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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: <title>IMaCh</title> 16: </head> 17: 18: <body bgcolor="#FFFFFF"> 19: 20: <hr size="3" color="#EC5E5E"> 21: 22: <h1 align="center">Computing Health 23: Expectancies using IMaCh</h1> 24: 25: <h1 align="center">(a Maximum 26: Likelihood Computer Program using Interpolation of Markov Chains)</h1> 27: 28:   29: 30: <a href="http://www.ined.fr/"><img 31: src="logo-ined.gif" border="0" width="151" height="76"></a><img 32: src="euroreves2.gif" width="151" height="75"> 33: 34: <h3 align="center"><a href="http://www.ined.fr/">INED</a> and <a 36: href="http://euroreves.ined.fr">EUROREVES</a></h3> 37: 38: Version 39: 0.8a, May 2002 40: 41: <hr size="3" color="#EC5E5E"> 42: 43: Authors of the 44: program: <a href="http://sauvy.ined.fr/brouard">Nicolas Brouard</a>, senior researcher at the <a 47: href="http://www.ined.fr">Institut 48: National d'Etudes Démographiques</a> (INED, Paris) in the "Mortality, 50: Health and Epidemiology" Research Unit 51: 52: and Agnès 53: Lièvre 54: 55: 56: <h4>Contribution to the mathematics: C. R. 57: Heathcote (Australian 58: National University, Canberra).</h4> 59: 60: <h4>Contact: Agnès Lièvre (<a 61: href="mailto:lievre@ined.fr">lievre@ined.fr</a>) </h4> 63: 64: <hr> 65: 66: <ul> 67: <li><a href="#intro">Introduction</a> </li> 68: <li><a href="#data">On what kind of data can it be used?</a></li> 69: <li><a href="#datafile">The data file</a> </li> 70: <li><a href="#biaspar">The parameter file</a> </li> 71: <li><a href="#running">Running Imach</a> </li> 72: <li><a href="#output">Output files and graphs</a> </li> 73: <li><a href="#example">Exemple</a> </li> 74: </ul> 75: 76: <hr> 77: 78: <h2><a name="intro">Introduction</a></h2> 79: 80: This program computes Healthy Life Expectancies from cross-longitudinal 81: data using the methodology pioneered by Laditka and Wolf (1). 82: Within the family of Health Expectancies (HE), Disability-free 83: life expectancy (DFLE) is probably the most important index to 84: monitor. In low mortality countries, there is a fear that when 85: mortality declines, the increase in DFLE is not proportionate to 86: the increase in total Life expectancy. This case is called the Expansion 87: of morbidity. Most of the data collected today, in 88: particular by the international <a href="http://www.reves.org">REVES</a> 89: network on Health expectancy, and most HE indices based on these 90: data, are cross-sectional. It means that the information 91: collected comes from a single cross-sectional survey: people from 92: various ages (but mostly old people) are surveyed on their health 93: status at a single date. Proportion of people disabled at each 94: age, can then be measured at that date. This age-specific 95: prevalence curve is then used to distinguish, within the 96: stationary population (which, by definition, is the life table 97: estimated from the vital statistics on mortality at the same 98: date), the disable population from the disability-free 99: population. Life expectancy (LE) (or total population divided by 100: the yearly number of births or deaths of this stationary 101: population) is then decomposed into DFLE and DLE. This method of 102: computing HE is usually called the Sullivan method (from the name 103: of the author who first described it). 104: 105: Age-specific proportions of people disable are very difficult 106: to forecast because each proportion corresponds to historical 107: conditions of the cohort and it is the result of the historical 108: flows from entering disability and recovering in the past until 109: today. The age-specific intensities (or incidence rates) of 110: entering disability or recovering a good health, are reflecting 111: actual conditions and therefore can be used at each age to 112: forecast the future of this cohort. For example if a country is 113: improving its technology of prosthesis, the incidence of 114: recovering the ability to walk will be higher at each (old) age, 115: but the prevalence of disability will only slightly reflect an 116: improve because the prevalence is mostly affected by the history 117: of the cohort and not by recent period effects. To measure the 118: period improvement we have to simulate the future of a cohort of 119: new-borns entering or leaving at each age the disability state or 120: dying according to the incidence rates measured today on 121: different cohorts. The proportion of people disabled at each age 122: in this simulated cohort will be much lower (using the exemple of 123: an improvement) that the proportions observed at each age in a 124: cross-sectional survey. This new prevalence curve introduced in a 125: life table will give a much more actual and realistic HE level 126: than the Sullivan method which mostly measured the History of 127: health conditions in this country. 128: 129: Therefore, the main question is how to measure incidence rates 130: from cross-longitudinal surveys? This is the goal of the IMaCH 131: program. From your data and using IMaCH you can estimate period 132: HE and not only Sullivan's HE. Also the standard errors of the HE 133: are computed. 134: 135: A cross-longitudinal survey consists in a first survey 136: ("cross") where individuals from different ages are 137: interviewed on their health status or degree of disability. At 138: least a second wave of interviews ("longitudinal") 139: should measure each new individual health status. Health 140: expectancies are computed from the transitions observed between 141: waves and are computed for each degree of severity of disability 142: (number of life states). More degrees you consider, more time is 143: necessary to reach the Maximum Likelihood of the parameters 144: involved in the model. Considering only two states of disability 145: (disable and healthy) is generally enough but the computer 146: program works also with more health statuses. 147: 148: The simplest model is the multinomial logistic model where pij 149: is the probability to be observed in state j at the second 150: wave conditional to be observed in state i at the first 151: wave. Therefore a simple model is: log(pij/pii)= aij + 152: bij*age+ cij*sex, where 'age' is age and 'sex' 153: is a covariate. The advantage that this computer program claims, 154: comes from that if the delay between waves is not identical for 155: each individual, or if some individual missed an interview, the 156: information is not rounded or lost, but taken into account using 157: an interpolation or extrapolation. hPijx is the 158: probability to be observed in state i at age x+h 159: conditional to the observed state i at age x. The 160: delay 'h' can be split into an exact number (nh*stepm) 161: of unobserved intermediate states. This elementary transition (by 162: month or quarter trimester, semester or year) is modeled as a 163: multinomial logistic. The hPx matrix is simply the matrix 164: product of nh*stepm elementary matrices and the 165: contribution of each individual to the likelihood is simply hPijx. 