Modelling Adult Mortality in Small Populations: The Saint Model

The mortality evolution of small populations often exhibits substantial variability and irregular improvement patterns making it hard to identify underlying trends and produce plausible projections. We propose a methodology for robust forecasting based on the existence of a larger reference population sharing the same long-term trend as the population of interest. The reference population is used to estimate the parameters in a frailty model for the underlying intensity surface. A multivariate time series model describing the deviations of the small population mortality from the underlying mortality is then fitted and forecasted. Coherent long-term forecasts are ensured by the underlying frailty model while the size and variability of short- to medium-term deviations are quantified by the time series model. The frailty model is particularly well suited to describe the changing improvement patterns in old age mortality. We apply the method to Danish mortality data with a pooled international data set as reference population.