- -
March -2000
- -Authors of the -program: Nicolas Brouard, senior researcher at the Institut -National d'Etudes Démographiques (INED, Paris) in the "Mortality, -Health and Epidemiology" Research Unit
- -and Agnès
-Lièvre
-
This program computes Healthy Life Expectancies from cross-longitudinal -data. Within the family of Health Expectancies (HE), -Disability-free life expectancy (DFLE) is probably the most -important index to monitor. In low mortality countries, there is -a fear that when mortality declines, the increase in DFLE is not -proportionate to the increase in total Life expectancy. This case -is called the Expansion of morbidity. Most of the data -collected today, in particular by the international REVES network on Health -expectancy, and most HE indices based on these data, are cross-sectional. -It means that the information collected comes from a single -cross-sectional survey: people from various ages (but mostly old -people) are surveyed on their health status at a single date. -Proportion of people disabled at each age, can then be measured -at that date. This age-specific prevalence curve is then used to -distinguish, within the stationary population (which, by -definition, is the life table estimated from the vital statistics -on mortality at the same date), the disable population from the -disability-free population. Life expectancy (LE) (or total -population divided by the yearly number of births or deaths of -this stationary population) is then decomposed into DFLE and DLE. -This method of computing HE is usually called the Sullivan method -(from the name of the author who first described it).
- -Age-specific proportions of people disable are very difficult -to forecast because each proportion corresponds to historical -conditions of the cohort and it is the result of the historical -flows from entering disability and recovering in the past until -today. The age-specific intensities (or incidence rates) of -entering disability or recovering a good health, are reflecting -actual conditions and therefore can be used at each age to -forecast the future of this cohort. For example if a country is -improving its technology of prosthesis, the incidence of -recovering the ability to walk will be higher at each (old) age, -but the prevalence of disability will only slightly reflect an -improve because the prevalence is mostly affected by the history -of the cohort and not by recent period effects. To measure the -period improvement we have to simulate the future of a cohort of -new-borns entering or leaving at each age the disability state or -dying according to the incidence rates measured today on -different cohorts. The proportion of people disabled at each age -in this simulated cohort will be much lower (using the exemple of -an improvement) that the proportions observed at each age in a -cross-sectional survey. This new prevalence curve introduced in a -life table will give a much more actual and realistic HE level -than the Sullivan method which mostly measured the History of -health conditions in this country.
- -Therefore, the main question is how to measure incidence rates -from cross-longitudinal surveys? This is the goal of the IMaCH -program. From your data and using IMaCH you can estimate period -HE and not only Sullivan's HE. Also the standard errors of the HE -are computed.
- -A cross-longitudinal survey consists in a first survey
-("cross") where individuals from different ages are
-interviewed on their health status or degree of disability. At
-least a second wave of interviews ("longitudinal")
-should measure each new individual health status. Health
-expectancies are computed from the transitions observed between
-waves and are computed for each degree of severity of disability
-(number of life states). More degrees you consider, more time is
-necessary to reach the Maximum Likelihood of the parameters
-involved in the model. Considering only two states of disability
-(disable and healthy) is generally enough but the computer
-program works also with more health statuses.
-
-The simplest model is the multinomial logistic model where pij
-is the probability to be observed in state j at the second
-wave conditional to be observed in state i at the first
-wave. Therefore a simple model is: log(pij/pii)= aij +
-bij*age+ cij*sex, where 'age' is age and 'sex'
-is a covariate. The advantage that this computer program claims,
-comes from that if the delay between waves is not identical for
-each individual, or if some individual missed an interview, the
-information is not rounded or lost, but taken into account using
-an interpolation or extrapolation. hPijx is the
-probability to be observed in state i at age x+h
-conditional to the observed state i at age x. The
-delay 'h' can be split into an exact number (nh*stepm)
-of unobserved intermediate states. This elementary transition (by
-month or quarter trimester, semester or year) is modeled as a
-multinomial logistic. The hPx matrix is simply the matrix
-product of nh*stepm elementary matrices and the
-contribution of each individual to the likelihood is simply hPijx.
-
-
The program presented in this manual is a quite general
-program named IMaCh (for Interpolated
-MArkov CHain), designed to
-analyse transition data from longitudinal surveys. The first step
-is the parameters estimation of a transition probabilities model
-between an initial status and a final status. From there, the
-computer program produces some indicators such as observed and
-stationary prevalence, life expectancies and their variances and
-graphs. Our transition model consists in absorbing and
-non-absorbing states with the possibility of return across the
-non-absorbing states. The main advantage of this package,
-compared to other programs for the analysis of transition data
-(For example: Proc Catmod of SAS®) is that the whole
-individual information is used even if an interview is missing, a
-status or a date is unknown or when the delay between waves is
-not identical for each individual. The program can be executed
-according to parameters: selection of a sub-sample, number of
-absorbing and non-absorbing states, number of waves taken in
-account (the user inputs the first and the last interview), a
-tolerance level for the maximization function, the periodicity of
-the transitions (we can compute annual, quaterly or monthly
-transitions), covariates in the model. It works on Windows or on
-Unix.
-
The minimum data required for a transition model is the -recording of a set of individuals interviewed at a first date and -interviewed again at least one another time. From the -observations of an individual, we obtain a follow-up over time of -the occurrence of a specific event. In this documentation, the -event is related to health status at older ages, but the program -can be applied on a lot of longitudinal studies in different -contexts. To build the data file explained into the next section, -you must have the month and year of each interview and the -corresponding health status. But in order to get age, date of -birth (month and year) is required (missing values is allowed for -month). Date of death (month and year) is an important -information also required if the individual is dead. Shorter -steps (i.e. a month) will more closely take into account the -survival time after the last interview.
- -In this example, 8,000 people have been interviewed in a -cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). -Some people missed 1, 2 or 3 interviews. Health statuses are -healthy (1) and disable (2). The survey is not a real one. It is -a simulation of the American Longitudinal Survey on Aging. The -disability state is defined if the individual missed one of four -ADL (Activity of daily living, like bathing, eating, walking). -Therefore, even is the individuals interviewed in the sample are -virtual, the information brought with this sample is close to the -situation of the United States. Sex is not recorded is this -sample.
