/yyyy. Missing dates 696: are coded as 99/9999 (field 9) <o:p></o:p></li> 697: <li class="MsoNormal" 698: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 699: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Status 700: at second interview positive number. Missing 701: values ar coded -1. (field 10) <o:p></o:p></li> 702: <li class="MsoNormal" 703: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 704: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 705: of third interview: coded as mm/yyyy. Missing dates 706: are coded as 99/9999 (field 11) <o:p></o:p></li> 707: <li class="MsoNormal" 708: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 709: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Status 710: at third interview positive number. Missing 711: values ar coded -1. (field 12) <o:p></o:p></li> 712: <li class="MsoNormal" 713: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 714: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Date 715: of fourth interview: coded as mm/yyyy. Missing dates 716: are coded as 99/9999 (field 13) <o:p></o:p></li> 717: <li class="MsoNormal" 718: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 719: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">Status 720: at fourth interview positive number. Missing 721: values are coded -1. (field 14) <o:p></o:p></li> 722: <li class="MsoNormal" 723: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 724: mso-list:l12 level1 lfo6;tab-stops:list 36.0pt">etc<o:p></o:p></li> 725: </ul> 726: 727:  <o:p></o:p> 728: 729: If your longitudinal survey do not 730: include information about weights or covariates, you must fill 731: the column with a number (e.g. 1) because a missing field is not 732: allowed.<o:p></o:p> 733: 734: <hr> 735: 736: <h2>Your first example parameter file<a 737: href="http://euroreves.ined.fr/imach"></a><a name="uio"><o:p></o:p></a></h2> 738: 739: <h2><a name="biaspar"></a>#Imach version 0.7, February 2002, 740: INED-EUROREVES <o:p></o:p></h2> 741: 742: This is a comment. Comments start with a '#'.<o:p></o:p> 743: 744: <h4>First uncommented line<o:p></o:p></h4> 745: 746: <pre style="text-align:justify">title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4<o:p></o:p></pre> 747: 748: <ul type="disc"> 749: <li class="MsoNormal" 750: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 751: text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt">title= 752: 1st_example is title of the run. <o:p></o:p></li> 753: <li class="MsoNormal" 754: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 755: text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt">datafile=data1.txt 756: is the name of the data set. Our example is a six years 757: follow-up survey. It consists in a baseline followed by 3 758: reinterviews. <o:p></o:p></li> 759: <li class="MsoNormal" 760: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 761: text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt">lastobs= 762: 8600 the program is able to run on a subsample where the 763: last observation number is lastobs. It can be set a 764: bigger number than the real number of observations (e.g. 765: 100000). In this example, maximisation will be done on 766: the 8600 first records. <o:p></o:p></li> 767: <li class="MsoNormal" 768: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 769: text-align:justify;mso-list:l1 level1 lfo9;tab-stops:list 36.0pt">firstpass=1 770: , lastpass=4 In case of more than two interviews 771: in the survey, the program can be run on selected 772: transitions periods. firstpass=1 means the first 773: interview included in the calculation is the baseline 774: survey. lastpass=4 means that the information brought by 775: the 4th interview is taken into account.<o:p></o:p></li> 776: </ul> 777: 778:  <o:p></o:p> 780: 781: <h4 782: 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">Second 783: uncommented line<a name="biaspar-2"><o:p></o:p></a></h4> 784: 785: <pre style="text-align:justify">ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></pre> 786: 787: <ul type="disc"> 788: <li class="MsoNormal" 789: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 790: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">ftol=1e-8 791: Convergence tolerance on the function value in the 792: maximisation of the likelihood. Choosing a correct value 793: for ftol is difficult. 1e-8 is a correct value for a 32 794: bits computer.<o:p></o:p></li> 795: <li class="MsoNormal" 796: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 797: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">stepm=1 798: Time unit in months for interpolation. Examples:<o:p></o:p></li> 799: <li><ul type="circle"> 800: <li class="MsoNormal" 801: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 802: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 803: stepm=1, the unit is a month <o:p></o:p></li> 804: <li class="MsoNormal" 805: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 806: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 807: stepm=4, the unit is a trimester<o:p></o:p></li> 808: <li class="MsoNormal" 809: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 810: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 811: stepm=12, the unit is a year <o:p></o:p></li> 812: <li class="MsoNormal" 813: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 814: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 815: stepm=24, the unit is two years<o:p></o:p></li> 816: <li class="MsoNormal" 817: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 818: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">... 819: <o:p></o:p> </li> 820: </ul> 821: </li> 822: <li class="MsoNormal" 823: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 824: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">ncov=2 825: Number of covariates in the datafile. The intercept and 826: the age parameter are counting for 2 covariates.<o:p></o:p></li> 827: <li class="MsoNormal" 828: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 829: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">nlstate=2 830: Number of non-absorbing (alive) states. Here we have two 831: alive states: disability-free is coded 1 and disability 832: is coded 2. <o:p></o:p></li> 833: <li class="MsoNormal" 834: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 835: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">ndeath=1 836: Number of absorbing states. The absorbing state death is 837: coded 3. <o:p></o:p></li> 838: <li class="MsoNormal" 839: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 840: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">maxwav=4 841: Number of waves in the datafile.