Using Singular Value Decomposition to Understand Variation Across Mortality Schedules from Multiple Populations

Understanding variation in mortality age schedules across populations is a key objective of demographic and epidemiological research. Commonly used decomposi- tion methods partition differences in demographic summary indicators—such as life expectancy at birth—into age-specific contributions for only two populations. Here, we demonstrate how singular value decomposition—an existing mathematical decomposition technique—can be used to summarize and understand variation among mortality schedules from multiple populations. We explain how singular value decomposition can be used to (a) extract key mortality age patterns from a set of mortality schedules; and (b) quantify the relative importance of these age patterns for the various mortality schedules included in the set. We demonstrate this method by decomposing variation in the mortality schedules of US states, showing that (1) most of the variation in 2019 was due to differences in young-adult mortality, and that (2) different US states achieved the same high level of life expectancy at birth with fundamentally different mortality profiles. The singular value decomposition approach complements existing pairwise decomposition methods for describing and summarizing mortality differences across populations, and we discuss further potential areas of application.