- -Each line of the data set (named data1.txt -in this first example) is an individual record which fields are:
- -- -
If your longitudinal survey do not include information about -weights or covariates, you must fill the column with a number -(e.g. 1) because a missing field is not allowed.
- -This is a comment. Comments start with a '#'.
- -title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4- -
- -
ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0- -
You must write the initial guess values of the parameters for
-optimization. The number of parameters, N depends on the
-number of absorbing states and non-absorbing states and on the
-number of covariates.
-N is given by the formula N=(nlstate +
-ndeath-1)*nlstate*ncov .
-
-Thus in the simple case with 2 covariates (the model is log
-(pij/pii) = aij + bij * age where intercept and age are the two
-covariates), and 2 health degrees (1 for disability-free and 2
-for disability) and 1 absorbing state (3), you must enter 8
-initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
-start with zeros as in this example, but if you have a more
-precise set (for example from an earlier run) you can enter it
-and it will speed up them
-Each of the four lines starts with indices "ij":
-
-ij aij bij
-- -# Guess values of aij and bij in log (pij/pii) = aij + bij * age -12 -14.155633 0.110794 -13 -7.925360 0.032091 -21 -1.890135 -0.029473 -23 -6.234642 0.022315-
or, to simplify:
- --- -12 0.0 0.0 -13 0.0 0.0 -21 0.0 0.0 -23 0.0 0.0-
This is an output if mle=1. But it can be -used as an input to get the vairous output data files (Health -expectancies, stationary prevalence etc.) and figures without -rerunning the rather long maximisation phase (mle=0).
- -The scales are small values for the evaluation of numerical -derivatives. These derivatives are used to compute the hessian -matrix of the parameters, that is the inverse of the covariance -matrix, and the variances of health expectancies. Each line -consists in indices "ij" followed by the initial scales -(zero to simplify) associated with aij and bij.
- --- -# Scales (for hessian or gradient estimation) -12 0. 0. -13 0. 0. -21 0. 0. -23 0. 0.-
This is an output if mle=1. But it can be -used as an input to get the vairous output data files (Health -expectancies, stationary prevalence etc.) and figures without -rerunning the rather long maximisation phase (mle=0).
- -Each line starts with indices "ijk" followed by the -covariances between aij and bij:
- -- 121 Var(a12) - 122 Cov(b12,a12) Var(b12) - ... - 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)- -
-- -# Covariance matrix -121 0. -122 0. 0. -131 0. 0. 0. -132 0. 0. 0. 0. -211 0. 0. 0. 0. 0. -212 0. 0. 0. 0. 0. 0. -231 0. 0. 0. 0. 0. 0. 0. -232 0. 0. 0. 0. 0. 0. 0. 0.-
agemin=70 agemax=100 bage=50 fage=100- -
Once we obtained the estimated parameters, the program is able -to calculated stationary prevalence, transitions probabilities -and life expectancies at any age. Choice of age ranges is useful -for extrapolation. In our data file, ages varies from age 70 to -102. Setting bage=50 and fage=100, makes the program computing -life expectancy from age bage to age fage. As we use a model, we -can compute life expectancy on a wider age range than the age -range from the data. But the model can be rather wrong on big -intervals.
- -Similarly, it is possible to get extrapolated stationary -prevalence by age raning from agemin to agemax.
- -We assume that you entered your 1st_example
-parameter file as explained above. To
-run the program you should click on the imach.exe icon and enter
-the name of the parameter file which is for example C:\usr\imach\mle\biaspar.txt
-(you also can click on the biaspar.txt icon located in
-C:\usr\imach\mle and put it with
-the mouse on the imach window).
-
The time to converge depends on the step unit that you used (1 -month is cpu consuming), on the number of cases, and on the -number of variables.
- -The program outputs many files. Most of them are files which -will be plotted for better understanding.
- -Once the optimization is finished, some graphics can be made
-with a grapher. We use Gnuplot which is an interactive plotting
-program copyrighted but freely distributed. Imach outputs the
-source of a gnuplot file, named 'graph.gp', which can be directly
-input into gnuplot.
-When the running is finished, the user should enter a caracter
-for plotting and output editing.
These caracters are:
- -The first line is the title and displays each field of the
-file. The first column is age. The fields 2 and 6 are the
-proportion of individuals in states 1 and 2 respectively as
-observed during the first exam. Others fields are the numbers of
-people in states 1, 2 or more. The number of columns increases if
-the number of states is higher than 2.
-The header of the file is
# Age Prev(1) N(1) N Age Prev(2) N(2) N -70 1.00000 631 631 70 0.00000 0 631 -71 0.99681 625 627 71 0.00319 2 627 -72 0.97125 1115 1148 72 0.02875 33 1148- -
# Age Prev(1) N(1) N Age Prev(2) N(2) N - 70 0.95721 604 631 70 0.04279 27 631- -
It means that at age 70, the prevalence in state 1 is 1.000
-and in state 2 is 0.00 . At age 71 the number of individuals in
-state 1 is 625 and in state 2 is 2, hence the total number of
-people aged 71 is 625+2=627.