166: 167: 168: 169: The program presented in this manual is a quite general 170: program named IMaCh (for Interpolated 171: MArkov CHain), designed to 172: analyse transition data from longitudinal surveys. The first step 173: is the parameters estimation of a transition probabilities model 174: between an initial status and a final status. From there, the 175: computer program produces some indicators such as observed and 176: stationary prevalence, life expectancies and their variances and 177: graphs. Our transition model consists in absorbing and 178: non-absorbing states with the possibility of return across the 179: non-absorbing states. The main advantage of this package, 180: compared to other programs for the analysis of transition data 181: (For example: Proc Catmod of SAS®) is that the whole 182: individual information is used even if an interview is missing, a 183: status or a date is unknown or when the delay between waves is 184: not identical for each individual. The program can be executed 185: according to parameters: selection of a sub-sample, number of 186: absorbing and non-absorbing states, number of waves taken in 187: account (the user inputs the first and the last interview), a 188: tolerance level for the maximization function, the periodicity of 189: the transitions (we can compute annual, quarterly or monthly 190: transitions), covariates in the model. It works on Windows or on 191: Unix. 192: 193: 194: <hr> 195: 196: (1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New 197: Methods for Analyzing Active Life Expectancy". Journal of 198: Aging and Health. Vol 10, No. 2. 199: 200: <hr> 201: 202: <h2><a name="data">On what kind of data can 203: it be used?</a></h2> 204: 205: The minimum data required for a transition model is the 206: recording of a set of individuals interviewed at a first date and 207: interviewed again at least one another time. From the 208: observations of an individual, we obtain a follow-up over time of 209: the occurrence of a specific event. In this documentation, the 210: event is related to health status at older ages, but the program 211: can be applied on a lot of longitudinal studies in different 212: contexts. To build the data file explained into the next section, 213: you must have the month and year of each interview and the 214: corresponding health status. But in order to get age, date of 215: birth (month and year) is required (missing values is allowed for 216: month). Date of death (month and year) is an important 217: information also required if the individual is dead. Shorter 218: steps (i.e. a month) will more closely take into account the 219: survival time after the last interview. 220: 221: <hr> 222: 223: <h2><a name="datafile">The data file</a></h2> 224: 225: In this example, 8,000 people have been interviewed in a 226: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). 227: Some people missed 1, 2 or 3 interviews. Health statuses are 228: healthy (1) and disable (2). The survey is not a real one. It is 229: a simulation of the American Longitudinal Survey on Aging. The 230: disability state is defined if the individual missed one of four 231: ADL (Activity of daily living, like bathing, eating, walking). 232: Therefore, even is the individuals interviewed in the sample are 233: virtual, the information brought with this sample is close to the 234: situation of the United States. Sex is not recorded is this 235: sample. 236: 237: Each line of the data set (named <a href="data1.txt">data1.txt</a> 238: in this first example) is an individual record which fields are: 239: 240: <ul> 241: <li>Index number: positive number (field 1) </li> 242: <li>First covariate positive number (field 2) </li> 243: <li>Second covariate positive number (field 3) </li> 244: <li><a name="Weight">Weight</a>: positive number 245: (field 4) . In most surveys individuals are weighted 246: according to the stratification of the sample.</li> 247: <li>Date of birth: coded as mm/yyyy. Missing dates are 248: coded as 99/9999 (field 5) </li> 249: <li>Date of death: coded as mm/yyyy. Missing dates are 250: coded as 99/9999 (field 6) </li> 251: <li>Date of first interview: coded as mm/yyyy. Missing 252: dates are coded as 99/9999 (field 7) </li> 253: <li>Status at first interview: positive number. 254: Missing values ar coded -1. (field 8) </li> 255: <li>Date of second interview: coded as mm/yyyy. 256: Missing dates are coded as 99/9999 (field 9) </li> 257: <li>Status at second interview positive 258: number. Missing values ar coded -1. (field 10) </li> 259: <li>Date of third interview: coded as mm/yyyy. Missing 260: dates are coded as 99/9999 (field 11) </li> 261: <li>Status at third interview positive 262: number. Missing values ar coded -1. (field 12) </li> 263: <li>Date of fourth interview: coded as mm/yyyy. 264: Missing dates are coded as 99/9999 (field 13) </li> 265: <li>Status at fourth interview positive 266: number. Missing values are coded -1. (field 14) </li> 267: <li>etc</li> 268: </ul> 269: 270:   271: 272: If your longitudinal survey do not include information about 273: weights or covariates, you must fill the column with a number 274: (e.g. 1) because a missing field is not allowed. 275: 276: <hr> 277: 278: <h2>Your first example parameter file<a 279: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> 280: 281: <h2><a name="biaspar"></a>#Imach version 0.8a, May 2002, 282: INED-EUROREVES </h2> 283: 284: This is a comment. Comments start with a '#'. 285: 286: <h4>First uncommented line</h4> 287: 288: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> 289: 290: <ul> 291: <li>title= 1st_example is title of the run. </li> 292: <li>datafile= data1.txt is the name of the data set. 293: Our example is a six years follow-up survey. It consists 294: in a baseline followed by 3 reinterviews. </li> 295: <li>lastobs= 8600 the program is able to run on a 296: subsample where the last observation number is lastobs. 297: It can be set a bigger number than the real number of 298: observations (e.g. 100000). In this example, maximisation 299: will be done on the 8600 first records. </li> 300: <li>firstpass=1 , lastpass=4 In case of more 301: than two interviews in the survey, the program can be run 302: on selected transitions periods. firstpass=1 means the 303: first interview included in the calculation is the 304: baseline survey. lastpass=4 means that the information 305: brought by the 4th interview is taken into account.