Social factors and lifespan inequality: a four-way factorial analysis of U.S. lifespan

Background: Lifespan inequality arises both from heterogeneity (e.g., in sex or race) and from unavoidable individual stochasticity. By treating a heterogeneous population as a mixture we can (and many have) partition variance in lifespan into a between-group component due to heterogeneity and a within-group component due to chance. Until now, such studies have treated factors singly. It is now possible to analyze multiple factors and their contributions to variance. Objective: This paper is the first to exploit the new analysis for multi-factor studies. Multi-factor data are painfully rare, but a remarkable study by Bergeron-Boucher et al. presented U.S. life tables under all 54 combinations of four factors (sex, marital status, education, race). Our objective is to quantify the contributions of these factors and their interactions to lifespan inequality. Methods: The population is treated as a mixture of 54 groups, with a mixture distribution either flat or proportional to population size of the different factor combinations. Components of the variance in remaining longevity, for starting ages from 30 to 85 years, are calculated using marginal mixture distributions. Results: Even accounting for four factors and their interactions, between-group heterogeneity accounts for only 7\% (population-weighted mixing) to 10\% (flat mixing) of lifespan variance. Education and its interactions make the largest contribution. Contributions of two-way, three-way, and four-way interactions are orders of magnitude smaller. This suggests new ways of displaying, summarizing, and interpreting inequality as measured in multi-factor studies. Contribution: Multi-factor studies can now be used to identify sources of variance in longevity and other demographic outcomes.