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.