</li> 306: </ul> 307: 308:   309: 310: <h4><a name="biaspar-2">Second uncommented 311: line</a></h4> 312: 313: <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 314: 315: <ul> 316: <li>ftol=1e-8 Convergence tolerance on the function 317: value in the maximisation of the likelihood. Choosing a 318: correct value for ftol is difficult. 1e-8 is a correct 319: value for a 32 bits computer.</li> 320: <li>stepm=1 Time unit in months for interpolation. 321: Examples:<ul> 322: <li>If stepm=1, the unit is a month </li> 323: <li>If stepm=4, the unit is a trimester</li> 324: <li>If stepm=12, the unit is a year </li> 325: <li>If stepm=24, the unit is two years</li> 326: <li>... </li> 327: </ul> 328: </li> 329: <li>ncovcol=2 Number of covariate columns in the 330: datafile which precede the date of birth. Here you can 331: put variables that won't necessary be used during the 332: run. It is not the number of covariates that will be 333: specified by the model. The 'model' syntax describe the 334: covariates to take into account. </li> 335: <li>nlstate=2 Number of non-absorbing (alive) states. 336: Here we have two alive states: disability-free is coded 1 337: and disability is coded 2. </li> 338: <li>ndeath=1 Number of absorbing states. The absorbing 339: state death is coded 3. </li> 340: <li>maxwav=4 Number of waves in the datafile.</li> 341: <li><a name="mle">mle</a>=1 Option for the 342: Maximisation Likelihood Estimation. <ul> 343: <li>If mle=1 the program does the maximisation and 344: the calculation of health expectancies </li> 345: <li>If mle=0 the program only does the calculation of 346: the health expectancies. </li> 347: </ul> 348: </li> 349: <li>weight=0 Possibility to add weights. <ul> 350: <li>If weight=0 no weights are included </li> 351: <li>If weight=1 the maximisation integrates the 352: weights which are in field <a href="#Weight">4</a></li> 353: </ul> 354: </li> 355: </ul> 356: 357: <h4>Covariates</h4> 358: 359: Intercept and age are systematically included in the model. 360: Additional covariates can be included with the command: 361: 362: <pre>model=list of covariates</pre> 363: 364: <ul> 365: <li>if model=. then no covariates are 366: included</li> 367: <li>if model=V1 the model includes the first 368: covariate (field 2)</li> 369: <li>if model=V2 the model includes the 370: second covariate (field 3)</li> 371: <li>if model=V1+V2 the model includes the 372: first and the second covariate (fields 2 and 3)</li> 373: <li>if model=V1*V2 the model includes the 374: product of the first and the second covariate (fields 2 375: and 3)</li> 376: <li>if model=V1+V1*age the model includes 377: the product covariate*age</li> 378: </ul> 379: 380: In this example, we have two covariates in the data file 381: (fields 2 and 3). The number of covariates included in the data 382: file between the id and the date of birth is ncovcol=2 (it was 383: named ncov in version prior to 0.8). If you have 3 covariates in 384: the datafile (fields 2, 3 and 4), you will set ncovcol=3. Then 385: you can run the programme with a new parametrisation taking into 386: account the third covariate. For example, model=V1+V3 estimates 387: a model with the first and third covariates. More complicated 388: models can be used, but it will takes more time to converge. With 389: a simple model (no covariates), the programme estimates 8 390: parameters. Adding covariates increases the number of parameters 391: : 12 for model=V1, 16 for model=V1+V1*age 392: and 20 for model=V1+V2+V3. 393: 394: <h4>Guess values for optimization </h4> 396: 397: You must write the initial guess values of the parameters for 398: optimization. The number of parameters, N depends on the 399: number of absorbing states and non-absorbing states and on the 400: number of covariates. 401: N is given by the formula N=(nlstate + 402: ndeath-1)*nlstate*ncovmodel . 403: 404: Thus in the simple case with 2 covariates (the model is log 405: (pij/pii) = aij + bij * age where intercept and age are the two 406: covariates), and 2 health degrees (1 for disability-free and 2 407: for disability) and 1 absorbing state (3), you must enter 8 408: initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can 409: start with zeros as in this example, but if you have a more 410: precise set (for example from an earlier run) you can enter it 411: and it will speed up them 412: Each of the four lines starts with indices "ij": ij 413: aij bij 414: 415: <blockquote> 416: <pre># Guess values of aij and bij in log (pij/pii) = aij + bij * age 417: 12 -14.155633 0.110794 418: 13 -7.925360 0.032091 419: 21 -1.890135 -0.029473 420: 23 -6.234642 0.022315 </pre> 421: </blockquote> 422: 423: or, to simplify (in most of cases it converges but there is no 424: warranty!): 425: 426: <blockquote> 427: <pre>12 0.0 0.0 428: 13 0.0 0.0 429: 21 0.0 0.0 430: 23 0.0 0.0</pre> 431: </blockquote> 432: 433: In order to speed up the convergence you can make a first run 434: with a large stepm i.e stepm=12 or 24 and then decrease the stepm 435: until stepm=1 month. If newstepm is the new shorter stepm and 436: stepm can be expressed as a multiple of newstepm, like newstepm=n 437: stepm, then the following approximation holds: 438: 439: <pre>aij(stepm) = aij(n . stepm) - ln(n) 440: </pre> 441: 442: and 443: 444: <pre>bij(stepm) = bij(n . stepm) .</pre> 445: 446: For example if you already ran for a 6 months interval and 447: got: 448: 449: 450: <pre># Parameters 451: 12 -13.390179 0.126133 452: 13 -7.493460 0.048069 453: 21 0.575975 -0.041322 454: 23 -4.748678 0.030626 455: </pre> 456: 457: If you now want to get the monthly estimates, you can guess 458: the aij by substracting ln(6)= 1,7917 459: and running 460: 461: 462: <pre>12 -15.18193847 0.126133 463: 13 -9.285219469 0.048069 464: 21 -1.215784469 -0.041322 465: 23 -6.540437469 0.030626 466: </pre> 467: 468: and get 469: 470: 471: <pre>12 -15.029768 0.124347 472: 13 -8.472981 0.036599 473: 21 -1.472527 -0.038394 474: 23 -6.553602 0.029856 475: 476: which is closer to the results. The approximation is probably useful 477: only for very small intervals and we don't have enough experience to 478: know if you will speed up the convergence or not. 479: </pre> 480: 481: <pre> -ln(12)= -2.484 482: -ln(6/1)=-ln(6)= -1.791 483: -ln(3/1)=-ln(3)= -1.0986 484: -ln(12/6)=-ln(2)= -0.693 485: </pre> 486: 487: <h4>Guess values for computing variances</h4> 488: 489: This is an output if <a href="#mle">mle</a>=1. But it can be 490: used as an input to get the various output data files (Health 491: expectancies, stationary prevalence etc.) and figures without 492: rerunning the rather long maximisation phase (mle=0). 493: 494: The scales are small values for the evaluation of numerical 495: derivatives. These derivatives are used to compute the hessian 496: matrix of the parameters, that is the inverse of the covariance 497: matrix, and the variances of health expectancies. Each line 498: consists in indices "ij" followed by the initial scales 499: (zero to simplify) associated with aij and bij. 500: 501: <ul> 502: <li>If mle=1 you can enter zeros:</li> 503: <li><blockquote> 504: <pre># Scales (for hessian or gradient estimation) 505: 12 0. 