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Wed Mar 13 17:27:44 2002 UTC (22 years, 4 months ago) by brouard
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CVS tags: Version-0-8a-jackson-revised, Version-0-8a, HEAD

CHANGE ncov to ncovcol
There was a confusion with older ncov parameter. In fact it was the
number of columns, between id and date of birth, which can be used for
covariates. In the program we use ncovmodel for the real number of
covariates. Version 0.8 !

1:  10: <html> 11: 12: <head> 13: <meta http-equiv="Content-Type" 14: content="text/html; charset=iso-8859-1"> 15: <meta name="GENERATOR" content="Microsoft FrontPage Express 2.0"> 16: <title></title> 17: </head> 18: 19: <body bgcolor="#FFFFFF"> 20: 21: <hr size="3" color="#EC5E5E"> 22: 23: <h1 align="center">Computing Health 24: Expectancies using IMaCh</h1> 25: 26: <h1 align="center">(a Maximum 27: Likelihood Computer Program using Interpolation of Markov Chains)</h1> 28: 29:   30: 31: <a href="http://www.ined.fr/"><img 32: src="logo-ined.gif" border="0" width="151" height="76"></a><img 33: src="euroreves2.gif" width="151" height="75"> 34: 35: <h3 align="center"><a href="http://www.ined.fr/">INED</a> and <a 37: href="http://euroreves.ined.fr">EUROREVES</a></h3> 38: 39: Version 40: 0.8, March 2002 41: 42: <hr size="3" color="#EC5E5E"> 43: 44: Authors of the 45: program: <a href="http://sauvy.ined.fr/brouard">Nicolas Brouard</a>, senior researcher at the <a 48: href="http://www.ined.fr">Institut 49: National d'Etudes Démographiques</a> (INED, Paris) in the "Mortality, 51: Health and Epidemiology" Research Unit 52: 53: and Agnès 54: Lièvre 55: 56: 57: <h4>Contribution to the mathematics: C. R. 58: Heathcote (Australian 59: National University, Canberra).</h4> 60: 61: <h4>Contact: Agnès Lièvre (<a 62: href="mailto:lievre@ined.fr">lievre@ined.fr</a>) </h4> 64: 65: <hr> 66: 67: <ul> 68: <li><a href="#intro">Introduction</a> </li> 69: <li><a href="#data">On what kind of data can it be used?</a></li> 70: <li><a href="#datafile">The data file</a> </li> 71: <li><a href="#biaspar">The parameter file</a> </li> 72: <li><a href="#running">Running Imach</a> </li> 73: <li><a href="#output">Output files and graphs</a> </li> 74: <li><a href="#example">Exemple</a> </li> 75: </ul> 76: 77: <hr> 78: 79: <h2><a name="intro">Introduction</a></h2> 80: 81: This program computes Healthy Life Expectancies from cross-longitudinal 82: data using the methodology pioneered by Laditka and Wolf (1). 83: Within the family of Health Expectancies (HE), Disability-free 84: life expectancy (DFLE) is probably the most important index to 85: monitor. In low mortality countries, there is a fear that when 86: mortality declines, the increase in DFLE is not proportionate to 87: the increase in total Life expectancy. This case is called the Expansion 88: of morbidity. Most of the data collected today, in 89: particular by the international <a href="http://www.reves.org">REVES</a> 90: network on Health expectancy, and most HE indices based on these 91: data, are cross-sectional. It means that the information 92: collected comes from a single cross-sectional survey: people from 93: various ages (but mostly old people) are surveyed on their health 94: status at a single date. Proportion of people disabled at each 95: age, can then be measured at that date. This age-specific 96: prevalence curve is then used to distinguish, within the 97: stationary population (which, by definition, is the life table 98: estimated from the vital statistics on mortality at the same 99: date), the disable population from the disability-free 100: population. Life expectancy (LE) (or total population divided by 101: the yearly number of births or deaths of this stationary 102: population) is then decomposed into DFLE and DLE. This method of 103: computing HE is usually called the Sullivan method (from the name 104: of the author who first described it). 105: 106: Age-specific proportions of people disable are very difficult 107: to forecast because each proportion corresponds to historical 108: conditions of the cohort and it is the result of the historical 109: flows from entering disability and recovering in the past until 110: today. The age-specific intensities (or incidence rates) of 111: entering disability or recovering a good health, are reflecting 112: actual conditions and therefore can be used at each age to 113: forecast the future of this cohort. For example if a country is 114: improving its technology of prosthesis, the incidence of 115: recovering the ability to walk will be higher at each (old) age, 116: but the prevalence of disability will only slightly reflect an 117: improve because the prevalence is mostly affected by the history 118: of the cohort and not by recent period effects. To measure the 119: period improvement we have to simulate the future of a cohort of 120: new-borns entering or leaving at each age the disability state or 121: dying according to the incidence rates measured today on 122: different cohorts. The proportion of people disabled at each age 123: in this simulated cohort will be much lower (using the exemple of 124: an improvement) that the proportions observed at each age in a 125: cross-sectional survey. This new prevalence curve introduced in a 126: life table will give a much more actual and realistic HE level 127: than the Sullivan method which mostly measured the History of 128: health conditions in this country. 129: 130: Therefore, the main question is how to measure incidence rates 131: from cross-longitudinal surveys? This is the goal of the IMaCH 132: program. From your data and using IMaCH you can estimate period 133: HE and not only Sullivan's HE. Also the standard errors of the HE 134: are computed. 135: 136: A cross-longitudinal survey consists in a first survey 137: ("cross") where individuals from different ages are 138: interviewed on their health status or degree of disability. At 139: least a second wave of interviews ("longitudinal") 140: should measure each new individual health status. Health 141: expectancies are computed from the transitions observed between 142: waves and are computed for each degree of severity of disability 143: (number of life states). More degrees you consider, more time is 144: necessary to reach the Maximum Likelihood of the parameters 145: involved in the model. Considering only two states of disability 146: (disable and healthy) is generally enough but the computer 147: program works also with more health statuses. 