Heterogeneity and its effect on mortality measurement.

Methods are presented to adjust total cause specific and ecological mortality analyses for the effects of differential rates of selection due to individual differences in mortality and morbidity risks. The 1st stage in the mathematical development of methods which adjust for the residual risk heterogeneity existing within population groups formed by stratification involves defining the concept of individual frailty as the individuals risk level determined as a fixed function of his profile of values on relevent risk variables. A general mathematical model of individual risk heterogeneity involving the assumptions that individual risk levels are gamma distributed and are proportional over age is presented. The general model is shown to underlie the 3 different types of mortality analyses presented. The 1st type is designed to adjust for the effects of mortality selection on the distribution of total mortality risks in both period and cohort life tables. For cause specific mortality analysis specialized procedures are presented to estimate the transition parameters for a 2-stage model of chronic disease morbidity and mortality in a heterogenous population. The 3rd type of mortality analysis shows how information on individual risks could be derived from the spatial distribution of cause specific mortality rates. Illustrations of the heterogeneity analyses are provided.