<o:p></o:p></li> 842: <li class="MsoNormal" 843: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 844: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt"><a 845: name="mle">mle</a>=1 Option for the 846: Maximisation Likelihood Estimation. <o:p></o:p></li> 847: <li><ul type="circle"> 848: <li class="MsoNormal" 849: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 850: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 851: mle=1 the program does the maximisation and the 852: calculation of health expectancies <o:p></o:p></li> 853: <li class="MsoNormal" 854: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 855: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 856: mle=0 the program only does the calculation of 857: the health expectancies. <o:p></o:p></li> 858: </ul> 859: </li> 860: <li class="MsoNormal" 861: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 862: text-align:justify;mso-list:l14 level1 lfo12;tab-stops:list 36.0pt">weight=0 863: Possibility to add weights. <o:p></o:p></li> 864: <li><ul type="circle"> 865: <li class="MsoNormal" 866: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 867: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 868: weight=0 no weights are included <o:p></o:p></li> 869: <li class="MsoNormal" 870: style="mso-margin-top-alt:auto;mso-margin-bottom-alt: 871: auto;text-align:justify;mso-list:l14 level2 lfo12;tab-stops:list 72.0pt">If 872: weight=1 the maximisation integrates the weights 873: which are in field <a href="#Weight">4<o:p></o:p></a></li> 874: </ul> 875: </li> 876: </ul> 877: 878: <h4 879: 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">Covariates<o:p></o:p></h4> 880: 881: Intercept 883: and age are systematically included in the model. Additional 884: covariates can be included with the command <o:p></o:p> 885: 886: <pre style="text-align:justify">model=list of covariates<o:p></o:p></pre> 887: 888: <ul type="disc"> 889: <li class="MsoNormal" 890: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 891: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 892: model=. then no covariates are included<o:p></o:p></li> 893: <li class="MsoNormal" 894: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 895: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 896: model=V1 the model includes the first 897: covariate (field 2)<o:p></o:p></li> 898: <li class="MsoNormal" 899: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 900: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 901: model=V2 the model includes the second 902: covariate (field 3)<o:p></o:p></li> 903: <li class="MsoNormal" 904: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 905: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 906: model=V1+V2 the model includes the first 907: and the second covariate (fields 2 and 3)<o:p></o:p></li> 908: <li class="MsoNormal" 909: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 910: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 911: model=V1*V2 the model includes the 912: product of the first and the second covariate (fields 2 913: and 3)<o:p></o:p></li> 914: <li class="MsoNormal" 915: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 916: text-align:justify;mso-list:l2 level1 lfo15;tab-stops:list 36.0pt">if 917: model=V1+V1*age the model includes the 918: product covariate*age<o:p></o:p></li> 919: </ul> 920: 921: <h4 922: 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">Guess 923: values for optimisation <o:p></o:p></h4> 924: 925: You 927: must write the initial guess values of the parameters for 928: optimisation. The number of parameters, N depends on the 929: number of absorbing states and non-absorbing states and on the 930: number of covariates. 931: N is given by the formula N=(nlstate + 932: ndeath-1)*nlstate*ncov . 933: 934: Thus in the simple case with 2 covariates (the model is log 935: (pij/pii) = aij + bij * age where intercept and age are the two 936: covariates), and 2 health degrees (1 for disability-free and 2 937: for disability) and 1 absorbing state (3), you must enter 8 938: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can 939: start with zeros as in this example, but if you have a more 940: precise set (for example from an earlier run) you can enter it 941: and it will speed up them 942: Each of the four lines starts with indices "ij": ij 943: aij bij <o:p></o:p> 944: 945: <pre 946: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left: 947: 36.0pt;margin-bottom:.0001pt;text-align:justify"># Guess values of aij and bij in log (pij/pii) = aij + bij * age<o:p></o:p></pre> 948: 949: <pre 950: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 951: margin-bottom:.0001pt;text-align:justify">12 -14.155633  0.110794 <o:p></o:p></pre> 953: 954: <pre 955: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 956: margin-bottom:.0001pt;text-align:justify">13  -7.925360  0.032091 <o:p></o:p></pre> 958: 959: <pre 960: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 961: margin-bottom:.0001pt;text-align:justify">21  -1.890135 -0.029473 <o:p></o:p></pre> 963: 964: <pre 965: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 966: margin-bottom:.0001pt;text-align:justify">23  -6.234642  0.022315 <o:p></o:p></pre> 968: 969: or, 971: to simplify: <o:p></o:p> 972: 973: <pre 974: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left: 975: 36.0pt;margin-bottom:.0001pt;text-align:justify">12 0.0 0.0<o:p></o:p></pre> 976: 977: <pre 978: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 979: margin-bottom:.0001pt;text-align:justify">13 0.0 0.0<o:p></o:p></pre> 981: 982: <pre 983: style="margin-top:0cm;margin-right: 984: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align: 985: justify">21 0.0 0.0<o:p></o:p></pre> 986: 987: <pre 988: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 989: margin-bottom:.0001pt;text-align:justify">23 0.0 0.0<o:p></o:p></pre> 991: 992: <h4 993: 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">Guess 994: values for computing variances<o:p></o:p></h4> 995: 996: This 998: is an output if <a href="#mle">mle</a>=1. But it can be used as 999: an input to get the various output data files (Health 1000: expectancies, stationary prevalence etc.) and figures without 1001: rerunning the rather long maximisation phase (mle=0). <o:p></o:p> 1002: 1003: The 1005: scales are small values for the evaluation of numerical 1006: derivatives. These derivatives are used to compute the hessian 1007: matrix of the parameters, that is the inverse of the covariance 1008: matrix, and the variances of health expectancies. Each line 1009: consists in indices "ij" followed by the initial scales 1010: (zero to simplify) associated with aij and bij. <o:p></o:p> 1011: 1012: <ul type="disc"> 1013: <li class="MsoNormal" 1014: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1015: text-align:justify;mso-list:l16 level1 lfo18;tab-stops:list 36.0pt">If 1016: mle=1 you can enter zeros:<o:p></o:p></li> 1017: </ul> 1018: 1019: <pre 1020: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left: 1021: 36.0pt;margin-bottom:.0001pt;text-align:justify"># Scales (for hessian or gradient estimation)<o:p></o:p></pre> 1022: 1023: <pre 1024: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1025: margin-bottom:.0001pt;text-align:justify">12 0. 0. <o:p></o:p></pre> 1027: 1028: <pre 1029: style="margin-top:0cm;margin-right: 1030: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align: 1031: justify">13 0. 0. <o:p></o:p></pre> 1032: 1033: <pre 1034: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1035: margin-bottom:.0001pt;text-align:justify">21 0. 0. <o:p></o:p></pre> 1037: 1038: <pre 1039: style="margin-top:0cm;margin-right: 1040: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align: 1041: justify">23 0. 0. <o:p></o:p></pre> 1042: 1043: <ul type="disc"> 1044: <li class="MsoNormal" 1045: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1046: text-align:justify;mso-list:l11 level1 lfo21;tab-stops:list 36.0pt">If 1047: mle=0 you must enter a covariance matrix (usually 1048: obtained from an earlier run).<o:p></o:p></li> 1049: </ul> 1050: 1051: <h4 1052: 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">Covariance 1053: matrix of parameters<o:p></o:p></h4> 1054: 1055: This 1057: is an output if <a href="#mle">mle</a>=1. But it can be used as 1058: an input to get the various output data files (Health 1059: expectancies, stationary prevalence etc.) and figures without 1060: rerunning the rather long maximisation phase (mle=0). <o:p></o:p> 1061: 1062: Each 1064: line starts with indices "ijk" followed by the 1065: covariances between aij and bij: <o:p></o:p> 1066: 1067: <pre style="text-align:justify"> <o:p></o:p></pre> 1068: 1069: <pre style="text-align:justify">   121 Var(a12) <o:p></o:p></pre> 1070: 1071: <pre style="text-align:justify">   122 Cov(b12,a12)  Var(b12) <o:p></o:p></pre> 1072: 1073: <pre style="text-align:justify">          ...