-
This file contains all the maximisation results:
- -Number of iterations=47 - -2 log likelihood=46553.005854373667 - Estimated parameters: a12 = -12.691743 b12 = 0.095819 - a13 = -7.815392 b13 = 0.031851 - a21 = -1.809895 b21 = -0.030470 - a23 = -7.838248 b23 = 0.039490 - Covariance matrix: Var(a12) = 1.03611e-001 - Var(b12) = 1.51173e-005 - Var(a13) = 1.08952e-001 - Var(b13) = 1.68520e-005 - Var(a21) = 4.82801e-001 - Var(b21) = 6.86392e-005 - Var(a23) = 2.27587e-001 - Var(b23) = 3.04465e-005 -- -
Here are the transitions probabilities Pij(x, x+nh) where nh -is a multiple of 2 years. The first column is the starting age x -(from age 50 to 100), the second is age (x+nh) and the others are -the transition probabilities p11, p12, p13, p21, p22, p23. For -example, line 5 of the file is:
- -100 106 0.03286 0.23512 0.73202 0.02330 0.19210 0.78460- -
and this means:
- -p11(100,106)=0.03286 -p12(100,106)=0.23512 -p13(100,106)=0.73202 -p21(100,106)=0.02330 -p22(100,106)=0.19210 -p22(100,106)=0.78460- -
#Age 1-1 2-2 -70 0.92274 0.07726 -71 0.91420 0.08580 -72 0.90481 0.09519 -73 0.89453 0.10547- -
At age 70 the stationary prevalence is 0.92274 in state 1 and -0.07726 in state 2. This stationary prevalence differs from -observed prevalence. Here is the point. The observed prevalence -at age 70 results from the incidence of disability, incidence of -recovery and mortality which occurred in the past of the cohort. -Stationary prevalence results from a simulation with actual -incidences and mortality (estimated from this cross-longitudinal -survey). It is the best predictive value of the prevalence in the -future if "nothing changes in the future". This is -exactly what demographers do with a Life table. Life expectancy -is the expected mean time to survive if observed mortality rates -(incidence of mortality) "remains constant" in the -future.
- -The stationary prevalence has to be compared with the observed -prevalence by age. But both are statistical estimates and -subjected to stochastic errors due to the size of the sample, the -design of the survey, and, for the stationary prevalence to the -model used and fitted. It is possible to compute the standard -deviation of the stationary prevalence at each age.
- -
-This graph exhibits the stationary prevalence in state (2) with
-the confidence interval in red. The green curve is the observed
-prevalence (or proportion of individuals in state (2)). Without
-discussing the results (it is not the purpose here), we observe
-that the green curve is rather below the stationary prevalence.
-It suggests an increase of the disability prevalence in the
-future.
This graph plots the conditional transition probabilities from -an initial state (1=healthy in red at the bottom, or 2=disable in -green on top) at age x to the final state 2=disable at -age x+h. Conditional means at the condition to be alive -at age x+h which is hP12x + hP22x. The -curves hP12x/(hP12x + hP22x) and hP22x/(hP12x -+ hP22x) converge with h, to the stationary -prevalence of disability. In order to get the stationary -prevalence at age 70 we should start the process at an earlier -age, i.e.50. If the disability state is defined by severe -disability criteria with only a few chance to recover, then the -incidence of recovery is low and the time to convergence is -probably longer. But we don't have experience yet.
- -# Health expectancies -# Age 1-1 1-2 2-1 2-2 -70 10.7297 2.7809 6.3440 5.9813 -71 10.3078 2.8233 5.9295 5.9959 -72 9.8927 2.8643 5.5305 6.0033 -73 9.4848 2.9036 5.1474 6.0035- -
For example 70 10.7297 2.7809 6.3440 5.9813 means: -e11=10.7297 e12=2.7809 e21=6.3440 e22=5.9813- -
- -
For example, life expectancy of a healthy individual at age 70 -is 10.73 in the healthy state and 2.78 in the disability state -(=13.51 years). If he was disable at age 70, his life expectancy -will be shorter, 6.34 in the healthy state and 5.98 in the -disability state (=12.32 years). The total life expectancy is a -weighted mean of both, 13.51 and 12.32; weight is the proportion -of people disabled at age 70. In order to get a pure period index -(i.e. based only on incidences) we use the computed or -stationary prevalence at age 70 (i.e. computed from -incidences at earlier ages) instead of the observed prevalence -(for example at first exam) (see -below).
- -For example, the covariances of life expectancies Cov(ei,ej) -at age 50 are (line 3)
- -Cov(e1,e1)=0.4667 Cov(e1,e2)=0.0605=Cov(e2,e1) Cov(e2,e2)=0.0183- -
#Total LEs with variances: e.. (std) e.1 (std) e.2 (std)- -
70 13.42 (0.18) 10.39 (0.15) 3.03 (0.10)70 13.81 (0.18) 11.28 (0.14) 2.53 (0.09)- -
Thus, at age 70 the total life expectancy, e..=13.42 years is -the weighted mean of e1.=13.51 and e2.=12.32 by the stationary -prevalence at age 70 which are 0.92274 in state 1 and 0.07726 in -state 2, respectively (the sum is equal to one). e.1=10.39 is the -Disability-free life expectancy at age 70 (it is again a weighted -mean of e11 and e21). e.2=3.03 is also the life expectancy at age -70 to be spent in the disability state.
- -This figure represents the health expectancies and the total -life expectancy with the confident interval in dashed curve.
- -- -
Standard deviations (obtained from the information matrix of -the model) of these quantities are very useful. -Cross-longitudinal surveys are costly and do not involve huge -samples, generally a few thousands; therefore it is very -important to have an idea of the standard deviation of our -estimates. It has been a big challenge to compute the Health -Expectancy standard deviations. Don't be confuse: life expectancy -is, as any expected value, the mean of a distribution; but here -we are not computing the standard deviation of the distribution, -but the standard deviation of the estimate of the mean.
- -Our health expectancies estimates vary according to the sample -size (and the standard deviations give confidence intervals of -the estimate) but also according to the model fitted. Let us -explain it in more details.
- -Choosing a model means ar least two kind of choices. First we -have to decide the number of disability states. Second we have to -design, within the logit model family, the model: variables, -covariables, confonding factors etc. to be included.
- -More disability states we have, better is our demographical -approach of the disability process, but smaller are the number of -transitions between each state and higher is the noise in the -measurement. We do not have enough experiments of the various -models to summarize the advantages and disadvantages, but it is -important to say that even if we had huge and unbiased samples, -the total life expectancy computed from a cross-longitudinal -survey, varies with the number of states. If we define only two -states, alive or dead, we find the usual life expectancy where it -is assumed that at each age, people are at the same risk to die. -If we are differentiating the alive state into healthy and -disable, and as the mortality from the disability state is higher -than the mortality from the healthy state, we are introducing -heterogeneity in the risk of dying. The total mortality at each -age is the weighted mean of the mortality in each state by the -prevalence in each state. Therefore if the proportion of people -at each age and in each state is different from the stationary -equilibrium, there is no reason to find the same total mortality -at a particular age. Life expectancy, even if it is a very useful -tool, has a very strong hypothesis of homogeneity of the -population. Our main purpose is not to measure differential -mortality but to measure the expected time in a healthy or -disability state in order to maximise the former and minimize the -latter. But the differential in mortality complexifies the -measurement.