0. 506: 13 0. 0. 507: 21 0. 0. 508: 23 0. 0. </pre> 509: </blockquote> 510: </li> 511: <li>If mle=0 you must enter a covariance matrix (usually 512: obtained from an earlier run).</li> 513: </ul> 514: 515: <h4>Covariance matrix of parameters</h4> 516: 517: This is an output if <a href="#mle">mle</a>=1. But it can be 518: used as an input to get the various output data files (Health 519: expectancies, stationary prevalence etc.) and figures without 520: rerunning the rather long maximisation phase (mle=0). 521: Each line starts with indices "ijk" followed by the 522: covariances between aij and bij: 523: 524: 525: <pre> 526: 121 Var(a12) 527: 122 Cov(b12,a12) Var(b12) 528: ... 529: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> 530: 531: <ul> 532: <li>If mle=1 you can enter zeros. </li> 533: <li><pre># Covariance matrix 534: 121 0. 535: 122 0. 0. 536: 131 0. 0. 0. 537: 132 0. 0. 0. 0. 538: 211 0. 0. 0. 0. 0. 539: 212 0. 0. 0. 0. 0. 0. 540: 231 0. 0. 0. 0. 0. 0. 0. 541: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> 542: </li> 543: <li>If mle=0 you must enter a covariance matrix (usually 544: obtained from an earlier run). </li> 545: </ul> 546: 547: <h4>Age range for calculation of stationary 548: prevalences and health expectancies</h4> 549: 550: <pre>agemin=70 agemax=100 bage=50 fage=100</pre> 551: 552: <pre> 553: Once we obtained the estimated parameters, the program is able 554: to calculated stationary prevalence, transitions probabilities 555: and life expectancies at any age. Choice of age range is useful 556: for extrapolation. In our data file, ages varies from age 70 to 557: 102. It is possible to get extrapolated stationary prevalence by 558: age ranging from agemin to agemax. 559: 560: 561: Setting bage=50 (begin age) and fage=100 (final age), makes 562: the program computing life expectancy from age 'bage' to age 563: 'fage'. As we use a model, we can interessingly compute life 564: expectancy on a wider age range than the age range from the data. 565: But the model can be rather wrong on much larger intervals. 566: Program is limited to around 120 for upper age! 567: </pre> 568: 569: <ul> 570: <li>agemin= Minimum age for calculation of the 571: stationary prevalence </li> 572: <li>agemax= Maximum age for calculation of the 573: stationary prevalence </li> 574: <li>bage= Minimum age for calculation of the health 575: expectancies </li> 576: <li>fage= Maximum age for calculation of the health 577: expectancies </li> 578: </ul> 579: 580: <h4><a name="Computing">Computing</a> the observed prevalence</h4> 582: 583: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</pre> 584: 585: <pre> 586: Statements 'begin-prev-date' and 'end-prev-date' allow to 587: select the period in which we calculate the observed prevalences 588: in each state. In this example, the prevalences are calculated on 589: data survey collected between 1 january 1984 and 1 june 1988. 590: </pre> 591: 592: <ul> 593: <li>begin-prev-date= Starting date 594: (day/month/year)</li> 595: <li>end-prev-date= Final date 596: (day/month/year)</li> 597: <li>estepm= Unit (in months).We compute the 598: life expectancy from trapezoids spaced every estepm 599: months. This is mainly to measure the difference between 600: two models: for example if stepm=24 months pijx are given 601: only every 2 years and by summing them we are calculating 602: an estimate of the Life Expectancy assuming a linear 603: progression inbetween and thus overestimating or 604: underestimating according to the curvature of the 605: survival function. If, for the same date, we estimate the 606: model with stepm=1 month, we can keep estepm to 24 months 607: to compare the new estimate of Life expectancy with the 608: same linear hypothesis. A more precise result, taking 609: into account a more precise curvature will be obtained if 610: estepm is as small as stepm.</li> 611: </ul> 612: 613: <h4>Population- or status-based health 614: expectancies</h4> 615: 616: <pre>pop_based=0</pre> 617: 618: The program computes status-based health expectancies, i.e 619: health expectancies which depends on your initial health state. 620: If you are healthy your healthy life expectancy (e11) is higher 621: than if you were disabled (e21, with e11 > e21). 622: To compute a healthy life expectancy independant of the initial 623: status we have to weight e11 and e21 according to the probability 624: to be in each state at initial age or, with other word, according 625: to the proportion of people in each state. 626: We prefer computing a 'pure' period healthy life expectancy based 627: only on the transtion forces. Then the weights are simply the 628: stationnary prevalences or 'implied' prevalences at the initial 629: age. 630: Some other people would like to use the cross-sectional 631: prevalences (the "Sullivan prevalences") observed at 632: the initial age during a period of time <a href="#Computing">defined 633: just above</a>. 634: 635: 636: <ul> 637: <li>popbased= 0 Health expectancies are 638: computed at each age from stationary prevalences 639: 'expected' at this initial age.</li> 640: <li>popbased= 1 Health expectancies are 641: computed at each age from cross-sectional 'observed' 642: prevalence at this initial age. As all the population is 643: not observed at the same exact date we define a short 644: period were the observed prevalence is computed.</li> 645: </ul> 646: 647: <h4>Prevalence forecasting ( Experimental)</h4> 648: 649: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre> 650: 651: Prevalence and population projections are only available if 652: the interpolation unit is a month, i.e. stepm=1 and if there are 653: no covariate. The programme estimates the prevalence in each 654: state at a precise date expressed in day/month/year. The 655: programme computes one forecasted prevalence a year from a 656: starting date (1 january of 1989 in this example) to a final date 657: (1 january 1992). The statement mov_average allows to compute 658: smoothed forecasted prevalences with a five-age moving average 659: centered at the mid-age of the five-age period. 660: 661: 662: <ul> 663: <li>starting-proj-date= starting date 664: (day/month/year) of forecasting</li> 665: <li>final-proj-date= final date 666: (day/month/year) of forecasting</li> 667: <li>mov_average= smoothing with a five-age 668: moving average centered at the mid-age of the five-age 669: period. The command mov_average takes 670: value 1 if the prevalences are smoothed and 0 otherwise.