An empirical Bayes formulation of cohort models in cancer epidemiology

This paper concerns the incidence rates of malignant skin melanoma for several age-sex groups and time periods in three geographic regions, uses a method of cohort analysis and employs a two-stage random effects model. The first stage entails the assumption that the within-region variation in the frequency of disease incidence for a fixed age-sex-cohort group has a Poisson distribution with mean proportional to the population at risk. The second stage, after adjusting for age and sex, entails the assumption that the between-region geographic variation in the logarithm of the true incidence rate has a prior distribution with parameters estimated by the method of maximum likelihood. After adjusting for age effects, we estimate random geographic-specific cohort effects for each sex with use of an empirical Bayes method and compare the results with the usual multiplicative Poisson model that assumes fixed geographic-specific cohort effects for each sex. This comparison shows that the method presented here provides more stable estimates of geographic-specific cohort effects, and in addition the random effects model describes these data more adequately.