- -Incidences of disability or recovery are not affected by the -number of states if these states are independant. But incidences -estimates are dependant on the specification of the model. More -covariates we added in the logit model better is the model, but -some covariates are not well measured, some are confounding -factors like in any statistical model. The procedure to "fit -the best model' is similar to logistic regression which itself is -similar to regression analysis. We haven't yet been sofar because -we also have a severe limitation which is the speed of the -convergence. On a Pentium III, 500 MHz, even the simplest model, -estimated by month on 8,000 people may take 4 hours to converge. -Also, the program is not yet a statistical package, which permits -a simple writing of the variables and the model to take into -account in the maximisation. The actual program allows only to -add simple variables without covariations, like age+sex but -without age+sex+ age*sex . This can be done from the source code -(you have to change three lines in the source code) but will -never be general enough. But what is to remember, is that -incidences or probability of change from one state to another is -affected by the variables specified into the model.
- -Also, the age range of the people interviewed has a link with -the age range of the life expectancy which can be estimated by -extrapolation. If your sample ranges from age 70 to 95, you can -clearly estimate a life expectancy at age 70 and trust your -confidence interval which is mostly based on your sample size, -but if you want to estimate the life expectancy at age 50, you -should rely in your model, but fitting a logistic model on a age -range of 70-95 and estimating probabilties of transition out of -this age range, say at age 50 is very dangerous. At least you -should remember that the confidence interval given by the -standard deviation of the health expectancies, are under the -strong assumption that your model is the 'true model', which is -probably not the case.
- -This copy of the parameter file can be useful to re-run the -program while saving the old output files.
- -Since you know how to run the program, it is time to test it -on your own computer. Try for example on a parameter file named imachpar.txt which is a -copy of mypar.txt -included in the subdirectory of imach, mytry. Edit it to change the name of -the data file to ..\data\mydata.txt -if you don't want to copy it on the same directory. The file mydata.txt is a smaller file of 3,000 -people but still with 4 waves.
- -Click on the imach.exe icon to open a window. Answer to the -question:'Enter the parameter file name:'
- -| IMACH, Version 0.63 Enter - the parameter file name: ..\mytry\imachpar.txt - |
-
Most of the data files or image files generated, will use the -'imachpar' string into their name. The running time is about 2-3 -minutes on a Pentium III. If the execution worked correctly, the -outputs files are created in the current directory, and should be -the same as the mypar files initially included in the directory mytry.
- -Output on the screen The output screen looks like this Log file -# - -title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 -ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0-
Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 - -Warning, no any valid information for:126 line=126 -Warning, no any valid information for:2307 line=2307 -Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 -These lines give some warnings on the data file and also some raw statistics on frequencies of transitions. -Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 - prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 -Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0-
- -
Calculation of the hessian matrix. Wait... -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 - -Inverting the hessian to get the covariance matrix. Wait... - -#Hessian matrix# -3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 -2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 --4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 --3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 --1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 --1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 -3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 -3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 -# Scales -12 1.00000e-004 1.00000e-006 -13 1.00000e-004 1.00000e-006 -21 1.00000e-003 1.00000e-005 -23 1.00000e-004 1.00000e-005 -# Covariance - 1 5.90661e-001 - 2 -7.26732e-003 8.98810e-005 - 3 8.80177e-002 -1.12706e-003 5.15824e-001 - 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 - 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 - 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 - 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 - 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 -# agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). - - -agemin=70 agemax=100 bage=50 fage=100 -Computing prevalence limit: result on file 'plrmypar.txt' -Computing pij: result on file 'pijrmypar.txt' -Computing Health Expectancies: result on file 'ermypar.txt' -Computing Variance-covariance of DFLEs: file 'vrmypar.txt' -Computing Total LEs with variances: file 'trmypar.txt' -Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' -End of Imach --
Once the running is finished, the program -requires a caracter:
- -| Type g for plotting (available
- if mle=1), e to edit output files, c to start again, and - q for exiting: - |
-
First you should enter g to -make the figures and then you can edit all the results by typing e. -
- -This software have been partly granted by Euro-REVES, a concerted -action from the European Union. It will be copyrighted -identically to a GNU software product, i.e. program and software -can be distributed freely for non commercial use. Sources are not -widely distributed today. You can get them by asking us with a -simple justification (name, email, institute) mailto:brouard@ined.fr and mailto:lievre@ined.fr .
- -Latest version (0.63 of 16 march 2000) can be accessed at http://euroreves.ined.fr/imach
-
+ +
Version +0.7, February 2002
+ +Authors of the +program: Nicolas Brouard, senior researcher at the Institut +National d'Etudes Démographiques (INED, Paris) in the "Mortality, +Health and Epidemiology" Research Unit
+ +and Agnès
+Lièvre
+
This program computes Healthy Life Expectancies from cross-longitudinal +data using the methodology pioneered by Laditka and Wolf (1). +Within the family of Health Expectancies (HE), Disability-free +life expectancy (DFLE) is probably the most important index to +monitor. In low mortality countries, there is a fear that when +mortality declines, the increase in DFLE is not proportionate to +the increase in total Life expectancy. This case is called the Expansion +of morbidity. Most of the data collected today, in +particular by the international REVES +network on Health expectancy, and most HE indices based on these +data, are cross-sectional. It means that the information +collected comes from a single cross-sectional survey: people from +various ages (but mostly old people) are surveyed on their health +status at a single date. Proportion of people disabled at each +age, can then be measured at that date. This age-specific +prevalence curve is then used to distinguish, within the +stationary population (which, by definition, is the life table +estimated from the vital statistics on mortality at the same +date), the disable population from the disability-free +population. Life expectancy (LE) (or total population divided by +the yearly number of births or deaths of this stationary +population) is then decomposed into DFLE and DLE. This method of +computing HE is usually called the Sullivan method (from the name +of the author who first described it).