</li> 671: </ul> 672: 673: <h4>Last uncommented line : Population 674: forecasting </h4> 675: 676: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre> 677: 678: This command is available if the interpolation unit is a 679: month, i.e. stepm=1 and if popforecast=1. From a data file 680: including age and number of persons alive at the precise date 681: popfiledate, you can forecast the number of persons 682: in each state until date last-popfiledate. In this 683: example, the popfile <a href="pyram.txt">pyram.txt</a> 684: includes real data which are the Japanese population in 1989. 685: 686: 687: <ul type="disc"> 688: <li class="MsoNormal" 689: 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= 690: 0 Option for population forecasting. If 691: popforecast=1, the programme does the forecasting.</li> 692: <li class="MsoNormal" 693: 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= 694: name of the population file</li> 695: <li class="MsoNormal" 696: 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= 697: date of the population population</li> 698: <li class="MsoNormal" 699: 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= 700: date of the last population projection </li> 701: </ul> 702: 703: <hr> 704: 705: <h2><a name="running"></a>Running Imach 706: with this example</h2> 707: 708: <pre>We assume that you typed in your <a href="biaspar.imach">1st_example 709: parameter file</a> as explained <a href="#biaspar">above</a>. 710: 711: To run the program you should either: 712: </pre> 713: 714: <ul> 715: <li>click on the imach.exe icon and enter the name of the 716: parameter file which is for example <a 717: href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a> 718: </li> 719: <li>You also can locate the biaspar.imach icon in <a 720: href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your 721: mouse and drag it with the mouse on the imach window). </li> 722: <li>With latest version (0.7 and higher) if you setup windows 723: in order to understand ".imach" extension you 724: can right click the biaspar.imach icon and either edit 725: with notepad the parameter file or execute it with imach 726: or whatever. </li> 727: </ul> 728: 729: <pre>The time to converge depends on the step unit that you used (1 730: month is cpu consuming), on the number of cases, and on the 731: number of variables. 732: 733: 734: The program outputs many files. Most of them are files which 735: will be plotted for better understanding. 736: 737: </pre> 738: 739: <hr> 740: 741: <h2><a name="output">Output of the program 742: and graphs </a></h2> 743: 744: Once the optimization is finished, some graphics can be made 745: with a grapher. We use Gnuplot which is an interactive plotting 746: program copyrighted but freely distributed. A gnuplot reference 747: manual is available <a href="http://www.gnuplot.info/">here</a>. 748: When the running is finished, the user should enter a caracter 749: for plotting and output editing. 750: These caracters are: 751: 752: 753: <ul> 754: <li>'c' to start again the program from the beginning.</li> 755: <li>'e' opens the <a href="biaspar.htm">biaspar.htm</a> 756: file to edit the output files and graphs. </li> 757: <li>'g' to graph again</li> 758: <li>'q' for exiting.</li> 759: </ul> 760: 761: <h5>Results files 762: 763: - <a 764: name="Observed prevalence in each state">Observed prevalence in each state</a> (and at first pass): 767: <a href="prbiaspar.txt">prbiaspar.txt</a> 768: </h5> 769: 770: The first line is the title and displays each field of the 771: file. The first column is age. The fields 2 and 6 are the 772: proportion of individuals in states 1 and 2 respectively as 773: observed during the first exam. Others fields are the numbers of 774: people in states 1, 2 or more. The number of columns increases if 775: the number of states is higher than 2. 776: The header of the file is 777: 778: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N 779: 70 1.00000 631 631 70 0.00000 0 631 780: 71 0.99681 625 627 71 0.00319 2 627 781: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> 782: 783: It means that at age 70, the prevalence in state 1 is 1.000 784: and in state 2 is 0.00 . At age 71 the number of individuals in 785: state 1 is 625 and in state 2 is 2, hence the total number of 786: people aged 71 is 625+2=627. 787: 788: 789: <h5>- Estimated parameters and 790: covariance matrix: <a href="rbiaspar.txt">rbiaspar.imach</a></h5> 791: 792: This file contains all the maximisation results: 793: 794: <pre> -2 log likelihood= 21660.918613445392 795: Estimated parameters: a12 = -12.290174 b12 = 0.092161 796: a13 = -9.155590 b13 = 0.046627 797: a21 = -2.629849 b21 = -0.022030 798: a23 = -7.958519 b23 = 0.042614 799: Covariance matrix: Var(a12) = 1.47453e-001 800: Var(b12) = 2.18676e-005 801: Var(a13) = 2.09715e-001 802: Var(b13) = 3.28937e-005 803: Var(a21) = 9.19832e-001 804: Var(b21) = 1.29229e-004 805: Var(a23) = 4.48405e-001 806: Var(b23) = 5.85631e-005 807: </pre> 808: 809: By substitution of these parameters in the regression model, 810: we obtain the elementary transition probabilities: 811: 812: <img src="pebiaspar1.gif" width="400" height="300"> 813: 814: <h5>- Transition probabilities: 815: <a href="pijrbiaspar.txt">pijrbiaspar.txt</a></h5> 816: 817: Here are the transitions probabilities Pij(x, x+nh) where nh 818: is a multiple of 2 years. The first column is the starting age x 819: (from age 50 to 100), the second is age (x+nh) and the others are 820: the transition probabilities p11, p12, p13, p21, p22, p23. For 821: example, line 5 of the file is: 822: 823: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre> 824: 825: and this means: 826: 827: <pre>p11(100,106)=0.02655 828: p12(100,106)=0.17622 829: p13(100,106)=0.79722 830: p21(100,106)=0.01809 831: p22(100,106)=0.13678 832: p22(100,106)=0.84513 </pre> 833: 834: <h5>- <a 835: name="Stationary prevalence in each state">Stationary prevalence in each state</a>: 837: <a href="plrbiaspar.txt">plrbiaspar.txt</a></h5> 838: 839: <pre>#Prevalence 840: #Age 1-1 2-2 841: 842: #************ 843: 70 0.90134 0.09866 844: 71 0.89177 0.10823 845: 72 0.88139 0.11861 846: 73 0.87015 0.12985 </pre> 847: 848: At age 70 the stationary prevalence is 0.90134 in state 1 and 849: 0.09866 in state 2. This stationary prevalence differs from 850: observed prevalence. Here is the point. The observed prevalence 851: at age 70 results from the incidence of disability, incidence of 852: recovery and mortality which occurred in the past of the cohort. 853: Stationary prevalence results from a simulation with actual 854: incidences and mortality (estimated from this cross-longitudinal 855: survey). It is the best predictive value of the prevalence in the 856: future if "nothing changes in the future". This is 857: exactly what demographers do with a Life table. Life expectancy 858: is the expected mean time to survive if observed mortality rates 859: (incidence of mortality) "remains constant" in the 860: future. 