Modeling Hazard Rates as Functional Data for the Analysis of Cohort Lifetables and Mortality Forecasting

Abstract

As world populations age, the analysis of demographic mortality data and demographic predictions of future mortality have met with increasing interest. The study of mortality patterns and the forecasting of future mortality with its associated impacts on social welfare, health care, and societal planning has become a more pressing issue. An ideal set of data to study patterns of change in long-term mortality is the well-known historical Swedish cohort mortality data, because of its high quality and long span of more than two centuries. We explore the use of functional data analysis to model these data and to derive mortality forecasts. Specifically, we address the challenge of flexibly modeling these data while including the effect of the birth year by regarding log-hazard functions, derived from observed cohort lifetables, as random functions. A functional model for the analysis of these cohort log-hazard functions, extending functional principal component approaches by introducing time-varying eigenfunctions, is found to adequately address these challenges. The associated analysis of the dependency structure of the cohort log-hazard functions leads to the concept of time-varying principal components of mortality. We then extend this analysis to mortality forecasting, by combining prediction of incompletely observed log-hazard functions with functional local extrapolation, and demonstrate these functional approaches for the Swedish cohort mortality data.