<o:p></o:p></pre> 1074: 1075: <pre style="text-align:justify">   232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23) <o:p></o:p></pre> 1076: 1077: <ul type="disc"> 1078: <li class="MsoNormal" 1079: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1080: text-align:justify;mso-list:l18 level1 lfo24;tab-stops:list 36.0pt">If 1081: mle=1 you can enter zeros. <o:p></o:p></li> 1082: </ul> 1083: 1084: <pre 1085: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left: 1086: 36.0pt;margin-bottom:.0001pt;text-align:justify"># Covariance matrix<o:p></o:p></pre> 1087: 1088: <pre 1089: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1090: margin-bottom:.0001pt;text-align:justify">121 0.<o:p></o:p></pre> 1092: 1093: <pre 1094: style="margin-top:0cm;margin-right: 1095: 36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt;text-align: 1096: justify">122 0. 0.<o:p></o:p></pre> 1097: 1098: <pre 1099: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1100: margin-bottom:.0001pt;text-align:justify">131 0. 0. 0. <o:p></o:p></pre> 1102: 1103: <pre 1104: style="margin-top:0cm; 1105: margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt; 1106: text-align:justify">132 0. 0. 0. 0. <o:p></o:p></pre> 1107: 1108: <pre 1109: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1110: margin-bottom:.0001pt;text-align:justify">211 0. 0. 0. 0. 0. <o:p></o:p></pre> 1112: 1113: <pre 1114: style="margin-top:0cm; 1115: margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom:.0001pt; 1116: text-align:justify">212 0. 0. 0. 0. 0. 0. <o:p></o:p></pre> 1117: 1118: <pre 1119: style="margin-top:0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt; 1120: margin-bottom:.0001pt;text-align:justify">231 0. 0. 0. 0. 0. 0. 0. <o:p></o:p></pre> 1122: 1123: <pre 1124: style="margin-top: 1125: 0cm;margin-right:36.0pt;margin-bottom:0cm;margin-left:36.0pt;margin-bottom: 1126: .0001pt;text-align:justify">232 0. 0. 0. 0. 0. 0. 0. 0.<o:p></o:p></pre> 1127: 1128: <ul type="disc"> 1129: <li class="MsoNormal" 1130: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1131: text-align:justify;mso-list:l7 level1 lfo27;tab-stops:list 36.0pt">If 1132: mle=0 you must enter a covariance matrix (usually 1133: obtained from an earlier run).<o:p></o:p></li> 1134: </ul> 1135: 1136: <h4 1137: 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">Age 1138: range for calculation of stationary prevalences and health 1139: expectancies<o:p></o:p></h4> 1140: 1141: <pre style="text-align:justify">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></pre> 1142: 1143: Once 1145: we obtained the estimated parameters, the program is able to 1146: calculated stationary prevalence, transitions probabilities and 1147: life expectancies at any age. Choice of age range is useful for 1148: extrapolation. In our data file, ages varies from age 70 to 102. 1149: Setting bage=50 and fage=100, makes the program computing life 1150: expectancy from age bage to age fage. As we use a model, we can 1151: compute life expectancy on a wider age range than the age range 1152: from the data. But the model can be rather wrong on big 1153: intervals.<o:p></o:p> 1154: 1155: Similarly, 1157: it is possible to get extrapolated stationary prevalence by age 1158: ranging from agemin to agemax. <o:p></o:p> 1159: 1160: <ul type="disc"> 1161: <li class="MsoNormal" 1162: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1163: text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt">agemin= 1164: Minimum age for calculation of the stationary prevalence <o:p></o:p></li> 1165: <li class="MsoNormal" 1166: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1167: text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt">agemax= 1168: Maximum age for calculation of the stationary prevalence <o:p></o:p></li> 1169: <li class="MsoNormal" 1170: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1171: text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt">bage= 1172: Minimum age for calculation of the health expectancies <o:p></o:p></li> 1173: <li class="MsoNormal" 1174: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1175: text-align:justify;mso-list:l13 level1 lfo30;tab-stops:list 36.0pt">fage= 1176: Maximum age for calculation of the health expectancies <o:p></o:p></li> 1177: </ul> 1178: 1179: <h4 1180: 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"><a 1181: name="Computing">Computing</a> the observed prevalence<o:p></o:p></h4> 1182: 1183: <pre style="text-align:justify">begin-prev-date=1/1/1984 end-prev-date=1/6/1988 <o:p></o:p></pre> 1184: 1185: Statements 1187: 'begin-prev-date' and 'end-prev-date' allow to select the period 1188: in which we calculate the observed prevalences in each state. In 1189: this example, the prevalences are calculated on data survey 1190: collected between 1 January 1984 and 1 June 1988. <o:p></o:p> 1191: 1192: <ul type="disc"> 1193: <li class="MsoNormal" 1194: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1195: text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt">begin-prev-date= 1196: Starting date (day/month/year)<o:p></o:p></li> 1197: <li class="MsoNormal" 1198: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1199: text-align:justify;mso-list:l3 level1 lfo33;tab-stops:list 36.0pt">end-prev-date= 1200: Final date (day/month/year)<o:p></o:p></li> 1201: </ul> 1202: 1203: <h4 1204: 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">Population- 1205: or status-based health expectancies<o:p></o:p></h4> 1207: 1208: <pre style="text-align:justify">pop_based=0<o:p></o:p></pre> 1209: 1210: The 1212: user has the possibility to choose between population-based or 1213: status-based health expectancies. If pop_based=0 then 1214: status-based health expectancies are computed and if pop_based=1, 1215: the programme computes population-based health expectancies. 1216: Health expectancies are weighted averages of health expectancies 1217: respective of the initial state. For a status-based index, the 1218: weights are the cross-sectional prevalences observed between two 1219: dates, as <a href="#Computing">previously explained</a>, whereas 1220: for a population-based index, the weights are the stationary 1221: prevalences.<o:p></o:p> 1222: 1223: <h4 1224: 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">Prevalence 1225: forecasting <o:p></o:p></h4> 1226: 1227: <pre style="text-align:justify">starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 <o:p></o:p></pre> 1228: 1229: Prevalence 1231: and population projections are available only if the 1232: interpolation unit is a month, i.e. stepm=1. The programme 1233: estimates the prevalence in each state at a precise date 1234: expressed in day/month/year. The programme computes one 1235: forecasted prevalence a year from a starting date (1 January of 1236: 1989 in this example) to a final date (1 January 1992). The 1237: statement mov_average allows to compute smoothed forecasted 1238: prevalences with a five-age moving average centred at the mid-age 1239: of the five-age period. <o:p></o:p> 1240: 1241: <ul type="disc"> 1242: <li class="MsoNormal" 1243: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1244: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">starting-proj-date= 1245: starting date (day/month/year) of forecasting<o:p></o:p></li> 1246: <li class="MsoNormal" 1247: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1248: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">final-proj-date= 1249: final date (day/month/year) of forecasting<o:p></o:p></li> 1250: <li class="MsoNormal" 1251: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1252: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">mov_average= 1253: smoothing with a five-age moving average centred at the 1254: mid-age of the five-age period. The command 1255: mov_average takes value 1 if the prevalences are 1256: smoothed and 0 otherwise.