Stochastic modelling and projection of mortality improvements using a hybrid parametric/semi-parametric age–period–cohort model

We propose a comprehensive and coherent approach for mortality projection using a maximum-likelihood method which benefits from full use of the substantial data available on mortality rates, their improvement rates, and the associated variability. Under this approach, we fit a negative binomial distribution to overcome one of the several limitations of existing approaches such as insufficiently robust mortality projections as a result of employing a model (e.g. Poisson) which provides a poor fit to the data. We also impose smoothness in parameter series which vary over age, cohort, and time in an integrated way. Generalised Additive Models (GAMs), being a flexible class of semi-parametric statistical models, allow us to differentially smooth components, such as cohorts, more heavily in areas of sparse data for the component concerned. While GAMs can provide a reasonable fit for the ages where there is adequate data, estimation and extrapolation of mortality rates using a GAM at higher ages is problematic due to high variation in crude rates. At these ages, parametric models can give a more robust fit, enabling a borrowing of strength across age groups. Our projection methodology assumes a smooth transition between a GAM at lower ages and a fully parametric model at higher ages.