861: 862: <h5>- Standard deviation of 863: stationary prevalence: <a 864: href="vplrbiaspar.txt">vplrbiaspar.txt</a></h5> 865: 866: The stationary prevalence has to be compared with the observed 867: prevalence by age. But both are statistical estimates and 868: subjected to stochastic errors due to the size of the sample, the 869: design of the survey, and, for the stationary prevalence to the 870: model used and fitted. It is possible to compute the standard 871: deviation of the stationary prevalence at each age. 872: 873: <h5>-Observed and stationary 874: prevalence in state (2=disable) with confidence interval: 875: <a href="vbiaspar21.htm">vbiaspar21.gif</a></h5> 876: 877: This graph exhibits the stationary prevalence in state (2) 878: with the confidence interval in red. The green curve is the 879: observed prevalence (or proportion of individuals in state (2)). 880: Without discussing the results (it is not the purpose here), we 881: observe that the green curve is rather below the stationary 882: prevalence. It suggests an increase of the disability prevalence 883: in the future. 884: 885: <img src="vbiaspar21.gif" width="400" height="300"> 886: 887: <h5>-Convergence to the 888: stationary prevalence of disability: <a 889: href="pbiaspar11.gif">pbiaspar11.gif</a> 890: <img src="pbiaspar11.gif" width="400" height="300"> </h5> 891: 892: This graph plots the conditional transition probabilities from 893: an initial state (1=healthy in red at the bottom, or 2=disable in 894: green on top) at age x to the final state 2=disable at 895: age x+h. Conditional means at the condition to be alive 896: at age x+h which is hP12x + hP22x. The 897: curves hP12x/(hP12x + hP22x) and hP22x/(hP12x 898: + hP22x) converge with h, to the stationary 899: prevalence of disability. In order to get the stationary 900: prevalence at age 70 we should start the process at an earlier 901: age, i.e.50. If the disability state is defined by severe 902: disability criteria with only a few chance to recover, then the 903: incidence of recovery is low and the time to convergence is 904: probably longer. But we don't have experience yet. 905: 906: <h5>- Life expectancies by age 907: and initial health status with standard deviation: <a 908: href="erbiaspar.txt">erbiaspar.txt</a></h5> 909: 910: <pre># Health expectancies 911: # Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE) 912: 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366) 913: 71 9.9325 (0.1409) 3.0495 (0.4234) 5.2627 (0.1107) 5.6384 (0.3129) 914: 72 9.4603 (0.1319) 3.0540 (0.3770) 4.8810 (0.1099) 5.5811 (0.2907) 915: 73 9.0009 (0.1246) 3.0565 (0.3345) 4.5188 (0.1098) 5.5187 (0.2702) 916: </pre> 917: 918: <pre>For example 70 10.4171 (0.1517) 3.0433 (0.4733) 5.6641 (0.1121) 5.6907 (0.3366) means: 919: e11=10.4171 e12=3.0433 e21=5.6641 e22=5.6907 </pre> 920: 921: <pre><img src="expbiaspar21.gif" width="400" height="300"><img 922: src="expbiaspar11.gif" width="400" height="300"></pre> 923: 924: For example, life expectancy of a healthy individual at age 70 925: is 10.42 in the healthy state and 3.04 in the disability state 926: (=13.46 years). If he was disable at age 70, his life expectancy 927: will be shorter, 5.66 in the healthy state and 5.69 in the 928: disability state (=11.35 years). The total life expectancy is a 929: weighted mean of both, 13.46 and 11.35; weight is the proportion 930: of people disabled at age 70. In order to get a pure period index 931: (i.e. based only on incidences) we use the <a 932: href="#Stationary prevalence in each state">computed or 933: stationary prevalence</a> at age 70 (i.e. computed from 934: incidences at earlier ages) instead of the <a 935: href="#Observed prevalence in each state">observed prevalence</a> 936: (for example at first exam) (<a href="#Health expectancies">see 937: below</a>). 938: 939: <h5>- Variances of life 940: expectancies by age and initial health status: <a 941: href="vrbiaspar.txt">vrbiaspar.txt</a></h5> 942: 943: For example, the covariances of life expectancies Cov(ei,ej) 944: at age 50 are (line 3) 945: 946: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre> 947: 948: <h5>-Variances of one-step 949: probabilities : <a href="probrbiaspar.txt">probrbiaspar.txt</a></h5> 950: 951: For example, at age 65 952: 953: <pre> p11=9.960e-001 standard deviation of p11=2.359e-004</pre> 954: 955: <h5>- <a 956: name="Health expectancies">Health 957: expectancies</a> 958: with standard errors in parentheses: <a 959: href="trbiaspar.txt">trbiaspar.txt</a></h5> 960: 961: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> 962: 963: <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre> 964: 965: Thus, at age 70 the total life expectancy, e..=13.26 years is 966: the weighted mean of e1.=13.46 and e2.=11.35 by the stationary 967: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in 968: state 2, respectively (the sum is equal to one). e.1=9.95 is the 969: Disability-free life expectancy at age 70 (it is again a weighted 970: mean of e11 and e21). e.2=3.30 is also the life expectancy at age 971: 70 to be spent in the disability state. 972: 973: <h5>-Total life expectancy by 974: age and health expectancies in states (1=healthy) and (2=disable): 975: <a href="ebiaspar1.gif">ebiaspar1.gif</a></h5> 976: 977: This figure represents the health expectancies and the total 978: life expectancy with the confident interval in dashed curve. 979: 980: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre> 981: 982: Standard deviations (obtained from the information matrix of 983: the model) of these quantities are very useful. 984: Cross-longitudinal surveys are costly and do not involve huge 985: samples, generally a few thousands; therefore it is very 986: important to have an idea of the standard deviation of our 987: estimates. It has been a big challenge to compute the Health 988: Expectancy standard deviations. Don't be confuse: life expectancy 989: is, as any expected value, the mean of a distribution; but here 990: we are not computing the standard deviation of the distribution, 991: but the standard deviation of the estimate of the mean. 992: 993: Our health expectancies estimates vary according to the sample 994: size (and the standard deviations give confidence intervals of 995: the estimate) but also according to the model fitted. Let us 996: explain it in more details. 997: 998: Choosing a model means ar least two kind of choices. First we 999: have to decide the number of disability states. Second we have to 1000: design, within the logit model family, the model: variables, 1001: covariables, confonding factors etc. to be included. 