DEMOGRAPHV@ Volume 18, Number 3 August 1981 METHODS FOR COMPARING THE MORTALITY EXPERIENCE OF HETEROGENEOUS POPULATIONS Kenneth G. Manton Center for Demographic Studies, and Department of Community and Family Medicine, Duke University, Durham, North Carolina 27706 EricStallard Center for Demographic Studies, Duke University, Durham, North Carolina 27706 James W. Vaupel Institute of Policy Sciencesand Public Affairs, Duke University, Durham, North Carolina 27706 Abstract-Methods are presented which produce Maximum Likelihood Esti- mates (MLE) of the degree of heterogeneity in individual mortality risks un- der a variety of assumptions about the age trajectory of those mortality risks. With these estimates of the degree of population heterogeneity it is possible to adjust comparisons of mortality risks across populations for the effects of population heterogeneity, differential mortality selection, and different age trajectories of the force of mortality. These methods are demonstrated by ap- plying a variety of standard assumptions about the age trajectory of the force of mortality to the analysis of a broad range of cohort mortality data for the U.S. and Swedish populations. The estimates of the degree of heterogeneity, produced under all of the selected force of mortality models, consistently in- dicated a considerable degree of heterogeneity in mortality risks. INTRODUCTION In a previous paper (Vaupel et al., 1979a) a model was presented which illus- trated the bias produced in life table pa- rameters by the operation, over age, of systematic mortality selection on a hetero- geneous population. The effects of such bias on a variety of different types of mor- tality analyses were discussed. Two im- portant types of mortality analyses-eom- parison of the mortality experience of different populations, or of different birth cohorts for the same population-are par- ticularly subject to the bias of population heterogeneity since the comparisons could involve populations under very different mortality conditions. Maximum likeli- hood (ML) estimation procedures which deal with this bias are presented in this paper. These procedures are designed to permit comparisons of the mortality expe- rience across cohorts within the same population by explicitly estimating the magnitude of heterogeneity in that popu- lation while simultaneously adjusting the comparisons for that level of hetero- geneity. These procedures are applied to com- parisons of the mortality experience across successive cohorts of males and fe- males in the U.S. and Swedish popu- lations. Estimates of the magnitude of population heterogeneity in these popu- lations are produced under a variety of assumptions about the age trajectory of the force of mortality for individuals. The estimates of heterogeneity under all of the models selected were consistent in in- dicating a fairly high degree of population heterogeneity. The remainder of this paper is orga- nized into three sections. In the methods section we (a) present a mathematical 389 Downloaded from http://read.dukeupress.edu/demography/article-pdf/18/3/389/905277/389manton.pdf by guest on 03 December 2021