148: 149: The simplest model is the multinomial logistic model where pij 150: is the probability to be observed in state j at the second 151: wave conditional to be observed in state i at the first 152: wave. Therefore a simple model is: log(pij/pii)= aij + 153: bij*age+ cij*sex, where 'age' is age and 'sex' 154: is a covariate. The advantage that this computer program claims, 155: comes from that if the delay between waves is not identical for 156: each individual, or if some individual missed an interview, the 157: information is not rounded or lost, but taken into account using 158: an interpolation or extrapolation. hPijx is the 159: probability to be observed in state i at age x+h 160: conditional to the observed state i at age x. The 161: delay 'h' can be split into an exact number (nh*stepm) 162: of unobserved intermediate states. This elementary transition (by 163: month or quarter trimester, semester or year) is modeled as a 164: multinomial logistic. The hPx matrix is simply the matrix 165: product of nh*stepm elementary matrices and the 166: contribution of each individual to the likelihood is simply hPijx. 167: 168: 169: 170: The program presented in this manual is a quite general 171: program named IMaCh (for Interpolated 172: MArkov CHain), designed to 173: analyse transition data from longitudinal surveys. The first step 174: is the parameters estimation of a transition probabilities model 175: between an initial status and a final status. From there, the 176: computer program produces some indicators such as observed and 177: stationary prevalence, life expectancies and their variances and 178: graphs. Our transition model consists in absorbing and 179: non-absorbing states with the possibility of return across the 180: non-absorbing states. The main advantage of this package, 181: compared to other programs for the analysis of transition data 182: (For example: Proc Catmod of SAS®) is that the whole 183: individual information is used even if an interview is missing, a 184: status or a date is unknown or when the delay between waves is 185: not identical for each individual. The program can be executed 186: according to parameters: selection of a sub-sample, number of 187: absorbing and non-absorbing states, number of waves taken in 188: account (the user inputs the first and the last interview), a 189: tolerance level for the maximization function, the periodicity of 190: the transitions (we can compute annual, quarterly or monthly 191: transitions), covariates in the model. It works on Windows or on 192: Unix. 193: 194: 195: <hr> 196: 197: (1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New 198: Methods for Analyzing Active Life Expectancy". Journal of 199: Aging and Health. Vol 10, No. 2. 200: 201: <hr> 202: 203: <h2><a name="data">On what kind of data can 204: it be used?</a></h2> 205: 206: The minimum data required for a transition model is the 207: recording of a set of individuals interviewed at a first date and 208: interviewed again at least one another time. From the 209: observations of an individual, we obtain a follow-up over time of 210: the occurrence of a specific event. In this documentation, the 211: event is related to health status at older ages, but the program 212: can be applied on a lot of longitudinal studies in different 213: contexts. To build the data file explained into the next section, 214: you must have the month and year of each interview and the 215: corresponding health status. But in order to get age, date of 216: birth (month and year) is required (missing values is allowed for 217: month). Date of death (month and year) is an important 218: information also required if the individual is dead. Shorter 219: steps (i.e. a month) will more closely take into account the 220: survival time after the last interview. 221: 222: <hr> 223: 224: <h2><a name="datafile">The data file</a></h2> 225: 226: In this example, 8,000 people have been interviewed in a 227: cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). 228: Some people missed 1, 2 or 3 interviews. Health statuses are 229: healthy (1) and disable (2). The survey is not a real one. It is 230: a simulation of the American Longitudinal Survey on Aging. The 231: disability state is defined if the individual missed one of four 232: ADL (Activity of daily living, like bathing, eating, walking). 233: Therefore, even is the individuals interviewed in the sample are 234: virtual, the information brought with this sample is close to the 235: situation of the United States. Sex is not recorded is this 236: sample. 237: 238: Each line of the data set (named <a href="data1.txt">data1.txt</a> 239: in this first example) is an individual record which fields are: 240: 241: <ul> 242: <li>Index number: positive number (field 1) </li> 243: <li>First covariate positive number (field 2) </li> 244: <li>Second covariate positive number (field 3) </li> 245: <li><a name="Weight">Weight</a>: positive number 246: (field 4) . In most surveys individuals are weighted 247: according to the stratification of the sample.</li> 248: <li>Date of birth: coded as mm/yyyy. Missing dates are 249: coded as 99/9999 (field 5) </li> 250: <li>Date of death: coded as mm/yyyy. Missing dates are 251: coded as 99/9999 (field 6) </li> 252: <li>Date of first interview: coded as mm/yyyy. Missing 253: dates are coded as 99/9999 (field 7) </li> 254: <li>Status at first interview: positive number. 255: Missing values ar coded -1. (field 8) </li> 256: <li>Date of second interview: coded as mm/yyyy. 257: Missing dates are coded as 99/9999 (field 9) </li> 258: <li>Status at second interview positive 259: number. Missing values ar coded -1. (field 10) </li> 260: <li>Date of third interview: coded as mm/yyyy. Missing 261: dates are coded as 99/9999 (field 11) </li> 262: <li>Status at third interview positive 263: number. Missing values ar coded -1. (field 12) </li> 264: <li>Date of fourth interview: coded as mm/yyyy. 265: Missing dates are coded as 99/9999 (field 13) </li> 266: <li>Status at fourth interview positive 267: number. Missing values are coded -1. (field 14) </li> 268: <li>etc</li> 269: </ul> 270: 271:   272: 273: If your longitudinal survey do not include information about 274: weights or covariates, you must fill the column with a number 275: (e.g. 1) because a missing field is not allowed. 