Christopher R. Heathcote

The Estimation Of Health Expectancies From Cross-Longitudinal Surveys

The method of maximum likelihood is used to estimate parameterized transition probabilities of a non-homogeneous Markov chain model of movements between the health states disability-free, disabled, and death. A complication is that individuals are observed at irregular intervals, implying that particular attention must be paid to computational issues. Numerical results including estimated health expectancies and their standard errors are given for data from the Longitudinal Study on Aging (LSOA) of 1984-86-88-90 (Kovar et al. 1992). The weak ergodicity of prevalence on the non-absorbing states is established and supports the hypothesis of the compression of morbidity.

The health expectancies of older Australians

Health expectancies of the states ‘Disability-free’ and ‘Disabled’ are estimated for Australian females and males aged 60 and over, both by cohort from 1980 and current for survey years 1981, 1988, 1993 and 1998. Modifications of recently developed logistic regression techniques are used rather than the standard 1971 method due to Sullivan. Results from 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, two-thirds or more of the increase in female life expectancy over the decade 1988–1998 is spent in the Disabled state. The situation is worse for elderly men, for whom all of the increased years of expected life are estimated to be spent in the Disabled state. The findings do not support rectangularization of the survival curve or Disability-free survival curve.

A Regression Model of Mortality, with Application to the Netherlands

Regression methods are used to model and estimate a measure of the mortality of a population as a function of time and age. The measure of mortality used is the logit (or log odds) of the cohort time and age-specific probability of death and it is shown how a parameterised model can be estimated by weighted least squares. The method is applied to historical 1890–1990 data of male and female mortality for ages 40 and above in the Netherlands. The fitted regressions provide the point of departure for the predictive model and forecasts developed in the next chapter.

Forecasting Mortality from Regression Models: The Case of the Netherlands

This chapter continues the discussion of Chapter 3 in which regressions for male and female mortality for ages 40 and above in the Netherlands were estimated. A naive forecast of mortality can be obtained by extrapolation. However, a plausible forecast may require modification of the fitted model to obtain what is called a predictive model. A model of this sort is described and the resulting forecasts of period and cohort life expectancy and log(odds) are compared with those produced by extrapolations of the descriptive model. Period and cohort life expectancy for selected ages above 40 and for selected years to 2050 are given. A final section discusses the forecasts obtained from regression models using the perspective of the official national forecasts of Dutch mortality.

REGRESSION MODELLING OF MORTALITY SURFACES AND THE DECELERATION OF MORTALITY

A mortality surface is a measure of mortality indexed by year and age. A central limit theorem for aggregate data is established for the mortality surface defined by the logistic transform of the year and age-specific probability of death and this is used to postulate and estimate a regression model. Extra variance may be the result of heterogeneity within cohorts, and it is shown how the model based on aggregate data could be decomposed to accommodate sub-cohorts by using proportional odds. In the absence of disaggregated data, excess variance is modelled as a function of age and year and estimation is done by maximum likelihood. The parametric surface so estimated is used to examine deceleration of mortality at old ages and trends in deceleration are discussed with reference to selection and heterogeneity. The results are applied to mortality data from the Netherlands for 1890–1991, ages 50–90.