<o:p></o:p></li> 1257: </ul> 1258: 1259: <h4 1260: 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">Last 1261: uncommented line : Population forecasting <o:p></o:p></h4> 1262: 1263: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992<o:p></o:p></pre> 1264: 1265: This 1267: command is available if the interpolation unit is a month, i.e. 1268: stepm=1 and if popforecast=1. From a data file including age and 1269: number of persons alive at the precise date popfiledate, 1271: you can forecast the number of persons in each state until date 1273: last-popfiledate. In this example, the popfile <a 1274: href="pyram.txt">pyram.txt</a>  includes real 1276: data which are the Japanese population in 1989.  <o:p></o:p> 1277: 1278: <ul type="disc"> 1279: <li class="MsoNormal" 1280: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1281: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">popforecast= 1282: 0 Option for population forecasting. If 1283: popforecast=1, the programme does the forecasting.<o:p></o:p></li> 1284: <li class="MsoNormal" 1285: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1286: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">popfile= 1287: name of the population file<o:p></o:p></li> 1288: <li class="MsoNormal" 1289: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1290: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">popfiledate= 1291: date of the population population<o:p></o:p></li> 1292: <li class="MsoNormal" 1293: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1294: text-align:justify;mso-list:l10 level1 lfo36;tab-stops:list 36.0pt">last-popfiledate= 1295: date of the last population projection <o:p></o:p></li> 1296: </ul> 1297: 1298: <hr> 1299: 1300: <h2 1301: 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"><a 1302: name="running"></a>Running Imach with this example<o:p></o:p></h2> 1303: 1304: We 1306: assume that you entered your <a href="biaspar.imach">1st_example 1307: parameter file</a> as explained <a href="#biaspar">above</a>. To 1309: run the program you should click on the imach.exe icon and enter 1310: the name of the parameter file which is for example <a 1311: href="..\mle\biaspar.txt">C:\usr\imach\mle\biaspar.txt</a> (you 1312: also can click on the biaspar.txt icon located in <a 1313: href="..\mle">C:\usr\imach\mle</a> and put it with the mouse on 1314: the imach window).<o:p></o:p> 1315: 1316: The 1318: time to converge depends on the step unit that you used (1 month 1319: is cpu consuming), on the number of cases, and on the number of 1320: variables.<o:p></o:p> 1321: 1322: The 1324: program outputs many files. Most of them are files which will be 1325: plotted for better understanding.<o:p></o:p> 1326: 1327: <hr> 1328: 1329: <h2 1330: 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"><a 1331: name="output">Output of the program and graphs</a> <o:p></o:p></h2> 1332: 1333: Once 1335: the optimization is finished, some graphics can be made with a 1336: grapher. We use Gnuplot which is an interactive plotting program 1337: copyrighted but freely distributed. A gnuplot reference manual is 1338: available <a href="http://www.gnuplot.info/">here</a>. 1339: When the running is finished, the user should enter a character 1340: for plotting and output editing. <o:p></o:p> 1341: 1342: These 1344: characters are:<o:p></o:p> 1345: 1346: <ul type="disc"> 1347: <li class="MsoNormal" 1348: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1349: text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt">'c' 1350: to start again the program from the beginning.<o:p></o:p></li> 1351: <li class="MsoNormal" 1352: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1353: text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt">'e' 1354: opens the <a href="biaspar.htm">biaspar.htm</a> 1355: file to edit the output files and graphs. <o:p></o:p></li> 1356: <li class="MsoNormal" 1357: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1358: text-align:justify;mso-list:l0 level1 lfo41;tab-stops:list 36.0pt">'q' 1359: for exiting.<o:p></o:p></li> 1360: </ul> 1361: 1362: <h5 1363: style="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">Results 1365: files 1366: 1367: - <a name="Observed_prevalence_in_each_state">Observed 1369: prevalence in each state</a> (and at first pass): 1370: <a href="prbiaspar.txt">prbiaspar.txt<o:p></o:p></a></h5> 1371: 1372: The 1374: first line is the title and displays each field of the file. The 1375: first column is age. The fields 2 and 6 are the proportion of 1376: individuals in states 1 and 2 respectively as observed during the 1377: first exam. Others fields are the numbers of people in states 1, 1378: 2 or more. The number of columns increases if the number of 1379: states is higher than 2. 1380: The header of the file is <o:p></o:p> 1381: 1382: <pre style="text-align:justify"># Age Prev(1) N(1) N Age Prev(2) N(2) N<o:p></o:p></pre> 1383: 1384: <pre style="text-align:justify">70 1.00000 631 631 70 0.00000 0 631<o:p></o:p></pre> 1385: 1386: <pre style="text-align:justify">71 0.99681 625 627 71 0.00319 2 627 <o:p></o:p></pre> 1387: 1388: <pre style="text-align:justify">72 0.97125 1115 1148 72 0.02875 33 1148 <o:p></o:p></pre> 1389: 1390: It 1392: means that at age 70, the prevalence in state 1 is 1.000 and in 1393: state 2 is 0.00 . At age 71 the number of individuals in state 1 1394: is 625 and in state 2 is 2, hence the total number of people aged 1395: 71 is 625+2=627. <o:p></o:p> 1396: 1397: <h5 1398: 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">- 1399: Estimated parameters and covariance matrix: <a 1400: href="rbiaspar.txt">rbiaspar.txt<o:p></o:p></a></h5> 1401: 1402: This 1404: file contains all the maximisation results: <o:p></o:p> 1405: 1406: <pre style="text-align:justify"> -2 log likelihood= 21660.918613445392<o:p></o:p></pre> 1407: 1408: <pre style="text-align:justify"> Estimated parameters: a12 = -12.290174 b12 = 0.092161 <o:p></o:p></pre> 1409: 1410: <pre style="text-align:justify">                       a13 = -9.155590  b13 = 0.046627 <o:p></o:p></pre> 1411: 1412: <pre style="text-align:justify">                       a21 = -2.629849  b21 = -0.022030 <o:p></o:p></pre> 1413: 1414: <pre style="text-align:justify">                       a23 = -7.958519  b23 = 0.042614  <o:p></o:p></pre> 1415: 1416: <pre style="text-align:justify"> Covariance matrix: Var(a12) = 1.47453e-001<o:p></o:p></pre> 1417: 1418: <pre style="text-align:justify">                    Var(b12) = 2.18676e-005<o:p></o:p></pre> 1419: 1420: <pre style="text-align:justify">                    Var(a13) = 2.09715e-001<o:p></o:p></pre> 1421: 1422: <pre style="text-align:justify">                    Var(b13) = 3.28937e-005  <o:p></o:p></pre> 1423: 1424: <pre style="text-align:justify">                    Var(a21) = 9.19832e-001<o:p></o:p></pre> 1425: 1426: <pre style="text-align:justify">                    