276: 277: <hr> 278: 279: <h2>Your first example parameter file<a 280: href="http://euroreves.ined.fr/imach"></a><a name="uio"></a></h2> 281: 282: <h2><a name="biaspar"></a>#Imach version 0.8, March 2002, 283: INED-EUROREVES </h2> 284: 285: This is a comment. Comments start with a '#'. 286: 287: <h4>First uncommented line</h4> 288: 289: <pre>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</pre> 290: 291: <ul> 292: <li>title= 1st_example is title of the run. </li> 293: <li>datafile=data1.txt is the name of the data set. 294: Our example is a six years follow-up survey. It consists 295: in a baseline followed by 3 reinterviews. </li> 296: <li>lastobs= 8600 the program is able to run on a 297: subsample where the last observation number is lastobs. 298: It can be set a bigger number than the real number of 299: observations (e.g. 100000). In this example, maximisation 300: will be done on the 8600 first records. </li> 301: <li>firstpass=1 , lastpass=4 In case of more 302: than two interviews in the survey, the program can be run 303: on selected transitions periods. firstpass=1 means the 304: first interview included in the calculation is the 305: baseline survey. lastpass=4 means that the information 306: brought by the 4th interview is taken into account.</li> 307: </ul> 308: 309:   310: 311: <h4><a name="biaspar-2">Second uncommented 312: line</a></h4> 313: 314: <pre>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 315: 316: <ul> 317: <li>ftol=1e-8 Convergence tolerance on the function 318: value in the maximisation of the likelihood. Choosing a 319: correct value for ftol is difficult. 1e-8 is a correct 320: value for a 32 bits computer.</li> 321: <li>stepm=1 Time unit in months for interpolation. 322: Examples:<ul> 323: <li>If stepm=1, the unit is a month </li> 324: <li>If stepm=4, the unit is a trimester</li> 325: <li>If stepm=12, the unit is a year </li> 326: <li>If stepm=24, the unit is two years</li> 327: <li>... </li> 328: </ul> 329: </li> 330: <li>ncovcol=2 Number of covariate columns in the datafile 331: which precede the date of birth. Here you can put variables that 332: won't necessary be used during the run. It is not the number of 333: covariates that will be specified by the model. The 'model' 334: syntax describe the covariates to take into account. </li> 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 file 382: between the id and the date of birth is ncovcol=2 (it was named ncov 383: in version prior to 0.8). If you have 3 covariates in the datafile 384: (fields 2, 3 and 4), you will set ncovcol=3. Then you can run the 385: programme with a new parametrisation taking into account the 386: 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 with 434: a large stepm i.e stepm=12 or 24 and then decrease the stepm until 435: stepm=1 month. If newstepm is the new shorter stepm and stepm can be 436: expressed as a multiple of newstepm, like newstepm=n stepm, then the 437: following approximation holds: 438: <pre>aij(stepm) = aij(n . stepm) - ln(n) 439: </pre> and 440: <pre>bij(stepm) = bij(n . stepm) .</pre> 441: 442: For example if you already ran for a 6 months interval and 443: got: 444: <pre># Parameters 445: 12 -13.390179 0.126133 446: 13 -7.493460 0.048069 447: 21 0.575975 -0.041322 448: 23 -4.748678 0.030626 449: </pre> 450: If you now want to get the monthly estimates, you can guess the aij by 451: substracting ln(6)= 1,7917 and running 452: <pre>12 -15.18193847 0.126133 453: 13 -9.285219469 0.048069 454: 21 -1.215784469 -0.041322 455: 23 -6.540437469 0.030626 456: </pre> 457: and get 458: <pre>12 -15.029768 0.124347 459: 13 -8.472981 0.036599 460: 21 -1.472527 -0.038394 461: 23 -6.553602 0.029856 462: 463: which is closer to the results. The approximation is probably useful 464: only for very small intervals and we don't have enough experience to 465: know if you will speed up the convergence or not. 466: <pre> -ln(12)= -2.484 467: -ln(6/1)=-ln(6)= -1.791 468: -ln(3/1)=-ln(3)= -1.0986 469: -ln(12/6)=-ln(2)= -0.693 470: </pre> 471: 472: <h4>Guess values for computing variances</h4> 473: 474: This is an output if <a href="#mle">mle</a>=1. But it can be 475: used as an input to get the various output data files (Health 476: expectancies, stationary prevalence etc.) and figures without 477: rerunning the rather long maximisation phase (mle=0). 478: 479: The scales are small values for the evaluation of numerical 480: derivatives. These derivatives are used to compute the hessian 481: matrix of the parameters, that is the inverse of the covariance 482: matrix, and the variances of health expectancies. Each line 483: consists in indices "ij" followed by the initial scales 484: (zero to simplify) associated with aij and bij. 485: <ul> <li>If mle=1 you can enter zeros:</li> 486: <blockquote><pre># Scales (for hessian or gradient estimation) 487: 12 0. 0. 488: 13 0. 0. 489: 21 0. 0. 490: 23 0. 0. </pre> 491: </blockquote> 492: <li>If mle=0 you must enter a covariance matrix (usually 493: obtained from an earlier run).</li> 494: </ul> 495: 496: <h4>Covariance matrix of parameters</h4> 497: 498: This is an output if <a href="#mle">mle</a>=1. But it can be 499: used as an input to get the various output data files (Health 500: expectancies, stationary prevalence etc.) and figures without 501: rerunning the rather long maximisation phase (mle=0). 502: Each line starts with indices "ijk" followed by the 503: covariances between aij and bij: 504: <pre> 505: 121 Var(a12) 506: 122 Cov(b12,a12) Var(b12) 507: ... 508: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </pre> 509: <ul> 510: <li>If mle=1 you can enter zeros. </li> 511: <pre># Covariance matrix 512: 121 0. 513: 122 0. 0. 514: 131 0. 0. 0. 515: 132 0. 0. 0. 0. 516: 211 0. 0. 0. 0. 0. 517: 212 0. 0. 0. 0. 0. 0. 518: 231 0. 0. 0. 0. 0. 0. 0. 519: 232 0. 0. 0. 0. 0. 0. 0. 0.