+ +Age-specific proportions of people disable are very difficult +to forecast because each proportion corresponds to historical +conditions of the cohort and it is the result of the historical +flows from entering disability and recovering in the past until +today. The age-specific intensities (or incidence rates) of +entering disability or recovering a good health, are reflecting +actual conditions and therefore can be used at each age to +forecast the future of this cohort. For example if a country is +improving its technology of prosthesis, the incidence of +recovering the ability to walk will be higher at each (old) age, +but the prevalence of disability will only slightly reflect an +improve because the prevalence is mostly affected by the history +of the cohort and not by recent period effects. To measure the +period improvement we have to simulate the future of a cohort of +new-borns entering or leaving at each age the disability state or +dying according to the incidence rates measured today on +different cohorts. The proportion of people disabled at each age +in this simulated cohort will be much lower (using the exemple of +an improvement) that the proportions observed at each age in a +cross-sectional survey. This new prevalence curve introduced in a +life table will give a much more actual and realistic HE level +than the Sullivan method which mostly measured the History of +health conditions in this country.
+ +Therefore, the main question is how to measure incidence rates +from cross-longitudinal surveys? This is the goal of the IMaCH +program. From your data and using IMaCH you can estimate period +HE and not only Sullivan's HE. Also the standard errors of the HE +are computed.
+ +A cross-longitudinal survey consists in a first survey
+("cross") where individuals from different ages are
+interviewed on their health status or degree of disability. At
+least a second wave of interviews ("longitudinal")
+should measure each new individual health status. Health
+expectancies are computed from the transitions observed between
+waves and are computed for each degree of severity of disability
+(number of life states). More degrees you consider, more time is
+necessary to reach the Maximum Likelihood of the parameters
+involved in the model. Considering only two states of disability
+(disable and healthy) is generally enough but the computer
+program works also with more health statuses.
+
+The simplest model is the multinomial logistic model where pij
+is the probability to be observed in state j at the second
+wave conditional to be observed in state i at the first
+wave. Therefore a simple model is: log(pij/pii)= aij +
+bij*age+ cij*sex, where 'age' is age and 'sex'
+is a covariate. The advantage that this computer program claims,
+comes from that if the delay between waves is not identical for
+each individual, or if some individual missed an interview, the
+information is not rounded or lost, but taken into account using
+an interpolation or extrapolation. hPijx is the
+probability to be observed in state i at age x+h
+conditional to the observed state i at age x. The
+delay 'h' can be split into an exact number (nh*stepm)
+of unobserved intermediate states. This elementary transition (by
+month or quarter trimester, semester or year) is modeled as a
+multinomial logistic. The hPx matrix is simply the matrix
+product of nh*stepm elementary matrices and the
+contribution of each individual to the likelihood is simply hPijx.
+
+
The program presented in this manual is a quite general
+program named IMaCh (for Interpolated
+MArkov CHain), designed to
+analyse transition data from longitudinal surveys. The first step
+is the parameters estimation of a transition probabilities model
+between an initial status and a final status. From there, the
+computer program produces some indicators such as observed and
+stationary prevalence, life expectancies and their variances and
+graphs. Our transition model consists in absorbing and
+non-absorbing states with the possibility of return across the
+non-absorbing states. The main advantage of this package,
+compared to other programs for the analysis of transition data
+(For example: Proc Catmod of SAS®) is that the whole
+individual information is used even if an interview is missing, a
+status or a date is unknown or when the delay between waves is
+not identical for each individual. The program can be executed
+according to parameters: selection of a sub-sample, number of
+absorbing and non-absorbing states, number of waves taken in
+account (the user inputs the first and the last interview), a
+tolerance level for the maximization function, the periodicity of
+the transitions (we can compute annual, quarterly or monthly
+transitions), covariates in the model. It works on Windows or on
+Unix.
+
(1) Laditka, Sarah B. and Wolf, Douglas A. (1998), "New +Methods for Analyzing Active Life Expectancy". Journal of +Aging and Health. Vol 10, No. 2.
+ +The minimum data required for a transition model is the +recording of a set of individuals interviewed at a first date and +interviewed again at least one another time. From the +observations of an individual, we obtain a follow-up over time of +the occurrence of a specific event. In this documentation, the +event is related to health status at older ages, but the program +can be applied on a lot of longitudinal studies in different +contexts. To build the data file explained into the next section, +you must have the month and year of each interview and the +corresponding health status. But in order to get age, date of +birth (month and year) is required (missing values is allowed for +month). Date of death (month and year) is an important +information also required if the individual is dead. Shorter +steps (i.e. a month) will more closely take into account the +survival time after the last interview.
+ +In this example, 8,000 people have been interviewed in a +cross-longitudinal survey of 4 waves (1984, 1986, 1988, 1990). +Some people missed 1, 2 or 3 interviews. Health statuses are +healthy (1) and disable (2). The survey is not a real one. It is +a simulation of the American Longitudinal Survey on Aging. The +disability state is defined if the individual missed one of four +ADL (Activity of daily living, like bathing, eating, walking). +Therefore, even is the individuals interviewed in the sample are +virtual, the information brought with this sample is close to the +situation of the United States. Sex is not recorded is this +sample.
+ +Each line of the data set (named data1.txt +in this first example) is an individual record which fields are:
+ ++ +
If your longitudinal survey do not include information about +weights or covariates, you must fill the column with a number +(e.g. 1) because a missing field is not allowed.
+ +This is a comment. Comments start with a '#'.
+ +title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4+ +
+ +
ftol=1.e-08 stepm=1 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0+ +
Intercept and age are systematically included in the model. +Additional covariates can be included with the command
+ +model=list of covariates+ +
You must write the initial guess values of the parameters for
+optimization. The number of parameters, N depends on the
+number of absorbing states and non-absorbing states and on the
+number of covariates.
+N is given by the formula N=(nlstate +
+ndeath-1)*nlstate*ncov .