Var(b21) = 1.29229e-004<o:p></o:p></pre> 1427: 1428: <pre style="text-align:justify">                    Var(a23) = 4.48405e-001<o:p></o:p></pre> 1429: 1430: <pre style="text-align:justify">                    Var(b23) = 5.85631e-005 <o:p></o:p></pre> 1431: 1432: <pre style="text-align:justify"> <o:p></o:p></pre> 1433: 1434: By 1436: substitution of these parameters in the regression model, we 1437: obtain the elementary transition probabilities:<o:p></o:p> 1438: 1439: <img 1441: src="pebiaspar1.gif" width="400" height="300" id="_x0000_i1037"> 1442: 1443: <h5 1444: 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">- 1445: Transition probabilities: <a href="pijrbiaspar.txt">pijrbiaspar.txt<o:p></o:p></a></h5> 1448: 1449: Here 1451: are the transitions probabilities Pij(x, x+nh) where nh is a 1452: multiple of 2 years. The first column is the starting age x (from 1453: age 50 to 100), the second is age (x+nh) and the others are the 1454: transition probabilities p11, p12, p13, p21, p22, p23. For 1455: example, line 5 of the file is: <o:p></o:p> 1456: 1457: <pre style="text-align:justify"> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 <o:p></o:p></pre> 1458: 1459: and 1461: this means: <o:p></o:p> 1462: 1463: <pre style="text-align:justify">p11(100,106)=0.02655<o:p></o:p></pre> 1464: 1465: <pre style="text-align:justify">p12(100,106)=0.17622<o:p></o:p></pre> 1466: 1467: <pre style="text-align:justify">p13(100,106)=0.79722<o:p></o:p></pre> 1468: 1469: <pre style="text-align:justify">p21(100,106)=0.01809<o:p></o:p></pre> 1470: 1471: <pre style="text-align:justify">p22(100,106)=0.13678<o:p></o:p></pre> 1472: 1473: <pre style="text-align:justify">p22(100,106)=0.84513 <o:p></o:p></pre> 1474: 1475: <h5 1476: 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">- 1477: <a name="Stationary_prevalence_in_each_state">Stationary 1478: prevalence in each state</a>: <a href="plrbiaspar.txt">plrbiaspar.txt<o:p></o:p></a></h5> 1479: 1480: <pre style="text-align:justify">#Prevalence<o:p></o:p></pre> 1481: 1482: <pre style="text-align:justify">#Age 1-1 2-2<o:p></o:p></pre> 1483: 1484: <pre style="text-align:justify"> <o:p></o:p></pre> 1485: 1486: <pre style="text-align:justify">#************ <o:p></o:p></pre> 1487: 1488: <pre style="text-align:justify">70 0.90134 0.09866<o:p></o:p></pre> 1489: 1490: <pre style="text-align:justify">71 0.89177 0.10823 <o:p></o:p></pre> 1491: 1492: <pre style="text-align:justify">72 0.88139 0.11861 <o:p></o:p></pre> 1493: 1494: <pre style="text-align:justify">73 0.87015 0.12985 <o:p></o:p></pre> 1495: 1496: At 1498: age 70 the stationary prevalence is 0.90134 in state 1 and 1499: 0.09866 in state 2. This stationary prevalence differs from 1500: observed prevalence. Here is the point. The observed prevalence 1501: at age 70 results from the incidence of disability, incidence of 1502: recovery and mortality which occurred in the past of the cohort. 1503: Stationary prevalence results from a simulation with actual 1504: incidences and mortality (estimated from this cross-longitudinal 1505: survey). It is the best predictive value of the prevalence in the 1506: future if "nothing changes in the future". This is 1507: exactly what demographers do with a Life table. Life expectancy 1508: is the expected mean time to survive if observed mortality rates 1509: (incidence of mortality) "remains constant" in the 1510: future. <o:p></o:p> 1511: 1512: <h5 1513: 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">- 1514: Standard deviation of stationary prevalence: <a 1515: href="vplrbiaspar.txt">vplrbiaspar.txt<o:p></o:p></a></h5> 1516: 1517: The 1519: stationary prevalence has to be compared with the observed 1520: prevalence by age. But both are statistical estimates and 1521: subjected to stochastic errors due to the size of the sample, the 1522: design of the survey, and, for the stationary prevalence to the 1523: model used and fitted. It is possible to compute the standard 1524: deviation of the stationary prevalence at each age.<o:p></o:p> 1525: 1526: <h5 1527: 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">-Observed 1528: and stationary prevalence in state (2=disable) with the confident 1529: interval: <a href="vbiaspar21.htm">vbiaspar21.gif<o:p></o:p></a></h5> 1530: 1531: This 1533: graph exhibits the stationary prevalence in state (2) with the 1534: confidence interval in red. The green curve is the observed 1535: prevalence (or proportion of individuals in state (2)). Without 1536: discussing the results (it is not the purpose here), we observe 1537: that the green curve is rather below the stationary prevalence. 1538: It suggests an increase of the disability prevalence in the 1539: future.<o:p></o:p> 1540: 1541: <img 1543: src="vbiaspar21.gif" width="400" height="300" id="_x0000_i1038"> 1544: 1545: <h5 1546: style="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">-Convergence 1547: to the stationary prevalence of disability: <a 1548: href="pbiaspar11.gif">pbiaspar11.gif</a> 1549: <img src="pbiaspar11.gif" width="400" height="300" 1550: id="_x0000_i1039"><o:p></o:p></h5> 1551: 1552: This 1554: graph plots the conditional transition probabilities from an 1555: initial state (1=healthy in red at the bottom, or 2=disable in 1556: green on top) at age x to the final state 2=disable at 1557: age x+h. Conditional means at the condition to be alive 1558: at age x+h which is hP12x + hP22x. The 1559: curves hP12x/(hP12x + hP22x) and hP22x/(hP12x 1560: + hP22x) converge with h, to the stationary 1561: prevalence of disability. In order to get the stationary 1562: prevalence at age 70 we should start the process at an earlier 1563: age, i.e.50. If the disability state is defined by severe 1564: disability criteria with only a few chance to recover, then the 1565: incidence of recovery is low and the time to convergence is 1566: probably longer. But we don't have experience yet.<o:p></o:p> 1567: 1568: <h5 1569: 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">- 1570: Life expectancies by age and initial health status: <a 1571: href="erbiaspar.txt">erbiaspar.txt<o:p></o:p></a></h5> 1572: 1573: <pre style="text-align:justify"># Health expectancies <o:p></o:p></pre> 1574: 1575: <pre style="text-align:justify"># Age 1-1 1-2 2-1 2-2 <o:p></o:p></pre> 1576: 1577: <pre style="text-align:justify">70 10.9226 3.0401 5.6488 6.2122 <o:p></o:p></pre> 1578: 1579: <pre style="text-align:justify">71 10.4384 3.0461 5.2477 6.1599 <o:p></o:p></pre> 1580: 1581: <pre style="text-align:justify">72 9.9667 3.0502 4.8663 6.1025 <o:p></o:p></pre> 1582: 1583: <pre style="text-align:justify">73 9.5077 3.0524 4.5044 6.0401 <o:p></o:p></pre> 1584: 1585: <pre style="text-align:justify">For example 70 10.9226 3.0401 5.6488 6.2122 means:<o:p></o:p></pre> 1586: 1587: <pre style="text-align:justify">e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122<o:p></o:p></pre> 1588: 1589: <pre style="text-align:justify"><img src="expbiaspar21.gif" 1590: width="400" height="300" id="_x0000_i1040"><img 1591: src="expbiaspar11.gif" width="400" height="300" id="_x0000_i1041"></pre> 1592: 1593: For 1595: example, life expectancy of a healthy individual at age 70 is 1596: 10.92 in the healthy state and 3.04 in the disability state 1597: (=13.96 years). If he was disable at age 70, his life expectancy 1598: will be shorter, 5.64 in the healthy state and 6.21 in the 1599: disability state (=11.85 years). The total life expectancy is a 1600: weighted mean of both, 13.96 and 11.85; weight is the proportion 1601: of people disabled at age 70. In order to get a pure period index 1602: (i.e. based only on incidences) we use the <a 1603: href="#Stationary prevalence in each state">computed or 1604: stationary prevalence</a> at age 70 (i.e. computed from 1605: incidences at earlier ages) instead of the <a 1606: href="#Observed prevalence in each state">observed prevalence</a> 1609: (for example at first exam) (<a href="#Health expectancies">see 1610: below</a>).