- -
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 example 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(r)) 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
+optimisation. 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 available only 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 centred 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 including age and
+number of persons alive at the precise date ‘popfiledate’,
+you can forecast the number of persons in each state until date
+‘last-popfiledate’. In this example, the popfile pyram.txt includes real
+data which are the Japanese population in 1989.
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 character
+for plotting and output editing.
These
+characters 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 at 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,
+confounding 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 so far
+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 probabilities 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.
First,
+we have estimated the observed prevalence between 1/1/1984 and
+1/6/1988. The mean date of interview (weighed average of
+the interviews performed between1/1/1984 and 1/6/1988) is
+estimated to be 13/9/1985, as written on the top on the file.
+Then we forecast the probability to be in each state.
Example,
+at date 1/1/1989 :
# StartingAge FinalAge P.1 P.2 P.3
# Forecasting at date 1/1/1989
73 0.807 0.078 0.115
Since
+the minimum age is 70 on the 13/9/1985, the youngest forecasted
+age is 73. This means that at age a person aged 70 at 13/9/1989
+has a probability to enter state1 of 0.807 at age 73 on 1/1/1989.
+Similarly, the probability to be in state 2 is 0.078 and the
+probability to die is 0.115. Then, on the 1/1/1989, the
+prevalence of disability at age 73 is estimated to be 0.088.
# 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 1/1/1990
+
+76 442986.68 92721.14 120775.48+ +
75 487781.02 91367.97 121915.51+ +
74 512892.07 85003.47 117282.76+ +
+ +
From the population file, we estimate the
+number of people in each state. At age 73, 645857 persons are in
+state 1 and 69320 are in state 2. One year latter, 512892 are
+still in state 1, 85003 are in state 2 and 117282 died before
+1/1/1990.
+
+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