+
+Thus in the simple case with 2 covariates (the model is log
+(pij/pii) = aij + bij * age where intercept and age are the two
+covariates), and 2 health degrees (1 for disability-free and 2
+for disability) and 1 absorbing state (3), you must enter 8
+initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can
+start with zeros as in this example, but if you have a more
+precise set (for example from an earlier run) you can enter it
+and it will speed up them
+Each of the four lines starts with indices "ij": ij
+aij bij
++ +# Guess values of aij and bij in log (pij/pii) = aij + bij * age +12 -14.155633 0.110794 +13 -7.925360 0.032091 +21 -1.890135 -0.029473 +23 -6.234642 0.022315+
or, to simplify:
+ +++ +12 0.0 0.0 +13 0.0 0.0 +21 0.0 0.0 +23 0.0 0.0+
This is an output if mle=1. But it can be +used as an input to get the various output data files (Health +expectancies, stationary prevalence etc.) and figures without +rerunning the rather long maximisation phase (mle=0).
+ +The scales are small values for the evaluation of numerical +derivatives. These derivatives are used to compute the hessian +matrix of the parameters, that is the inverse of the covariance +matrix, and the variances of health expectancies. Each line +consists in indices "ij" followed by the initial scales +(zero to simplify) associated with aij and bij.
+ +++ +# Scales (for hessian or gradient estimation) +12 0. 0. +13 0. 0. +21 0. 0. +23 0. 0.+
This is an output if mle=1. But it can be +used as an input to get the various output data files (Health +expectancies, stationary prevalence etc.) and figures without +rerunning the rather long maximisation phase (mle=0).
+ +Each line starts with indices "ijk" followed by the +covariances between aij and bij:
+ ++ 121 Var(a12) + 122 Cov(b12,a12) Var(b12) + ... + 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)+ +
++ +# Covariance matrix +121 0. +122 0. 0. +131 0. 0. 0. +132 0. 0. 0. 0. +211 0. 0. 0. 0. 0. +212 0. 0. 0. 0. 0. 0. +231 0. 0. 0. 0. 0. 0. 0. +232 0. 0. 0. 0. 0. 0. 0. 0.+
agemin=70 agemax=100 bage=50 fage=100+ +
Once we obtained the estimated parameters, the program is able +to calculated stationary prevalence, transitions probabilities +and life expectancies at any age. Choice of age range is useful +for extrapolation. In our data file, ages varies from age 70 to +102. Setting bage=50 and fage=100, makes the program computing +life expectancy from age bage to age fage. As we use a model, we +can compute life expectancy on a wider age range than the age +range from the data. But the model can be rather wrong on big +intervals.
+ +Similarly, it is possible to get extrapolated stationary +prevalence by age ranging from agemin to agemax.
+ +begin-prev-date=1/1/1984 end-prev-date=1/6/1988+ +
Statements 'begin-prev-date' and 'end-prev-date' allow to +select the period in which we calculate the observed prevalences +in each state. In this example, the prevalences are calculated on +data survey collected between 1 january 1984 and 1 june 1988.
+ +pop_based=0+ +
The user has the possibility to choose between +population-based or status-based health expectancies. If +pop_based=0 then status-based health expectancies are computed +and if pop_based=1, the programme computes population-based +health expectancies. Health expectancies are weighted averages of +health expectancies respective of the initial state. For a +status-based index, the weights are the cross-sectional +prevalences observed between two dates, as previously +explained, whereas for a population-based index, the weights +are the stationary prevalences.
+ +starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0+ +
Prevalence and population projections are only available if +the interpolation unit is a month, i.e. stepm=1. The programme +estimates the prevalence in each state at a precise date +expressed in day/month/year. The programme computes one +forecasted prevalence a year from a starting date (1 january of +1989 in this example) to a final date (1 january 1992). The +statement mov_average allows to compute smoothed forecasted +prevalences with a five-age moving average centered at the +mid-age of the five-age period.
+ +popforecast=0 popfile=pyram.txt popfiledate=1/1/1989 last-popfiledate=1/1/1992+ +
This command is available if the interpolation unit is a +month, i.e. stepm=1 and if popforecast=1. From a data file
+ +Structure of the data file pyram.txt +: age numbers
+ ++ +
We assume that you entered your 1st_example
+parameter file as explained above. To
+run the program you should click on the imach.exe icon and enter
+the name of the parameter file which is for example C:\usr\imach\mle\biaspar.txt
+(you also can click on the biaspar.txt icon located in
+C:\usr\imach\mle and put it with
+the mouse on the imach window).
+
The time to converge depends on the step unit that you used (1 +month is cpu consuming), on the number of cases, and on the +number of variables.
+ +The program outputs many files. Most of them are files which +will be plotted for better understanding.
+ +Once the optimization is finished, some graphics can be made
+with a grapher. We use Gnuplot which is an interactive plotting
+program copyrighted but freely distributed. A gnuplot reference
+manual is available here.
+When the running is finished, the user should enter a caracter
+for plotting and output editing.
These caracters are:
+ +The first line is the title and displays each field of the
+file. The first column is age. The fields 2 and 6 are the
+proportion of individuals in states 1 and 2 respectively as
+observed during the first exam. Others fields are the numbers of
+people in states 1, 2 or more. The number of columns increases if
+the number of states is higher than 2.
+The header of the file is
# Age Prev(1) N(1) N Age Prev(2) N(2) N +70 1.00000 631 631 70 0.00000 0 631 +71 0.99681 625 627 71 0.00319 2 627 +72 0.97125 1115 1148 72 0.02875 33 1148+ +
It means that at age 70, the prevalence in state 1 is 1.000
+and in state 2 is 0.00 . At age 71 the number of individuals in
+state 1 is 625 and in state 2 is 2, hence the total number of
+people aged 71 is 625+2=627.