<o:p></o:p> 1611: 1612: <h5 1613: 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">- 1614: Variances of life expectancies by age and initial health status: <a 1615: href="vrbiaspar.txt">vrbiaspar.txt<o:p></o:p></a></h5> 1616: 1617: For 1619: example, the covariances of life expectancies Cov(ei,ej) at age 1620: 50 are (line 3) <o:p></o:p> 1621: 1622: <pre style="text-align:justify">   Cov(e1,e1)=0.4776  Cov(e1,e2)=0.0488=Cov(e2,e1)  Cov(e2,e2)=0.0424<o:p></o:p></pre> 1623: 1624: <h5 1625: 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">- 1626: <a name="Health_expectancies">Health expectancies</a> with 1627: standard errors in parentheses: <a href="trbiaspar.txt">trbiaspar.txt<o:p></o:p></a></h5> 1629: 1630: <pre style="text-align:justify">#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) <o:p></o:p></pre> 1631: 1632: <pre style="text-align:justify">70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14) <o:p></o:p></pre> 1633: 1634: Thus, 1636: at age 70 the total life expectancy, e..=13.76years is the 1637: weighted mean of e1.=13.96 and e2.=11.85 by the stationary 1638: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in 1639: state 2, respectively (the sum is equal to one). e.1=10.40 is the 1640: Disability-free life expectancy at age 70 (it is again a weighted 1641: mean of e11 and e21). e.2=3.35 is also the life expectancy at age 1642: 70 to be spent in the disability state.<o:p></o:p> 1643: 1644: <h5 1645: 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">-Total 1646: life expectancy by age and health expectancies in states 1647: (1=healthy) and (2=disable): <a href="ebiaspar1.gif">ebiaspar1.gif<o:p></o:p></a></h5> 1648: 1649: This 1651: figure represents the health expectancies and the total life 1652: expectancy with the confident interval in dashed curve. <o:p></o:p> 1653: 1654: <pre style="text-align:justify">        <img 1655: src="ebiaspar1.gif" width="400" height="300" id="_x0000_i1042"></pre> 1656: 1657: Standard 1659: deviations (obtained from the information matrix of the model) of 1660: these quantities are very useful. Cross-longitudinal surveys are 1661: costly and do not involve huge samples, generally a few 1662: thousands; therefore it is very important to have an idea of the 1663: standard deviation of our estimates. It has been a big challenge 1664: to compute the Health Expectancy standard deviations. Don't be 1665: confuse: life expectancy is, as any expected value, the mean of a 1666: distribution; but here we are not computing the standard 1667: deviation of the distribution, but the standard deviation of the 1668: estimate of the mean.<o:p></o:p> 1669: 1670: Our 1672: health expectancies estimates vary according to the sample size 1673: (and the standard deviations give confidence intervals of the 1674: estimate) but also according to the model fitted. Let us explain 1675: it in more details.<o:p></o:p> 1676: 1677: Choosing 1679: a model means at least two kind of choices. First we have to 1680: decide the number of disability states. Second we have to design, 1681: within the logit model family, the model: variables, covariables, 1682: confounding factors etc. to be included.<o:p></o:p> 1683: 1684: More 1686: disability states we have, better is our demographical approach 1687: of the disability process, but smaller are the number of 1688: transitions between each state and higher is the noise in the 1689: measurement. We do not have enough experiments of the various 1690: models to summarize the advantages and disadvantages, but it is 1691: important to say that even if we had huge and unbiased samples, 1692: the total life expectancy computed from a cross-longitudinal 1693: survey, varies with the number of states. If we define only two 1694: states, alive or dead, we find the usual life expectancy where it 1695: is assumed that at each age, people are at the same risk to die. 1696: If we are differentiating the alive state into healthy and 1697: disable, and as the mortality from the disability state is higher 1698: than the mortality from the healthy state, we are introducing 1699: heterogeneity in the risk of dying. The total mortality at each 1700: age is the weighted mean of the mortality in each state by the 1701: prevalence in each state. Therefore if the proportion of people 1702: at each age and in each state is different from the stationary 1703: equilibrium, there is no reason to find the same total mortality 1704: at a particular age. Life expectancy, even if it is a very useful 1705: tool, has a very strong hypothesis of homogeneity of the 1706: population. Our main purpose is not to measure differential 1707: mortality but to measure the expected time in a healthy or 1708: disability state in order to maximise the former and minimize the 1709: latter. But the differential in mortality complexifies the 1710: measurement.<o:p></o:p> 1711: 1712: Incidences 1714: of disability or recovery are not affected by the number of 1715: states if these states are independant. But incidences estimates 1716: are dependant on the specification of the model. More covariates 1717: we added in the logit model better is the model, but some 1718: covariates are not well measured, some are confounding factors 1719: like in any statistical model. The procedure to "fit the 1720: best model' is similar to logistic regression which itself is 1721: similar to regression analysis. We haven't yet been so far 1722: because we also have a severe limitation which is the speed of 1723: the convergence. On a Pentium III, 500 MHz, even the simplest 1724: model, estimated by month on 8,000 people may take 4 hours to 1725: converge. Also, the program is not yet a statistical package, 1726: which permits a simple writing of the variables and the model to 1727: take into account in the maximisation. The actual program allows 1728: only to add simple variables like age+sex or age+sex+ age*sex but 1729: will never be general enough. But what is to remember, is that 1730: incidences or probability of change from one state to another is 1731: affected by the variables specified into the model.<o:p></o:p> 1732: 1733: Also, 1735: the age range of the people interviewed has a link with the age 1736: range of the life expectancy which can be estimated by 1737: extrapolation. If your sample ranges from age 70 to 95, you can 1738: clearly estimate a life expectancy at age 70 and trust your 1739: confidence interval which is mostly based on your sample size, 1740: but if you want to estimate the life expectancy at age 50, you 1741: should rely in your model, but fitting a logistic model on a age 1742: range of 70-95 and estimating probabilities of transition out of 1743: this age range, say at age 50 is very dangerous. At least you 1744: should remember that the confidence interval given by the 1745: standard deviation of the health expectancies, are under the 1746: strong assumption that your model is the 'true model', which is 1747: probably not the case.