Bayesian Modelling of Lexis Mortality Data

TL;DR

This paper introduces a Bayesian spatial model for mortality data structured over a Lexis diagram, decomposing mortality into smooth and shock components, and applies it to data from 37 countries to identify significant patterns of excess mortality among the elderly.

Contribution

It develops a hierarchical Bayesian framework with MCMC for modeling mortality as a combination of smooth and shock components over age, time, and cohort, applied to extensive international data.

Findings

Identified a band of excess mortality in the 60-90 age group across several countries.

Quantified the importance of smooth versus shock components in mortality patterns.

Discovered significant extra mortality among the elderly in populous countries.

Abstract

In this work we present a spatial approach to model and investigate mortality data referenced over a Lexis structure. We decompose the force of mortality into two interpretable components: a Markov random field, smooth with respect to time, age and cohort which explains the main pattern of mortality; and a secondary component of independent shocks, accounting for additional non-smooth mortality. Inference is based on a hierarchical Bayesian approach with Markov chain Monte Carlo computations. We present an extensive application to data from the Human Mortality Database about 37 countries. For each country the primary smooth surface and the secondary surface of additional mortality are estimated. The importance of each component is evaluated by the estimated value of the respective precision parameter. For several countries we discovered a band of extra mortality in the secondary surface across the time domain, in the age interval between 60 and 90 years, with a slightly positive slope. The band is significant in the most populated countries, but might be present also in the others. The band represents a significant amount of extra mortality for the elderly population, which is otherwise incompatible with a regular and smooth dynamics in age, year and cohort.