</pre> 520: <li>If mle=0 you must enter a covariance matrix (usually 521: obtained from an earlier run). </li> 522: </ul> 523: 524: <h4>Age range for calculation of stationary 525: prevalences and health expectancies</h4> 526: 527: <pre>agemin=70 agemax=100 bage=50 fage=100</pre> 528: 529: Once we obtained the estimated parameters, the program is able 530: to calculated stationary prevalence, transitions probabilities 531: and life expectancies at any age. Choice of age range is useful 532: for extrapolation. In our data file, ages varies from age 70 to 533: 102. It is possible to get extrapolated stationary prevalence by 534: age ranging from agemin to agemax. 535: 536: Setting bage=50 (begin age) and fage=100 (final age), makes 537: the program computing life expectancy from age 'bage' to age 538: 'fage'. As we use a model, we can interessingly compute life 539: expectancy on a wider age range than the age range from the data. 540: But the model can be rather wrong on much larger intervals. 541: Program is limited to around 120 for upper age! 542: <ul> 543: <li>agemin= Minimum age for calculation of the 544: stationary prevalence </li> 545: <li>agemax= Maximum age for calculation of the 546: stationary prevalence </li> 547: <li>bage= Minimum age for calculation of the health 548: expectancies </li> 549: <li>fage= Maximum age for calculation of the health 550: expectancies </li> 551: </ul> 552: 553: <h4><a name="Computing">Computing</a> the observed prevalence</h4> 555: 556: <pre>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 </pre> 557: 558: Statements 'begin-prev-date' and 'end-prev-date' allow to 559: select the period in which we calculate the observed prevalences 560: in each state. In this example, the prevalences are calculated on 561: data survey collected between 1 january 1984 and 1 june 1988. 562: <ul> 563: <li>begin-prev-date= Starting date 564: (day/month/year)</li> 565: <li>end-prev-date= Final date 566: (day/month/year)</li> 567: </ul> 568: 569: <h4>Population- or status-based health 570: expectancies</h4> 571: 572: <pre>pop_based=0</pre> 573: 574: The program computes status-based health expectancies, i.e 575: health expectancies which depends on your initial health state. 576: If you are healthy your healthy life expectancy (e11) is higher 577: than if you were disabled (e21, with e11 > e21). 578: To compute a healthy life expectancy independant of the initial 579: status we have to weight e11 and e21 according to the probability 580: to be in each state at initial age or, with other word, according 581: to the proportion of people in each state. 582: We prefer computing a 'pure' period healthy life expectancy based 583: only on the transtion forces. Then the weights are simply the 584: stationnary prevalences or 'implied' prevalences at the initial 585: age. 586: Some other people would like to use the cross-sectional 587: prevalences (the "Sullivan prevalences") observed at 588: the initial age during a period of time <a href="#Computing">defined 589: just above</a>. 590: 591: <ul> 592: <li>popbased= 0 Health expectancies are 593: computed at each age from stationary prevalences 594: 'expected' at this initial age.</li> 595: <li>popbased= 1 Health expectancies are 596: computed at each age from cross-sectional 'observed' 597: prevalence at this initial age. As all the population is 598: not observed at the same exact date we define a short 599: period were the observed prevalence is computed.</li> 600: </ul> 601: 602: <h4>Prevalence forecasting ( Experimental)</h4> 603: 604: <pre>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </pre> 605: 606: Prevalence and population projections are only available if 607: the interpolation unit is a month, i.e. stepm=1 and if there are 608: no covariate. The programme estimates the prevalence in each 609: state at a precise date expressed in day/month/year. The 610: programme computes one forecasted prevalence a year from a 611: starting date (1 january of 1989 in this example) to a final date 612: (1 january 1992). The statement mov_average allows to compute 613: smoothed forecasted prevalences with a five-age moving average 614: centered at the mid-age of the five-age period. 615: 616: <ul> 617: <li>starting-proj-date= starting date 618: (day/month/year) of forecasting</li> 619: <li>final-proj-date= final date 620: (day/month/year) of forecasting</li> 621: <li>mov_average= smoothing with a five-age 622: moving average centered at the mid-age of the five-age 623: period. The command mov_average takes 624: value 1 if the prevalences are smoothed and 0 otherwise.</li> 625: </ul> 626: 627: <h4>Last uncommented line : Population 628: forecasting </h4> 629: 630: <pre>popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992</pre> 631: 632: This command is available if the interpolation unit is a 633: month, i.e. stepm=1 and if popforecast=1. From a data file 634: including age and number of persons alive at the precise date 635: popfiledate, you can forecast the number of persons 636: in each state until date last-popfiledate. In this 637: example, the popfile <a href="pyram.txt">pyram.txt</a> 638: includes real data which are the Japanese population in 1989. 639: 640: <ul type="disc"> 641: <li class="MsoNormal" 642: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popforecast= 643: 0 Option for population forecasting. If 644: popforecast=1, the programme does the forecasting.</li> 645: <li class="MsoNormal" 646: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popfile= 647: name of the population file</li> 648: <li class="MsoNormal" 649: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">popfiledate= 650: date of the population population</li> 651: <li class="MsoNormal" 652: style="TEXT-ALIGN: justify; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l10 level1 lfo36; tab-stops: list 36.0pt">last-popfiledate= 653: date of the last population projection </li> 654: </ul> 655: 656: <hr> 657: 658: <h2><a name="running"></a>Running Imach 659: with this example</h2> 660: 661: We assume that you typed in your <a href="biaspar.imach">1st_example 662: parameter file</a> as explained <a href="#biaspar">above</a>. 663: To run the program you should either: 664: <ul> <li> click on the imach.exe icon and enter 665: the name of the parameter file which is for example <a 666: href="C:\usr\imach\mle\biaspar.imach">C:\usr\imach\mle\biaspar.imach</a> 667: <li> You also can locate the biaspar.imach icon in 668: <a href="C:\usr\imach\mle">C:\usr\imach\mle</a> with your mouse and drag it with 669: the mouse on the imach window). 