An empirical bayes formulation of cohort models in cancer epidemiology

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Abstract
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.

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