Segmentation of mortality surfaces by hidden Markov models

Gender-specific mortality surfaces are panels of time series of mortality rates that allow to examine the temporal evolution of male and female mortality across ages. The analysis of these surfaces is often complicated by time-varying effects that reflect the association of age and gender with mortality under unobserved time-varying conditions of the population under study. We propose a hidden Markov model as a simple tool to estimate time-varying effects in mortality surfaces. Under this model, age and gender effects depend on the evolution of an unobserved (hidden) Markov chain, which segments each time series of rates according to time-varying latent classes. We describe the details of an efficient EM algorithm for maximum likelihood estimation of the parameters and suggest a straightforward parametric bootstrap routine to compute standard errors. These methods are illustrated on cardiovascular and cancer mortality rates, observed in Italy during the period 1980–2014.