<o:p></o:p> 1748: 1749: <h5 1750: 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">- 1751: Copy of the parameter file: <a href="orbiaspar.txt">orbiaspar.txt<o:p></o:p></a></h5> 1754: 1755: This 1757: copy of the parameter file can be useful to re-run the program 1758: while saving the old output files. <o:p></o:p> 1759: 1760: <h5 1761: 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">- 1762: Prevalence forecasting: <a href="frbiaspar.txt">frbiaspar.txt<o:p></o:p></a></h5> 1763: 1764: First, 1766: we have estimated the observed prevalence between 1/1/1984 and 1767: 1/6/1988.  The mean date of interview (weighed average of 1769: the interviews performed between1/1/1984 and 1/6/1988) is 1770: estimated to be 13/9/1985, as written on the top on the file. 1771: Then we forecast the probability to be in each state. <o:p></o:p> 1772: 1773: Example, 1775: at date 1/1/1989 : <o:p></o:p> 1776: 1777: # StartingAge FinalAge P.1 P.2 P.3<o:p></o:p> 1778: 1779: # Forecasting at date 1/1/1989 <o:p></o:p> 1780: 1781: 73 0.807 0.078 0.115 <o:p></o:p> 1782: 1783: Since 1785: the minimum age is 70 on the 13/9/1985, the youngest forecasted 1786: age is 73. This means that at age a person aged 70 at 13/9/1989 1787: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989. 1788: Similarly, the probability to be in state 2 is 0.078 and the 1789: probability to die is 0.115. Then, on the 1/1/1989, the 1790: prevalence of disability at age 73 is estimated to be 0.088.<o:p></o:p> 1791: 1792: <h5 1793: 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">- 1794: Population forecasting: <a href="poprbiaspar.txt">poprbiaspar.txt<o:p></o:p></a></h5> 1797: 1798: <pre style="text-align:justify"># Age P.1 P.2 P.3 [Population]<o:p></o:p></pre> 1799: 1800: <pre style="text-align:justify"># Forecasting at date 1/1/1989 <o:p></o:p></pre> 1801: 1802: <pre style="text-align:justify">75 572685.22 83798.08 <o:p></o:p></pre> 1803: 1804: <pre style="text-align:justify">74 621296.51 79767.99 <o:p></o:p></pre> 1805: 1806: <pre style="text-align:justify">73 645857.70 69320.60 <o:p></o:p></pre> 1807: 1808: <pre style="text-align:justify"># Forecasting at date 1/1/1990<o:p></o:p></pre> 1809: 1810: <pre style="text-align:justify">76 442986.68 92721.14 120775.48</pre> 1811: 1812: <pre style="text-align:justify">75 487781.02 91367.97 121915.51</pre> 1813: 1814: <pre style="text-align:justify">74 512892.07 85003.47 117282.76 </pre> 1815: 1816: <pre style="text-align:justify"> <o:p></o:p></pre> 1817: 1818: From the population file, we estimate the 1819: number of people in each state. At age 73, 645857 persons are in 1820: state 1 and 69320 are in state 2. One year latter, 512892 are 1821: still in state 1, 85003 are in state 2 and 117282 died before 1822: 1/1/1990.<o:p></o:p> 1823: 1824: <pre style="text-align:justify"> <o:p></o:p></pre> 1825: 1826: <hr> 1827: 1828: <h2 1829: 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"><a 1830: name="example"></a>Trying an example<o:p></o:p></h2> 1831: 1832: Since 1834: you know how to run the program, it is time to test it on your 1835: own computer. Try for example on a parameter file named <a 1836: href="..\mytry\imachpar.txt">imachpar.txt</a> which is a copy of mypar.txt 1837: included in the subdirectory of imach, mytry. Edit it to change 1840: the name of the data file to ..\data\mydata.txt if you don't want 1842: to copy it on the same directory. The file mydata.txt is a 1843: smaller file of 3,000 people but still with 4 waves. <o:p></o:p> 1844: 1845: Click 1847: on the imach.exe icon to open a window. Answer to the question: 'Enter 1848: the parameter file name:'<o:p></o:p> 1849: 1850: <table border="1" cellpadding="0" 1851: style="mso-cellspacing:1.5pt;mso-padding-alt: 1852: 0cm 0cm 0cm 0cm"> 1853: <tr> 1854: <td width="100%" 1855: style="width:100.0%;padding:.75pt .75pt .75pt .75pt">IMACH, 1856: Version 0.7<o:p></o:p>Enter 1858: the parameter file name: ..\mytry\imachpar.txt<o:p></o:p> 1859: </td> 1860: </tr> 1861: </table> 1862: 1863: Most 1865: of the data files or image files generated, will use the 1866: 'imachpar' string into their name. The running time is about 2-3 1867: minutes on a Pentium III. If the execution worked correctly, the 1868: outputs files are created in the current directory, and should be 1869: the same as the mypar files initially included in the directory mytry.<o:p></o:p> 1870: 1871: <pre 1872: style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l5 level1 lfo43">�                Output on the screen The output screen looks like <a 1873: href="imachrun.LOG">this Log file<o:p></o:p></a></pre> 1874: 1875: <pre style="margin-left:18.0pt"> <o:p></o:p></pre> 1876: 1877: <pre style="margin-left:18.0pt">#title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3<o:p></o:p></pre> 1878: 1879: <pre style="margin-left:18.0pt">ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0<o:p></o:p></pre> 1880: 1881: <pre style="margin-left:18.0pt">Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92<o:p></o:p></pre> 1882: 1883: <pre style="margin-left:18.0pt"> <o:p></o:p></pre> 1884: 1885: <pre style="margin-left:18.0pt">Warning, no any valid information for:126 line=126<o:p></o:p></pre> 1886: 1887: <pre style="margin-left:18.0pt">Warning, no any valid information for:2307 line=2307<o:p></o:p></pre> 1888: 1889: <pre style="margin-left:18.0pt;text-align:justify">Delay (in months) between two waves Min=21 Max=51 Mean=24.495826<o:p></o:p></pre> 1890: 1891: <pre style="margin-left:18.0pt;text-align:justify">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.<o:p></o:p></pre> 1892: 1893: <pre style="margin-left:18.0pt;text-align:justify">Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14<o:p></o:p></pre> 1894: 1895: <pre style="margin-left:18.0pt;text-align:justify"> prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1<o:p></o:p></pre> 1896: 1897: <pre style="margin-left:18.0pt;text-align:justify">Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 <o:p></o:p></pre> 1898: 1899: <ul type="disc"> 1900: <li class="MsoNormal" 1901: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 1902: mso-list:l6 level1 lfo46;tab-stops:list 36.0pt">Maximisation 1903: with the Powell algorithm. 8 directions are given 1904: corresponding to the 8 parameters. This can be rather 1905: long to get convergence. 1906: 1908: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 1909: 0.000000000000 3 1910: 0.000000000000 4 0.000000000000 5 0.000000000000 6 1911: 0.000000000000 7 1912: 0.000000000000 8 0.000000000000 1913: 1..........2.................3..........4.................5......... 1914: 6................7........8............... 1915: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 1916: 1917: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 1918: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 1919: 8 0.051272038506 1920: 1..............2...........3..............4........... 1921: 5..........6................7...........8......... 1922: #Number of iterations = 23, -2 Log likelihood = 1923: 6744.954042573691 1924: # Parameters 1925: 12 -12.966061 0.135117 1926: 13 -7.401109 0.067831 1927: 21 -0.672648 -0.006627 1928: 23 -5.051297 0.051271 <o:p></o:p></li> 1930: </ul> 1931: 1932: <pre 1933: style="margin-left:36.0pt;text-align:justify;text-indent:-18.0pt; 1934: mso-list:l6 level1 lfo46">�                Calculation of the hessian matrix. Wait...<o:p></o:p></pre> 1935: 1936: <pre style="margin-left:18.0pt;text-align:justify">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<o:p></o:p></pre> 1937: 1938: <pre style="margin-left:18.0pt;text-align:justify"> <o:p></o:p></pre> 1939: 1940: <pre style="margin-left:18.0pt;text-align:justify">Inverting the hessian to get the covariance matrix. Wait...