670: <li> With latest version (0.7 and higher) if you setup windows in order to 671: understand ".imach" extension you can right click the 672: biaspar.imach icon and either edit with notepad the parameter file or 673: execute it with imach or whatever. 674: </ul> 675: 676: The time to converge depends on the step unit that you used (1 677: month is cpu consuming), on the number of cases, and on the 678: number of variables. 679: 680: The program outputs many files. Most of them are files which 681: will be plotted for better understanding. 682: 683: <hr> 684: 685: <h2><a name="output">Output of the program 686: and graphs </a></h2> 687: 688: Once the optimization is finished, some graphics can be made 689: with a grapher. We use Gnuplot which is an interactive plotting 690: program copyrighted but freely distributed. A gnuplot reference 691: manual is available <a href="http://www.gnuplot.info/">here</a>. 692: When the running is finished, the user should enter a caracter 693: for plotting and output editing. 694: 695: These caracters are: 696: 697: <ul> 698: <li>'c' to start again the program from the beginning.</li> 699: <li>'e' opens the <a href="biaspar.htm">biaspar.htm</a> 700: file to edit the output files and graphs. </li> 701: <li>'q' for exiting.</li> 702: </ul> 703: 704: <h5>Results files 705: 706: - <a 707: name="Observed prevalence in each state">Observed prevalence in each state</a> (and at first pass): 710: <a href="prbiaspar.txt">prbiaspar.txt</a> 711: </h5> 712: 713: The first line is the title and displays each field of the 714: file. The first column is age. The fields 2 and 6 are the 715: proportion of individuals in states 1 and 2 respectively as 716: observed during the first exam. Others fields are the numbers of 717: people in states 1, 2 or more. The number of columns increases if 718: the number of states is higher than 2. 719: The header of the file is 720: 721: <pre># Age Prev(1) N(1) N Age Prev(2) N(2) N 722: 70 1.00000 631 631 70 0.00000 0 631 723: 71 0.99681 625 627 71 0.00319 2 627 724: 72 0.97125 1115 1148 72 0.02875 33 1148 </pre> 725: 726: It means that at age 70, the prevalence in state 1 is 1.000 727: and in state 2 is 0.00 . At age 71 the number of individuals in 728: state 1 is 625 and in state 2 is 2, hence the total number of 729: people aged 71 is 625+2=627. 730: 731: 732: <h5>- Estimated parameters and 733: covariance matrix: <a href="rbiaspar.txt">rbiaspar.imach</a></h5> 734: 735: This file contains all the maximisation results: 736: 737: <pre> -2 log likelihood= 21660.918613445392 738: Estimated parameters: a12 = -12.290174 b12 = 0.092161 739: a13 = -9.155590 b13 = 0.046627 740: a21 = -2.629849 b21 = -0.022030 741: a23 = -7.958519 b23 = 0.042614 742: Covariance matrix: Var(a12) = 1.47453e-001 743: Var(b12) = 2.18676e-005 744: Var(a13) = 2.09715e-001 745: Var(b13) = 3.28937e-005 746: Var(a21) = 9.19832e-001 747: Var(b21) = 1.29229e-004 748: Var(a23) = 4.48405e-001 749: Var(b23) = 5.85631e-005 750: </pre> 751: 752: By substitution of these parameters in the regression model, 753: we obtain the elementary transition probabilities: 754: 755: <img src="pebiaspar1.gif" width="400" height="300"> 756: 757: <h5>- Transition probabilities: 758: <a href="pijrbiaspar.txt">pijrbiaspar.txt</a></h5> 759: 760: Here are the transitions probabilities Pij(x, x+nh) where nh 761: is a multiple of 2 years. The first column is the starting age x 762: (from age 50 to 100), the second is age (x+nh) and the others are 763: the transition probabilities p11, p12, p13, p21, p22, p23. For 764: example, line 5 of the file is: 765: 766: <pre> 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </pre> 767: 768: and this means: 769: 770: <pre>p11(100,106)=0.02655 771: p12(100,106)=0.17622 772: p13(100,106)=0.79722 773: p21(100,106)=0.01809 774: p22(100,106)=0.13678 775: p22(100,106)=0.84513 </pre> 776: 777: <h5>- <a 778: name="Stationary prevalence in each state">Stationary prevalence in each state</a>: 780: <a href="plrbiaspar.txt">plrbiaspar.txt</a></h5> 781: 782: <pre>#Prevalence 783: #Age 1-1 2-2 784: 785: #************ 786: 70 0.90134 0.09866 787: 71 0.89177 0.10823 788: 72 0.88139 0.11861 789: 73 0.87015 0.12985 </pre> 790: 791: At age 70 the stationary prevalence is 0.90134 in state 1 and 792: 0.09866 in state 2. This stationary prevalence differs from 793: observed prevalence. Here is the point. The observed prevalence 794: at age 70 results from the incidence of disability, incidence of 795: recovery and mortality which occurred in the past of the cohort. 796: Stationary prevalence results from a simulation with actual 797: incidences and mortality (estimated from this cross-longitudinal 798: survey). It is the best predictive value of the prevalence in the 799: future if "nothing changes in the future". This is 800: exactly what demographers do with a Life table. Life expectancy 801: is the expected mean time to survive if observed mortality rates 802: (incidence of mortality) "remains constant" in the 803: future. 804: 805: <h5>- Standard deviation of 806: stationary prevalence: <a 807: href="vplrbiaspar.txt">vplrbiaspar.txt</a></h5> 808: 809: The stationary prevalence has to be compared with the observed 810: prevalence by age. But both are statistical estimates and 811: subjected to stochastic errors due to the size of the sample, the 812: design of the survey, and, for the stationary prevalence to the 813: model used and fitted. It is possible to compute the standard 814: deviation of the stationary prevalence at each age. 815: 816: <h5>-Observed and stationary 817: prevalence in state (2=disable) with the confident interval: 818: <a href="vbiaspar21.htm">vbiaspar21.gif</a></h5> 819: 820: This graph exhibits the stationary prevalence in state (2) 821: with the confidence interval in red. The green curve is the 822: observed prevalence (or proportion of individuals in state (2)). 823: Without discussing the results (it is not the purpose here), we 824: observe that the green curve is rather below the stationary 825: prevalence. It suggests an increase of the disability prevalence 826: in the future. 