+
This file contains all the maximisation results:
+ +-2 log likelihood= 21660.918613445392 + Estimated parameters: a12 = -12.290174 b12 = 0.092161 + a13 = -9.155590 b13 = 0.046627 + a21 = -2.629849 b21 = -0.022030 + a23 = -7.958519 b23 = 0.042614 + Covariance matrix: Var(a12) = 1.47453e-001 + Var(b12) = 2.18676e-005 + Var(a13) = 2.09715e-001 + Var(b13) = 3.28937e-005 + Var(a21) = 9.19832e-001 + Var(b21) = 1.29229e-004 + Var(a23) = 4.48405e-001 + Var(b23) = 5.85631e-005 ++ +
By substitution of these parameters in the regression model, +we obtain the elementary transition probabilities:
+ +
Here are the transitions probabilities Pij(x, x+nh) where nh +is a multiple of 2 years. The first column is the starting age x +(from age 50 to 100), the second is age (x+nh) and the others are +the transition probabilities p11, p12, p13, p21, p22, p23. For +example, line 5 of the file is:
+ +100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513+ +
and this means:
+ +p11(100,106)=0.02655 +p12(100,106)=0.17622 +p13(100,106)=0.79722 +p21(100,106)=0.01809 +p22(100,106)=0.13678 +p22(100,106)=0.84513+ +
#Prevalence +#Age 1-1 2-2 + +#************ +70 0.90134 0.09866 +71 0.89177 0.10823 +72 0.88139 0.11861 +73 0.87015 0.12985+ +
At age 70 the stationary prevalence is 0.90134 in state 1 and +0.09866 in state 2. This stationary prevalence differs from +observed prevalence. Here is the point. The observed prevalence +at age 70 results from the incidence of disability, incidence of +recovery and mortality which occurred in the past of the cohort. +Stationary prevalence results from a simulation with actual +incidences and mortality (estimated from this cross-longitudinal +survey). It is the best predictive value of the prevalence in the +future if "nothing changes in the future". This is +exactly what demographers do with a Life table. Life expectancy +is the expected mean time to survive if observed mortality rates +(incidence of mortality) "remains constant" in the +future.
+ +The stationary prevalence has to be compared with the observed +prevalence by age. But both are statistical estimates and +subjected to stochastic errors due to the size of the sample, the +design of the survey, and, for the stationary prevalence to the +model used and fitted. It is possible to compute the standard +deviation of the stationary prevalence at each age.
+ +This graph exhibits the stationary prevalence in state (2) +with the confidence interval in red. The green curve is the +observed prevalence (or proportion of individuals in state (2)). +Without discussing the results (it is not the purpose here), we +observe that the green curve is rather below the stationary +prevalence. It suggests an increase of the disability prevalence +in the future.
+ +
This graph plots the conditional transition probabilities from +an initial state (1=healthy in red at the bottom, or 2=disable in +green on top) at age x to the final state 2=disable at +age x+h. Conditional means at the condition to be alive +at age x+h which is hP12x + hP22x. The +curves hP12x/(hP12x + hP22x) and hP22x/(hP12x ++ hP22x) converge with h, to the stationary +prevalence of disability. In order to get the stationary +prevalence at age 70 we should start the process at an earlier +age, i.e.50. If the disability state is defined by severe +disability criteria with only a few chance to recover, then the +incidence of recovery is low and the time to convergence is +probably longer. But we don't have experience yet.
+ +# Health expectancies +# Age 1-1 1-2 2-1 2-2 +70 10.9226 3.0401 5.6488 6.2122 +71 10.4384 3.0461 5.2477 6.1599 +72 9.9667 3.0502 4.8663 6.1025 +73 9.5077 3.0524 4.5044 6.0401+ +
For example 70 10.9226 3.0401 5.6488 6.2122 means: +e11=10.9226 e12=3.0401 e21=5.6488 e22=6.2122+ +
+ +
For example, life expectancy of a healthy individual at age 70 +is 10.92 in the healthy state and 3.04 in the disability state +(=13.96 years). If he was disable at age 70, his life expectancy +will be shorter, 5.64 in the healthy state and 6.21 in the +disability state (=11.85 years). The total life expectancy is a +weighted mean of both, 13.96 and 11.85; weight is the proportion +of people disabled at age 70. In order to get a pure period index +(i.e. based only on incidences) we use the computed or +stationary prevalence at age 70 (i.e. computed from +incidences at earlier ages) instead of the observed prevalence +(for example at first exam) (see +below).
+ +For example, the covariances of life expectancies Cov(ei,ej) +at age 50 are (line 3)
+ +Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424+ +
#Total LEs with variances: e.. (std) e.1 (std) e.2 (std)+ +
70 13.76 (0.22) 10.40 (0.20) 3.35 (0.14)+ +
Thus, at age 70 the total life expectancy, e..=13.76years is +the weighted mean of e1.=13.96 and e2.=11.85 by the stationary +prevalence at age 70 which are 0.90134 in state 1 and 0.09866 in +state 2, respectively (the sum is equal to one). e.1=10.40 is the +Disability-free life expectancy at age 70 (it is again a weighted +mean of e11 and e21). e.2=3.35 is also the life expectancy at age +70 to be spent in the disability state.
+ +This figure represents the health expectancies and the total +life expectancy with the confident interval in dashed curve.
+ ++ +
Standard deviations (obtained from the information matrix of +the model) of these quantities are very useful. +Cross-longitudinal surveys are costly and do not involve huge +samples, generally a few thousands; therefore it is very +important to have an idea of the standard deviation of our +estimates. It has been a big challenge to compute the Health +Expectancy standard deviations. Don't be confuse: life expectancy +is, as any expected value, the mean of a distribution; but here +we are not computing the standard deviation of the distribution, +but the standard deviation of the estimate of the mean.
+ +Our health expectancies estimates vary according to the sample +size (and the standard deviations give confidence intervals of +the estimate) but also according to the model fitted. Let us +explain it in more details.
+ +Choosing a model means ar least two kind of choices. First we +have to decide the number of disability states. Second we have to +design, within the logit model family, the model: variables, +covariables, confonding factors etc. to be included.
