The geometry of mortality change: Convex hulls for demographic analysis

Abstract

We introduce convex hulls as a data visualization and analytic tool for demography. Convex hulls are widely used in computer science, and have been applied in fields such as ecology, but are heretofore underutilized in population studies. We briefly discuss convex hulls, then we show how they may profitably be applied to demography. We do this through three examples, drawn from the relationship between child and adult mortality (₅q₀ and ₄₅q₁₅ in life table notation). The three examples are: (i) sex differences in mortality; (ii) period and cohort differences and (iii) outlier identification. Convex hulls can be useful in robust compilation of demographic databases. Moreover, the gap/lag framework for sex differences or period/cohort differences is more complex when mortality data are arrayed by two components as opposed to a unidimensional measure such as life expectancy. Our examples show how, in certain cases, convex hulls can identify patterns in demographic data more readily than other techniques. The potential applicability of convex hulls in population studies goes beyond mortality.