827: 828: <img src="vbiaspar21.gif" width="400" height="300"> 829: 830: <h5>-Convergence to the 831: stationary prevalence of disability: <a 832: href="pbiaspar11.gif">pbiaspar11.gif</a> 833: <img src="pbiaspar11.gif" width="400" height="300"> </h5> 834: 835: This graph plots the conditional transition probabilities from 836: an initial state (1=healthy in red at the bottom, or 2=disable in 837: green on top) at age x to the final state 2=disable at 838: age x+h. Conditional means at the condition to be alive 839: at age x+h which is hP12x + hP22x. The 840: curves hP12x/(hP12x + hP22x) and hP22x/(hP12x 841: + hP22x) converge with h, to the stationary 842: prevalence of disability. In order to get the stationary 843: prevalence at age 70 we should start the process at an earlier 844: age, i.e.50. If the disability state is defined by severe 845: disability criteria with only a few chance to recover, then the 846: incidence of recovery is low and the time to convergence is 847: probably longer. But we don't have experience yet. 848: 849: <h5>- Life expectancies by age 850: and initial health status: <a 851: href="erbiaspar.txt">erbiaspar.txt</a></h5> 852: 853: <pre># Health expectancies 854: # Age 1-1 1-2 2-1 2-2 855: 70 10.9226 3.0401 5.6488 6.2122 856: 71 10.4384 3.0461 5.2477 6.1599 857: 72 9.9667 3.0502 4.8663 6.1025 858: 73 9.5077 3.0524 4.5044 6.0401 </pre> 859: 860: <pre>For example 70 10.4227 3.0402 5.6488 5.7123 means: 861: e11=10.4227 e12=3.0402 e21=5.6488 e22=5.7123</pre> 862: 863: <pre><img src="expbiaspar21.gif" width="400" height="300"><img 864: src="expbiaspar11.gif" width="400" height="300"></pre> 865: 866: For example, life expectancy of a healthy individual at age 70 867: is 10.42 in the healthy state and 3.04 in the disability state 868: (=13.46 years). If he was disable at age 70, his life expectancy 869: will be shorter, 5.64 in the healthy state and 5.71 in the 870: disability state (=11.35 years). The total life expectancy is a 871: weighted mean of both, 13.46 and 11.35; weight is the proportion 872: of people disabled at age 70. In order to get a pure period index 873: (i.e. based only on incidences) we use the <a 874: href="#Stationary prevalence in each state">computed or 875: stationary prevalence</a> at age 70 (i.e. computed from 876: incidences at earlier ages) instead of the <a 877: href="#Observed prevalence in each state">observed prevalence</a> 878: (for example at first exam) (<a href="#Health expectancies">see 879: below</a>). 880: 881: <h5>- Variances of life 882: expectancies by age and initial health status: <a 883: href="vrbiaspar.txt">vrbiaspar.txt</a></h5> 884: 885: For example, the covariances of life expectancies Cov(ei,ej) 886: at age 50 are (line 3) 887: 888: <pre> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</pre> 889: 890: <h5>- <a 891: name="Health expectancies">Health 892: expectancies</a> 893: with standard errors in parentheses: <a 894: href="trbiaspar.txt">trbiaspar.txt</a></h5> 895: 896: <pre>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </pre> 897: 898: <pre>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </pre> 899: 900: Thus, at age 70 the total life expectancy, e..=13.26 years is 901: the weighted mean of e1.=13.46 and e2.=11.35 by the stationary 902: prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in 903: state 2, respectively (the sum is equal to one). e.1=9.95 is the 904: Disability-free life expectancy at age 70 (it is again a weighted 905: mean of e11 and e21). e.2=3.30 is also the life expectancy at age 906: 70 to be spent in the disability state. 907: 908: <h5>-Total life expectancy by 909: age and health expectancies in states (1=healthy) and (2=disable): 910: <a href="ebiaspar1.gif">ebiaspar1.gif</a></h5> 911: 912: This figure represents the health expectancies and the total 913: life expectancy with the confident interval in dashed curve. 914: 915: <pre> <img src="ebiaspar1.gif" width="400" height="300"></pre> 916: 917: Standard deviations (obtained from the information matrix of 918: the model) of these quantities are very useful. 919: Cross-longitudinal surveys are costly and do not involve huge 920: samples, generally a few thousands; therefore it is very 921: important to have an idea of the standard deviation of our 922: estimates. It has been a big challenge to compute the Health 923: Expectancy standard deviations. Don't be confuse: life expectancy 924: is, as any expected value, the mean of a distribution; but here 925: we are not computing the standard deviation of the distribution, 926: but the standard deviation of the estimate of the mean. 927: 928: Our health expectancies estimates vary according to the sample 929: size (and the standard deviations give confidence intervals of 930: the estimate) but also according to the model fitted. Let us 931: explain it in more details. 932: 933: Choosing a model means ar least two kind of choices. First we 934: have to decide the number of disability states. Second we have to 935: design, within the logit model family, the model: variables, 936: covariables, confonding factors etc. to be included. 937: 938: More disability states we have, better is our demographical 939: approach of the disability process, but smaller are the number of 940: transitions between each state and higher is the noise in the 941: measurement. We do not have enough experiments of the various 942: models to summarize the advantages and disadvantages, but it is 943: important to say that even if we had huge and unbiased samples, 944: the total life expectancy computed from a cross-longitudinal 945: survey, varies with the number of states. If we define only two 946: states, alive or dead, we find the usual life expectancy where it 947: is assumed that at each age, people are at the same risk to die. 948: If we are differentiating the alive state into healthy and 949: disable, and as the mortality from the disability state is higher 950: than the mortality from the healthy state, we are introducing 951: heterogeneity in the risk of dying. The total mortality at each 952: age is the weighted mean of the mortality in each state by the 953: prevalence in each state. Therefore if the proportion of people 954: at each age and in each state is different from the stationary 955: equilibrium, there is no reason to find the same total mortality 956: at a particular age. Life expectancy, even if it is a very useful 957: tool, has a very strong hypothesis of homogeneity of the 958: population. Our main purpose is not to measure differential 959: mortality but to measure the expected time in a healthy or 960: disability state in order to maximise the former and minimize the 961: latter. But the differential in mortality complexifies the 962: measurement. 