+ +More disability states we have, better is our demographical +approach of the disability process, but smaller are the number of +transitions between each state and higher is the noise in the +measurement. We do not have enough experiments of the various +models to summarize the advantages and disadvantages, but it is +important to say that even if we had huge and unbiased samples, +the total life expectancy computed from a cross-longitudinal +survey, varies with the number of states. If we define only two +states, alive or dead, we find the usual life expectancy where it +is assumed that at each age, people are at the same risk to die. +If we are differentiating the alive state into healthy and +disable, and as the mortality from the disability state is higher +than the mortality from the healthy state, we are introducing +heterogeneity in the risk of dying. The total mortality at each +age is the weighted mean of the mortality in each state by the +prevalence in each state. Therefore if the proportion of people +at each age and in each state is different from the stationary +equilibrium, there is no reason to find the same total mortality +at a particular age. Life expectancy, even if it is a very useful +tool, has a very strong hypothesis of homogeneity of the +population. Our main purpose is not to measure differential +mortality but to measure the expected time in a healthy or +disability state in order to maximise the former and minimize the +latter. But the differential in mortality complexifies the +measurement.
+ +Incidences of disability or recovery are not affected by the +number of states if these states are independant. But incidences +estimates are dependant on the specification of the model. More +covariates we added in the logit model better is the model, but +some covariates are not well measured, some are confounding +factors like in any statistical model. The procedure to "fit +the best model' is similar to logistic regression which itself is +similar to regression analysis. We haven't yet been sofar because +we also have a severe limitation which is the speed of the +convergence. On a Pentium III, 500 MHz, even the simplest model, +estimated by month on 8,000 people may take 4 hours to converge. +Also, the program is not yet a statistical package, which permits +a simple writing of the variables and the model to take into +account in the maximisation. The actual program allows only to +add simple variables like age+sex or age+sex+ age*sex but will +never be general enough. But what is to remember, is that +incidences or probability of change from one state to another is +affected by the variables specified into the model.
+ +Also, the age range of the people interviewed has a link with +the age range of the life expectancy which can be estimated by +extrapolation. If your sample ranges from age 70 to 95, you can +clearly estimate a life expectancy at age 70 and trust your +confidence interval which is mostly based on your sample size, +but if you want to estimate the life expectancy at age 50, you +should rely in your model, but fitting a logistic model on a age +range of 70-95 and estimating probabilties of transition out of +this age range, say at age 50 is very dangerous. At least you +should remember that the confidence interval given by the +standard deviation of the health expectancies, are under the +strong assumption that your model is the 'true model', which is +probably not the case.
+ +This copy of the parameter file can be useful to re-run the +program while saving the old output files.
+ +On a d'abord estimé la date moyenne des interviaew. ie +13/9/1995. This file contains
+ +Example, at date 1/1/1989 :
+ +73 0.807 0.078 0.115
+ +This means that at age 73, the probability for a person age 70 +at 13/9/1989 to be in state 1 is 0.807, in state 2 is 0.078 and +to die is 0.115 at 1/1/1989.
+ +# Age P.1 P.2 P.3 [Population] +# Forecasting at date 1/1/1989 +75 572685.22 83798.08 +74 621296.51 79767.99 +73 645857.70 69320.60+ +
# Forecasting at date 1/1/19909 +76 442986.68 92721.14 120775.48 +75 487781.02 91367.97 121915.51 +74 512892.07 85003.47 117282.76+ +
Since you know how to run the program, it is time to test it +on your own computer. Try for example on a parameter file named imachpar.txt which is a copy of mypar.txt included in the +subdirectory of imach, mytry. +Edit it to change the name of the data file to ..\data\mydata.txt if you don't want to +copy it on the same directory. The file mydata.txt +is a smaller file of 3,000 people but still with 4 waves.
+ +Click on the imach.exe icon to open a window. Answer to the +question:'Enter the parameter file name:'
+ +| IMACH, Version 0.7 Enter + the parameter file name: ..\mytry\imachpar.txt + |
+
Most of the data files or image files generated, will use the +'imachpar' string into their name. The running time is about 2-3 +minutes on a Pentium III. If the execution worked correctly, the +outputs files are created in the current directory, and should be +the same as the mypar files initially included in the directory mytry.
+ +Output on the screen The output screen looks like this Log file +# + +title=MLE datafile=..\data\mydata.txt lastobs=3000 firstpass=1 lastpass=3 +ftol=1.000000e-008 stepm=24 ncov=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0+
Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92 + +Warning, no any valid information for:126 line=126 +Warning, no any valid information for:2307 line=2307 +Delay (in months) between two waves Min=21 Max=51 Mean=24.495826 +These lines give some warnings on the data file and also some raw statistics on frequencies of transitions. +Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14 + prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1 +Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0+
+ +
Calculation of the hessian matrix. Wait... +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 + +Inverting the hessian to get the covariance matrix. Wait... + +#Hessian matrix# +3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001 +2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003 +-4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001 +-3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003 +-1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003 +-1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005 +3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004 +3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006 +# Scales +12 1.00000e-004 1.00000e-006 +13 1.00000e-004 1.00000e-006 +21 1.00000e-003 1.00000e-005 +23 1.00000e-004 1.00000e-005 +# Covariance + 1 5.90661e-001 + 2 -7.26732e-003 8.98810e-005 + 3 8.80177e-002 -1.12706e-003 5.15824e-001 + 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005 + 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000 + 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004 + 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000 + 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 +# agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood). + + +agemin=70 agemax=100 bage=50 fage=100 +Computing prevalence limit: result on file 'plrmypar.txt' +Computing pij: result on file 'pijrmypar.txt' +Computing Health Expectancies: result on file 'ermypar.txt' +Computing Variance-covariance of DFLEs: file 'vrmypar.txt' +Computing Total LEs with variances: file 'trmypar.txt' +Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt' +End of Imach ++
Once the running is finished, the program +requires a caracter:
+ +| Type e to edit output files, c + to start again, and q for exiting: | +
First you should enter e to +edit the master file mypar.htm.
+ +This software have been partly granted by Euro-REVES, a concerted +action from the European Union. It will be copyrighted +identically to a GNU software product, i.e. program and software +can be distributed freely for non commercial use. Sources are not +widely distributed today. You can get them by asking us with a +simple justification (name, email, institute) mailto:brouard@ined.fr and mailto:lievre@ined.fr .
+ +Latest version (0.7 of February 2002) can be accessed at http://euroreves.ined.fr/imach
+