1002: 1003: More disability states we have, better is our demographical 1004: approach of the disability process, but smaller are the number of 1005: transitions between each state and higher is the noise in the 1006: measurement. We do not have enough experiments of the various 1007: models to summarize the advantages and disadvantages, but it is 1008: important to say that even if we had huge and unbiased samples, 1009: the total life expectancy computed from a cross-longitudinal 1010: survey, varies with the number of states. If we define only two 1011: states, alive or dead, we find the usual life expectancy where it 1012: is assumed that at each age, people are at the same risk to die. 1013: If we are differentiating the alive state into healthy and 1014: disable, and as the mortality from the disability state is higher 1015: than the mortality from the healthy state, we are introducing 1016: heterogeneity in the risk of dying. The total mortality at each 1017: age is the weighted mean of the mortality in each state by the 1018: prevalence in each state. Therefore if the proportion of people 1019: at each age and in each state is different from the stationary 1020: equilibrium, there is no reason to find the same total mortality 1021: at a particular age. Life expectancy, even if it is a very useful 1022: tool, has a very strong hypothesis of homogeneity of the 1023: population. Our main purpose is not to measure differential 1024: mortality but to measure the expected time in a healthy or 1025: disability state in order to maximise the former and minimize the 1026: latter. But the differential in mortality complexifies the 1027: measurement. 1028: 1029: Incidences of disability or recovery are not affected by the 1030: number of states if these states are independant. But incidences 1031: estimates are dependant on the specification of the model. More 1032: covariates we added in the logit model better is the model, but 1033: some covariates are not well measured, some are confounding 1034: factors like in any statistical model. The procedure to "fit 1035: the best model' is similar to logistic regression which itself is 1036: similar to regression analysis. We haven't yet been sofar because 1037: we also have a severe limitation which is the speed of the 1038: convergence. On a Pentium III, 500 MHz, even the simplest model, 1039: estimated by month on 8,000 people may take 4 hours to converge. 1040: Also, the program is not yet a statistical package, which permits 1041: a simple writing of the variables and the model to take into 1042: account in the maximisation. The actual program allows only to 1043: add simple variables like age+sex or age+sex+ age*sex but will 1044: never be general enough. But what is to remember, is that 1045: incidences or probability of change from one state to another is 1046: affected by the variables specified into the model. 1047: 1048: Also, the age range of the people interviewed has a link with 1049: the age range of the life expectancy which can be estimated by 1050: extrapolation. If your sample ranges from age 70 to 95, you can 1051: clearly estimate a life expectancy at age 70 and trust your 1052: confidence interval which is mostly based on your sample size, 1053: but if you want to estimate the life expectancy at age 50, you 1054: should rely in your model, but fitting a logistic model on a age 1055: range of 70-95 and estimating probabilties of transition out of 1056: this age range, say at age 50 is very dangerous. At least you 1057: should remember that the confidence interval given by the 1058: standard deviation of the health expectancies, are under the 1059: strong assumption that your model is the 'true model', which is 1060: probably not the case. 1061: 1062: <h5>- Copy of the parameter 1063: file: <a href="orbiaspar.txt">orbiaspar.txt</a></h5> 1064: 1065: This copy of the parameter file can be useful to re-run the 1066: program while saving the old output files. 1067: 1068: <h5>- Prevalence forecasting: 1069: <a href="frbiaspar.txt">frbiaspar.txt</a></h5> 1070: 1071: First, 1073: we have estimated the observed prevalence between 1/1/1984 and 1074: 1/6/1988. The mean date of interview (weighed average of the 1075: interviews performed between1/1/1984 and 1/6/1988) is estimated 1076: to be 13/9/1985, as written on the top on the file. Then we 1077: forecast the probability to be in each state. 1078: 1079: Example, 1081: at date 1/1/1989 : 1082: 1083: <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3 1084: # Forecasting at date 1/1/1989 1085: 73 0.807 0.078 0.115</pre> 1086: 1087: Since 1089: the minimum age is 70 on the 13/9/1985, the youngest forecasted 1090: age is 73. This means that at age a person aged 70 at 13/9/1989 1091: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989. 1092: Similarly, the probability to be in state 2 is 0.078 and the 1093: probability to die is 0.115. Then, on the 1/1/1989, the 1094: prevalence of disability at age 73 is estimated to be 0.088. 1095: 1096: <h5>- Population forecasting: 1097: <a href="poprbiaspar.txt">poprbiaspar.txt</a></h5> 1098: 1099: <pre># Age P.1 P.2 P.3 [Population] 1100: # Forecasting at date 1/1/1989 1101: 75 572685.22 83798.08 1102: 74 621296.51 79767.99 1103: 73 645857.70 69320.60 </pre> 1104: 1105: <pre># Forecasting at date 1/1/19909 1106: 76 442986.68 92721.14 120775.48 1107: 75 487781.02 91367.97 121915.51 1108: 74 512892.07 85003.47 117282.76 </pre> 1109: 1110: From the population file, we estimate the number of people in 1111: each state. At age 73, 645857 persons are in state 1 and 69320 1112: are in state 2. One year latter, 512892 are still in state 1, 1113: 85003 are in state 2 and 117282 died before 1/1/1990. 1114: 1115: <hr> 1116: 1117: <h2><a name="example"></a>Trying an example</h2> 1118: 1119: Since you know how to run the program, it is time to test it 1120: on your own computer. Try for example on a parameter file named <a 1121: href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy 1122: of mypar.imach included 1123: in the subdirectory of imach, mytry. 1124: Edit it to change the name of the data file to ..\data\mydata.txt if you don't want to 1126: copy it on the same directory. The file mydata.txt 1127: is a smaller file of 3,000 people but still with 4 waves. 1128: 1129: Click on the imach.exe icon to open a window. Answer to the 1130: question:'Enter the parameter file name:' 1131: 1132: <table border="1"> 1133: <tr> 1134: <td width="100%">IMACH, Version 0.8aEnter 1135: the parameter file name: ..\mytry\imachpar.imach 1136: </td> 1137: </tr> 1138: </table> 1139: 1140: Most of the data files or image files generated, will use the 1141: 'imachpar' string into their name. The running time is about 2-3 1142: minutes on a Pentium III. If the execution worked correctly, the 1143: outputs files are created in the current directory, and should be 1144: the same as the mypar files initially included in the directory mytry. 