963: 964: Incidences of disability or recovery are not affected by the 965: number of states if these states are independant. But incidences 966: estimates are dependant on the specification of the model. More 967: covariates we added in the logit model better is the model, but 968: some covariates are not well measured, some are confounding 969: factors like in any statistical model. The procedure to "fit 970: the best model' is similar to logistic regression which itself is 971: similar to regression analysis. We haven't yet been sofar because 972: we also have a severe limitation which is the speed of the 973: convergence. On a Pentium III, 500 MHz, even the simplest model, 974: estimated by month on 8,000 people may take 4 hours to converge. 975: Also, the program is not yet a statistical package, which permits 976: a simple writing of the variables and the model to take into 977: account in the maximisation. The actual program allows only to 978: add simple variables like age+sex or age+sex+ age*sex but will 979: never be general enough. But what is to remember, is that 980: incidences or probability of change from one state to another is 981: affected by the variables specified into the model. 982: 983: Also, the age range of the people interviewed has a link with 984: the age range of the life expectancy which can be estimated by 985: extrapolation. If your sample ranges from age 70 to 95, you can 986: clearly estimate a life expectancy at age 70 and trust your 987: confidence interval which is mostly based on your sample size, 988: but if you want to estimate the life expectancy at age 50, you 989: should rely in your model, but fitting a logistic model on a age 990: range of 70-95 and estimating probabilties of transition out of 991: this age range, say at age 50 is very dangerous. At least you 992: should remember that the confidence interval given by the 993: standard deviation of the health expectancies, are under the 994: strong assumption that your model is the 'true model', which is 995: probably not the case. 996: 997: <h5>- Copy of the parameter 998: file: <a href="orbiaspar.txt">orbiaspar.txt</a></h5> 999: 1000: This copy of the parameter file can be useful to re-run the 1001: program while saving the old output files. 1002: 1003: <h5>- Prevalence forecasting: 1004: <a href="frbiaspar.txt">frbiaspar.txt</a></h5> 1005: 1006: First, 1008: we have estimated the observed prevalence between 1/1/1984 and 1009: 1/6/1988. The mean date of interview (weighed average of the 1010: interviews performed between1/1/1984 and 1/6/1988) is estimated 1011: to be 13/9/1985, as written on the top on the file. Then we 1012: forecast the probability to be in each state. 1013: 1014: Example, 1016: at date 1/1/1989 : 1017: 1018: <pre class="MsoNormal"># StartingAge FinalAge P.1 P.2 P.3 1019: # Forecasting at date 1/1/1989 1020: 73 0.807 0.078 0.115</pre> 1021: 1022: Since 1024: the minimum age is 70 on the 13/9/1985, the youngest forecasted 1025: age is 73. This means that at age a person aged 70 at 13/9/1989 1026: has a probability to enter state1 of 0.807 at age 73 on 1/1/1989. 1027: Similarly, the probability to be in state 2 is 0.078 and the 1028: probability to die is 0.115. Then, on the 1/1/1989, the 1029: prevalence of disability at age 73 is estimated to be 0.088. 1030: 1031: <h5>- Population forecasting: 1032: <a href="poprbiaspar.txt">poprbiaspar.txt</a></h5> 1033: 1034: <pre># Age P.1 P.2 P.3 [Population] 1035: # Forecasting at date 1/1/1989 1036: 75 572685.22 83798.08 1037: 74 621296.51 79767.99 1038: 73 645857.70 69320.60 </pre> 1039: 1040: <pre># Forecasting at date 1/1/19909 1041: 76 442986.68 92721.14 120775.48 1042: 75 487781.02 91367.97 121915.51 1043: 74 512892.07 85003.47 117282.76 </pre> 1044: 1045: From the population file, we estimate the number of people in 1046: each state. At age 73, 645857 persons are in state 1 and 69320 1047: are in state 2. One year latter, 512892 are still in state 1, 1048: 85003 are in state 2 and 117282 died before 1/1/1990. 1049: 1050: <hr> 1051: 1052: <h2><a name="example"></a>Trying an example</h2> 1053: 1054: Since you know how to run the program, it is time to test it 1055: on your own computer. Try for example on a parameter file named <a 1056: href="..\mytry\imachpar.imach">imachpar.imach</a> which is a copy of mypar.imach included in the 1058: subdirectory of imach, mytry. 1059: Edit it to change the name of the data file to ..\data\mydata.txt if you don't want to 1061: copy it on the same directory. The file mydata.txt 1062: is a smaller file of 3,000 people but still with 4 waves. 1063: 1064: Click on the imach.exe icon to open a window. Answer to the 1065: question:'Enter the parameter file name:' 1066: 1067: <table border="1"> 1068: <tr> 1069: <td width="100%">IMACH, Version 0.8Enter 1070: the parameter file name: ..\mytry\imachpar.imach 1071: </td> 1072: </tr> 1073: </table> 1074: 1075: Most of the data files or image files generated, will use the 1076: 'imachpar' string into their name. The running time is about 2-3 1077: minutes on a Pentium III. If the execution worked correctly, the 1078: outputs files are created in the current directory, and should be 1079: the same as the mypar files initially included in the directory mytry. 1081: 1082: <ul> 1083: <li><pre>Output on the screen The output screen looks like <a 1084: href="imachrun.LOG">this Log file</a> 1085: # 1086: 1087: title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 1088: ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</pre> 1089: </li> 1090: <li><pre>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 1091: 1092: Warning, no any valid information for:126 line=126 1093: Warning, no any valid information for:2307 line=2307 1094: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 1095: These lines give some warnings on the data file and also some raw statistics on frequencies of transitions. 