Mortality crossovers: a simple model to disentangle "real" effects from compositional effects

Roland Rau, University of Rostock

Empirical studies often find that differences in mortality by socioeconomic status tend to converge and even cross-over with increasing age. Does this imply that risks are also converging on the individual level? Not necessarily. The decreasing gap can be also explained by compositional changes: people who are frailer than others tend to die younger, resulting in a selected healthier sub-population with an observed leveling-off in the observed mortality at higher ages. We present here a simple model that allows to disentangle direct effects from compositional effects. The model assumes that individuals in two groups are subject to a Gompertz mortality schedule and that the hazards of the two groups are proportional to each other. Individuals within the two groups differ in their frailty, which is assumed to be Gamma-distributed. We show that a simple mathematical expression allows us to estimate at what age the two hazards would converge if only compositional effects were present. If the observed crossover age is earlier, we can postulate that hazards do actually converge on the individual level. If the two trajectories have not yet converged at the estimated age, we hypothesize that individuals hazards are diverging with increasing age. Our model is not restricted to analyze only converging socioeconomic mortality differentials. It can be employed whenever two groups exist whose observed mortality hazards converge or crossover (e.g. smokers and non-smokers).