1146: 1147: <ul> 1148: <li><pre>Output on the screen The output screen looks like <a 1149: href="imachrun.LOG">this Log file</a> 1150: # 1151: 1152: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 1153: ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 1154: </li> 1155: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 1156: 1157: Warning, no any valid information for:126 line=126 1158: Warning, no any valid information for:2307 line=2307 1159: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 1160: These lines give some warnings on the data file and also some raw statistics on frequencies of transitions. 1161: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 1162: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 1163: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> 1164: </li> 1165: </ul> 1166: 1167:   1168: 1169: <ul> 1170: <li>Maximisation with the Powell algorithm. 8 directions are 1171: given corresponding to the 8 parameters. this can be 1172: rather long to get convergence. 1173: 1174: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 1175: 0.000000000000 3 1176: 0.000000000000 4 0.000000000000 5 0.000000000000 6 1177: 0.000000000000 7 1178: 0.000000000000 8 0.000000000000 1179: 1..........2.................3..........4.................5......... 1180: 6................7........8............... 1181: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 1182: 1183: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 1184: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 1185: 8 0.051272038506 1186: 1..............2...........3..............4........... 1187: 5..........6................7...........8......... 1188: #Number of iterations = 23, -2 Log likelihood = 1189: 6744.954042573691 1190: # Parameters 1191: 12 -12.966061 0.135117 1192: 13 -7.401109 0.067831 1193: 21 -0.672648 -0.006627 1194: 23 -5.051297 0.051271 1195: </li> 1196: <li><pre>Calculation of the hessian matrix. Wait... 1197: 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 1198: 1199: Inverting the hessian to get the covariance matrix. Wait... 1200: 1201: #Hessian matrix# 1202: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 1203: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 1204: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 1205: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 1206: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 1207: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 1208: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 1209: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 1210: # Scales 1211: 12 1.00000e-004 1.00000e-006 1212: 13 1.00000e-004 1.00000e-006 1213: 21 1.00000e-003 1.00000e-005 1214: 23 1.00000e-004 1.00000e-005 1215: # Covariance 1216: 1 5.90661e-001 1217: 2 -7.26732e-003 8.98810e-005 1218: 3 8.80177e-002 -1.12706e-003 5.15824e-001 1219: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 1220: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 1221: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 1222: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 1223: 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 1224: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). 1225: 1226: 1227: agemin=70 agemax=100 bage=50 fage=100 1228: Computing prevalence limit: result on file 'plrmypar.txt' 1229: Computing pij: result on file 'pijrmypar.txt' 1230: Computing Health Expectancies: result on file 'ermypar.txt' 1231: Computing Variance-covariance of DFLEs: file 'vrmypar.txt' 1232: Computing Total LEs with variances: file 'trmypar.txt' 1233: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' 1234: End of Imach 1235: </pre> 1236: </li> 1237: </ul> 1238: 1239: Once the running is finished, the program 1240: requires a caracter: 1241: 1242: <table border="1"> 1243: <tr> 1244: <td width="100%">Type e to edit output files, g 1245: to graph again, c to start again, and q for exiting:</td> 1246: </tr> 1247: </table> 1248: 1249: First you should enter e to 1250: edit the master file mypar.htm. 1251: 1252: <ul> 1253: <li>Outputs files 1254: 1255: - Copy of the parameter file: <a href="ormypar.txt">ormypar.txt</a> 1256: - Gnuplot file name: <a href="mypar.gp.txt">mypar.gp.txt</a> 1257: - Observed prevalence in each state: <a 1258: href="prmypar.txt">prmypar.txt</a> 1259: - Stationary prevalence in each state: <a 1260: href="plrmypar.txt">plrmypar.txt</a> 1261: - Transition probabilities: <a href="pijrmypar.txt">pijrmypar.txt</a> 1262: - Life expectancies by age and initial health status 1263: (estepm=24 months): <a href="ermypar.txt">ermypar.txt</a> 1264: 1265: - Parameter file with estimated parameters and the 1266: covariance matrix: <a href="rmypar.txt">rmypar.txt</a> 1267: - Variance of one-step probabilities: <a 1268: href="probrmypar.txt">probrmypar.txt</a> 1269: - Variances of life expectancies by age and initial 1270: health status (estepm=24 months): <a href="vrmypar.txt">vrmypar.txt</a> 1271: - Health expectancies with their variances: <a 1272: href="trmypar.txt">trmypar.txt</a> 1273: - Standard deviation of stationary prevalences: <a 1274: href="vplrmypar.txt">vplrmypar.txt</a> 1275: No population forecast: popforecast = 0 (instead of 1) or 1276: stepm = 24 (instead of 1) or model=. (instead of .) 1277: 1278: </li> 1279: <li>Graphs 1280: 1281: -<a href="../mytry/pemypar1.gif">One-step transition 1282: probabilities</a> 1283: -<a href="../mytry/pmypar11.gif">Convergence to the 1284: stationary prevalence</a> 1285: -<a href="..\mytry\vmypar11.gif">Observed and stationary 1286: prevalence in state (1) with the confident interval</a> 1287: -<a href="..\mytry\vmypar21.gif">Observed and stationary 1288: prevalence in state (2) with the confident interval</a> 1289: -<a href="..\mytry\expmypar11.gif">Health life 1290: expectancies by age and initial health state (1)</a> 1291: -<a href="..\mytry\expmypar21.gif">Health life 1292: expectancies by age and initial health state (2)</a> 1293: -<a href="..\mytry\emypar1.gif">Total life expectancy by 1294: age and health expectancies in states (1) and (2).</a> </li> 1295: </ul> 1296: 1297: This software have been partly granted by <a 1298: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted 1299: action from the European Union. It will be copyrighted 1300: identically to a GNU software product, i.e. program and software 1301: can be distributed freely for non commercial use. Sources are not 1302: widely distributed today. You can get them by asking us with a 1303: simple justification (name, email, institute) <a 1304: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a 1305: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> . 1306: 1307: Latest version (0.8a of May 2002) can be accessed at <a 1308: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a> 1309: 1310: </body> 1311: </html>