1096: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 1097: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 1098: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </pre> 1099: </li> 1100: </ul> 1101: 1102:   1103: 1104: <ul> 1105: <li>Maximisation with the Powell algorithm. 8 directions are 1106: given corresponding to the 8 parameters. this can be 1107: rather long to get convergence. 1108: 1109: Powell iter=1 -2*LL=11531.405658264877 1 0.000000000000 2 1110: 0.000000000000 3 1111: 0.000000000000 4 0.000000000000 5 0.000000000000 6 1112: 0.000000000000 7 1113: 0.000000000000 8 0.000000000000 1114: 1..........2.................3..........4.................5......... 1115: 6................7........8............... 1116: Powell iter=23 -2*LL=6744.954108371555 1 -12.967632334283 1117: 1118: 2 0.135136681033 3 -7.402109728262 4 0.067844593326 1119: 5 -0.673601538129 6 -0.006615504377 7 -5.051341616718 1120: 8 0.051272038506 1121: 1..............2...........3..............4........... 1122: 5..........6................7...........8......... 1123: #Number of iterations = 23, -2 Log likelihood = 1124: 6744.954042573691 1125: # Parameters 1126: 12 -12.966061 0.135117 1127: 13 -7.401109 0.067831 1128: 21 -0.672648 -0.006627 1129: 23 -5.051297 0.051271 1130: </li> 1131: <li><pre>Calculation of the hessian matrix. Wait... 1132: 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78 1133: 1134: Inverting the hessian to get the covariance matrix. Wait... 1135: 1136: #Hessian matrix# 1137: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 1138: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 1139: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 1140: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 1141: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 1142: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 1143: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 1144: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 1145: # Scales 1146: 12 1.00000e-004 1.00000e-006 1147: 13 1.00000e-004 1.00000e-006 1148: 21 1.00000e-003 1.00000e-005 1149: 23 1.00000e-004 1.00000e-005 1150: # Covariance 1151: 1 5.90661e-001 1152: 2 -7.26732e-003 8.98810e-005 1153: 3 8.80177e-002 -1.12706e-003 5.15824e-001 1154: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 1155: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 1156: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 1157: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 1158: 8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004 1159: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). 1160: 1161: 1162: agemin=70 agemax=100 bage=50 fage=100 1163: Computing prevalence limit: result on file 'plrmypar.txt' 1164: Computing pij: result on file 'pijrmypar.txt' 1165: Computing Health Expectancies: result on file 'ermypar.txt' 1166: Computing Variance-covariance of DFLEs: file 'vrmypar.txt' 1167: Computing Total LEs with variances: file 'trmypar.txt' 1168: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' 1169: End of Imach 1170: </pre> 1171: </li> 1172: </ul> 1173: 1174: Once the running is finished, the program 1175: requires a caracter: 1176: 1177: <table border="1"> 1178: <tr> 1179: <td width="100%">Type e to edit output files, c 1180: to start again, and q for exiting:</td> 1181: </tr> 1182: </table> 1183: 1184: First you should enter e to 1185: edit the master file mypar.htm. 1186: 1187: <ul> 1188: <li>Outputs files 1189: 1190: - Observed prevalence in each state: <a 1191: href="..\mytry\prmypar.txt">pmypar.txt</a> 1192: - Estimated parameters and the covariance matrix: <a 1193: href="..\mytry\rmypar.txt">rmypar.imach</a> 1194: - Stationary prevalence in each state: <a 1195: href="..\mytry\plrmypar.txt">plrmypar.txt</a> 1196: - Transition probabilities: <a 1197: href="..\mytry\pijrmypar.txt">pijrmypar.txt</a> 1198: - Copy of the parameter file: <a 1199: href="..\mytry\ormypar.txt">ormypar.txt</a> 1200: - Life expectancies by age and initial health status: <a 1201: href="..\mytry\ermypar.txt">ermypar.txt</a> 1202: - Variances of life expectancies by age and initial 1203: health status: <a href="..\mytry\vrmypar.txt">vrmypar.txt</a> 1204: 1205: - Health expectancies with their variances: <a 1206: href="..\mytry\trmypar.txt">trmypar.txt</a> 1207: - Standard deviation of stationary prevalence: <a 1208: href="..\mytry\vplrmypar.txt">vplrmypar.txt</a> 1209: - Prevalences forecasting: <a href="frmypar.txt">frmypar.txt</a> 1210: 1211: - Population forecasting (if popforecast=1): <a 1212: href="poprmypar.txt">poprmypar.txt</a> 1213: </li> 1214: <li>Graphs 1215: 1216: -<a href="../mytry/pemypar1.gif">One-step transition probabilities</a> 1217: -<a href="../mytry/pmypar11.gif">Convergence to the stationary prevalence</a> 1218: -<a href="..\mytry\vmypar11.gif">Observed and stationary prevalence in state (1) with the confident interval</a> 1219: -<a href="..\mytry\vmypar21.gif">Observed and stationary prevalence in state (2) with the confident interval</a> 1220: -<a href="..\mytry\expmypar11.gif">Health life expectancies by age and initial health state (1)</a> 1221: -<a href="..\mytry\expmypar21.gif">Health life expectancies by age and initial health state (2)</a> 1222: -<a href="..\mytry\emypar1.gif">Total life expectancy by age and health expectancies in states (1) and (2).</a> </li> 1223: </ul> 1224: 1225: This software have been partly granted by <a 1226: href="http://euroreves.ined.fr">Euro-REVES</a>, a concerted 1227: action from the European Union. It will be copyrighted 1228: identically to a GNU software product, i.e. program and software 1229: can be distributed freely for non commercial use. Sources are not 1230: widely distributed today. You can get them by asking us with a 1231: simple justification (name, email, institute) <a 1232: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</a> and <a 1233: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</a> . 1234: 1235: Latest version (0.8 of March 2002) can be accessed at <a 1236: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</a> 1237: 1238: </body> 1239: </html>