</pre> 1941: 1942: <pre style="margin-left:18.0pt;text-align:justify"> <o:p></o:p></pre> 1943: 1944: <pre style="margin-left:18.0pt;text-align:justify">#Hessian matrix#</pre> 1945: 1946: <pre style="margin-left:18.0pt">3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 <o:p></o:p></pre> 1947: 1948: <pre style="margin-left:18.0pt">2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 <o:p></o:p></pre> 1949: 1950: <pre style="margin-left:18.0pt">-4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 <o:p></o:p></pre> 1951: 1952: <pre style="margin-left:18.0pt">-3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 <o:p></o:p></pre> 1953: 1954: <pre style="margin-left:18.0pt">-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 <o:p></o:p></pre> 1955: 1956: <pre style="margin-left:18.0pt">-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 <o:p></o:p></pre> 1957: 1958: <pre style="margin-left:18.0pt">3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 <o:p></o:p></pre> 1959: 1960: <pre style="margin-left:18.0pt">3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 <o:p></o:p></pre> 1961: 1962: <pre style="margin-left:18.0pt;text-align:justify"># Scales<o:p></o:p></pre> 1964: 1965: <pre style="margin-left:18.0pt;text-align: 1966: justify">12 1.00000e-004 1.00000e-006<o:p></o:p></pre> 1967: 1968: <pre style="margin-left:18.0pt;text-align:justify">13 1.00000e-004 1.00000e-006<o:p></o:p></pre> 1970: 1971: <pre style="margin-left: 1972: 18.0pt;text-align:justify">21 1.00000e-003 1.00000e-005<o:p></o:p></pre> 1973: 1974: <pre style="margin-left:18.0pt;text-align:justify">23 1.00000e-004 1.00000e-005<o:p></o:p></pre> 1976: 1977: <pre style="margin-left: 1978: 18.0pt;text-align:justify"># Covariance<o:p></o:p></pre> 1979: 1980: <pre style="margin-left:18.0pt;text-align:justify">  1 5.90661e-001<o:p></o:p></pre> 1982: 1983: <pre style="margin-left:18.0pt;text-align:justify">  2 -7.26732e-003 8.98810e-005<o:p></o:p></pre> 1985: 1986: <pre style="margin-left:18.0pt;text-align:justify">  3 8.80177e-002 -1.12706e-003 5.15824e-001<o:p></o:p></pre> 1988: 1989: <pre style="margin-left:18.0pt;text-align:justify">  4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005<o:p></o:p></pre> 1991: 1992: <pre style="margin-left:18.0pt;text-align:justify">  5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000<o:p></o:p></pre> 1994: 1995: <pre style="margin-left:18.0pt;text-align:justify">  6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004<o:p></o:p></pre> 1997: 1998: <pre style="margin-left:18.0pt;text-align:justify">  7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000<o:p></o:p></pre> 2000: 2001: <pre style="margin-left:18.0pt;text-align:justify">  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<o:p></o:p></pre> 2003: 2004: <pre style="margin-left:18.0pt;text-align:justify"># agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).<o:p></o:p></pre> 2005: 2006: <pre style="margin-left:18.0pt;text-align:justify"> <o:p></o:p></pre> 2007: 2008: <pre style="margin-left:18.0pt;text-align:justify"> <o:p></o:p></pre> 2009: 2010: <pre style="margin-left:18.0pt;text-align:justify">agemin=70 agemax=100 bage=50 fage=100<o:p></o:p></pre> 2011: 2012: <pre style="margin-left:18.0pt;text-align:justify">Computing prevalence limit: result on file 'plrmypar.txt' <o:p></o:p></pre> 2013: 2014: <pre style="margin-left:18.0pt;text-align:justify">Computing pij: result on file 'pijrmypar.txt' <o:p></o:p></pre> 2015: 2016: <pre style="margin-left:18.0pt;text-align:justify">Computing Health Expectancies: result on file 'ermypar.txt' <o:p></o:p></pre> 2017: 2018: <pre style="margin-left:18.0pt;text-align:justify">Computing Variance-covariance of DFLEs: file 'vrmypar.txt' <o:p></o:p></pre> 2019: 2020: <pre style="margin-left:18.0pt;text-align:justify">Computing Total LEs with variances: file 'trmypar.txt' <o:p></o:p></pre> 2021: 2022: <pre style="margin-left:18.0pt;text-align:justify">Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' <o:p></o:p></pre> 2023: 2024: <pre style="margin-left:18.0pt;text-align:justify">End of Imach<o:p></o:p></pre> 2025: 2026: Once 2028: the running is finished, the program requires a caracter:<o:p></o:p> 2029: 2030: <table border="1" cellpadding="0" 2031: style="mso-cellspacing:1.5pt;mso-padding-alt: 2032: 0cm 0cm 0cm 0cm"> 2033: <tr> 2034: <td width="100%" 2035: style="width:100.0%;padding:.75pt .75pt .75pt .75pt">Type 2036: e to edit output files, c to start again, and q for 2037: exiting:<o:p></o:p></td> 2039: </tr> 2040: </table> 2041: 2042: First 2044: you should enter e to edit the master file 2045: mypar.htm. <o:p></o:p> 2046: 2047: <ul type="disc"> 2048: <li class="MsoNormal" 2049: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 2050: mso-list:l9 level1 lfo49;tab-stops:list 36.0pt">Outputs 2051: files 2052: 2053: - Observed prevalence in each state: <a 2054: href="..\mytry\prmypar.txt">pmypar.txt</a> 2055: - Estimated parameters and the covariance matrix: <a 2056: href="..\mytry\rmypar.txt">rmypar.txt</a> 2057: - Stationary prevalence in each state: <a 2058: href="..\mytry\plrmypar.txt">plrmypar.txt</a> 2061: - Transition probabilities: <a 2062: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> 2063: - Copy of the parameter file: <a 2064: href="..\mytry\ormypar.txt">ormypar.txt</a> 2065: - Life expectancies by age and initial health status: <a 2066: href="..\mytry\ermypar.txt">ermypar.txt</a> 2069: - Variances of life expectancies by age and initial 2070: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> 2073: 2074: - Health expectancies with their variances: <a 2075: href="..\mytry\trmypar.txt">trmypar.txt</a> 2078: - Standard deviation of stationary prevalence: <a 2079: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> 2082: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a> 2083: 2084: - Population forecasting (if popforecast=1): <a 2085: href="poprmypar.txt">poprmypar.txt</a> <o:p></o:p></li> 2086: <li class="MsoNormal" 2087: style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; 2088: mso-list:l9 level1 lfo49;tab-stops:list 36.0pt">Graphs 2089: 2090: 2091: -<a href="..\mytry\pemypar1.gif">One-step transition 2093: probabilities</a> 2094: -<a href="..\mytry\pmypar11.gif">Convergence to the 2096: stationary prevalence</a> 2097: -<a href="..\mytry\vmypar11.gif">Observed and stationary 2099: prevalence in state (1) with the confident interval</a> 2100: -<a href="..\mytry\vmypar21.gif">Observed and stationary 2102: prevalence in state (2) with the confident interval</a> 2103: -<a href="..\mytry\expmypar11.gif">Health life 2104: expectancies by age and initial health state (1)</a> 2106: -<a href="..\mytry\expmypar21.gif">Health life 2107: expectancies by age and initial health state (2)</a> 2109: -<a href="..\mytry\emypar1.gif">Total life expectancy by 2111: age and health expectancies in states (1) and (2).</a> <o:p></o:p></li> 2112: </ul> 2113: 2114: This 2116: software have been partly granted by <a 2117: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted 2118: action from the European Union. It will be copyrighted 2119: identically to a GNU software product, i.e. program and software 2120: can be distributed freely for non commercial use. Sources are not 2121: widely distributed today. You can get them by asking us with a 2122: simple justification (name, email, institute) <a 2123: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a 2124: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> .<o:p></o:p> 2125: 2126: Latest 2128: version (0.7 of February 2002) can be accessed at <a 2129: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach<o:p></o:p></a> 2130: </body> 2131: </html>