Modelling seasonal mortality: An age–period–cohort approach

Age–period–cohort (APC) mortality models have become the standard approach in actuarial science to project mortality improvements for uses such as pricing annuities and setting contributions in pension plans. Annual mortality rates are sufficient for such long-term applications; yet, for understanding excess mortality due to, e.g., epidemics and heat waves, annual observations have important limitations, and high-frequency data need to be used. This study introduces a seasonal overlay that can be used in the context of APC models. Based on a periodic spline, this extra layer allows the model to capture seasonal features parsimoniously. In an empirical application, we fit a CBDX variant of the APC family to daily mortality data from the province of Quebec in Canada. Our dataset covers over 3.6 million individuals aged at least 60 between 1996 and 2019. Our results show significant seasonal patterns consistent with the flu season, which are similar between males and females. We also test different parametric models and find that the shape of seasonality remained constant over time for most age groups. As part of a sensitivity analysis, we investigate intra-annual mortality patterns between subgroups and report that the local climate, scheme of urbanization, and individual socio-economic status do not affect seasonal patterns. Excess mortality during 2020–2022 is also explored using our modelling framework.