Bayesian Estimation of the Incidence Rate in Birth Defects Monitoring

Abstract

Abstract Although non‐Bayesian statistical methods have been used to detect a significant increase of birth defect incidence in monitoring, they require a large number of data. In this paper Bayesian statistics is applied to estimate the incidence rate particularly in a small population. The Bayesian method is as follows. Assuming that the incidence follows a binomial distribution and the prior distribution of the incidence rate is a beta distribution, the posterior distribution of the incidence rate is a beta distribution. The hyperparameters of the prior distribution are determined objectively by the method of maximum marginal likelihood or minimum ABIC of the posterior distribution based on past observations. The Bayesian method is compared with the non‐Bayesian method when applied to the monthly data of anencephaly from the birth defects monitoring program in the Tokyo Metropolitan hospitals between 1979 and 1984. The variation of the Bayesian point estimates is 25% that of the non‐Bayesian ones. The average confidence interval by the Bayesian method is 29% that by the non‐Bayesian method. The results indicate that the Bayesian estimation is more appropriate than the non‐Bayesian estimation in this type of monitoring analysis.