Statistical Modelling 2010; 10(2): 177–196 Smooth models of mortality with period shocks

Abstract: We suppose that we have mortality data arranged in two tables: one of deaths and the other of exposures to the risk of death, each classified by age at death and year of death. It is natural to suppose that there is a smooth underlying force of mortality, the mortality surface, that varies with age and year (or period). However, observed mortality is subject to more than stochastic deviation from this smooth surface. For example, flu epidemics, hot summers or cold winters can disproportionately affect the mortality of certain age groups in particular years. We call such an effect a period shock. We describe the mortality surface with an additive model with two components: the underlying smooth surface is modelled with two-dimensional P-splines and the period shocks are modelled with one-dimensional P-splines in the age direction, one P-spline for each year. This large regression model is written as an additive generalized linear array model and this enables the computations to be performed efficiently. We illustrate our methods with Swedish mortality data taken from the Human Mortality Database. Key words: generalized linear array model; mortality; period shock; P-splines; smoothin