Estimating processes of counts from cross-sectional aggregate data, with an application to multistate life tables and health expectancies

This paper discusses the estimation of time-dependent probabilities of a finite state-space discrete-time process using aggregate cross-sectional data. A large-sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability-free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988-1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability-free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability

The use of aggregate data to estimate gompertz-type old-age mortality in heterogeneous populations

We consider two related aspects of the study of old-age mortality. One is the estimation of a parameterized hazard function from grouped data, and the other is its possible deceleration at extreme old age owing to heterogeneity described by a mixture of distinct sub-populations. The first is treated by half of a logistic transform, which is known to be free of discretization bias at older ages, and also preserves the increasing slope of the log hazard in the Gompertz case. It is assumed that data are available in the form published by official statistical agencies, that is, as aggregated frequencies in discrete time. Local polynomial modelling and weighted least squares are applied to cause-of-death mortality counts. The second, related, problem is to discover what conditions are necessary for population mortality to exhibit deceleration for a mixture of Gompertz sub-populations. The general problem remains open but, in the case of three groups, we demonstrate that heterogeneity may be such that it is possible for a population to show decelerating mortality and then return to a Gompertz-like increase at a later age. This implies that there are situations, depending on the extent of heterogeneity, in which there is at least one age interval in which the hazard function decreases before increasing again

The health expectancies of older Australians

Based on the Australian Bureau of Statistics surveys of 1981, 1988, 1993 and 1998 the paper present estimates of health expectancies of the states Disability-free and Disabled, for females and males aged 60 and over by cohort from 1980, and current for the survey years. Recently developed logistic regression techniques are used instead of the standard methods due to Sullivan, and a major aim of this report is to present these techniques in a readily useable form. An informal presentation of the approach is given in Section 2, with a more rigorous methodological exposition in Section 4. Section 3 contains graphical and numerical results. Amongst our findings is that the results of the three later surveys are broadly similar and differ in important respects from those of the 1981 survey. Based on the last three surveys our estimates support the view that, depending on age, roughly two thirds or more of the increase in life expectancy over the decade 1988-1998 is taken in a state of disability. Also, our findings do not support rectangularisation of the survival or disability-free survival curve