Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 1, pp. 145--165

BAYESIAN ANALYSIS OF MORTALITY RATES FOR U.S. HEALTH SERVICE AREAS

By

B. NANDRAM* Worcester Polytechnic Institute, Worcester MA,
J. SEDRANSK* Case Western Reserve University, Cleveland OH
and
L. PICKLE National Center for Health Statistics, Hyattsville MD

SUMMARY.This paper summarizes our research on alternative models for estimating age specific and age adjusted mortality rates for one of the disease categories, all cancer for white males, presented in the Atlas of United States Mortality, published in 1996. We use Bayesian methods, applied to four different models. Each assumes that the number of deaths, dij, in health service area i, age class j has a Poisson distribution with mean nijlij where nij is the population at risk. The alternative specifications differ in their assumptions about the variation in ln lij over health service areas and age classes. We use expected predictive deviances, posterior predictive p-values and a cross-validation exercise to evaluate the concordance between the models and the observed data. The models captured both the small area and regional effects sufficiently well that no remaining spatial correlation of the residuals was detectable, thus simplifying the estimation. We summarize by presenting point estimates, measures of variation and maps.

AMS (1991) subject classification.62D05 and 62C10.

Key words and phrases. Cancer for white males, diagnostics for nonlinear Bayes models, hierarchical models, measures of fit for Bayes models, mortality

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