Empirical Bayesian analysis of the Poisson intervention and incidence parameters

In some population the AIDS/HIV incidence rate θ∈(0,∞) is altered in the middle of a data collection period due to preventive treatments imposed by the health service agencies. The intervened Poisson (IP) model in [Comput. Programs Biomed. 17 (1983) 89; Biometrics 48 (1985) 559] was introduced which is appropriate to analyze data of this type. However, the classical approach leading to the maximum likelihood (ML), moment (M) or minimum variance unbiased (MVU) estimator of θ is mathematically formidable and practically inconvenient as far as sequentially updating the estimate when new data arrive. Previous subjective Bayesian work has been done to overcome these issues. Hence, there is a need to devise a more practical empirical Bayesian technique to estimate θ, and it is done in this article. The results are illustrated using a data on AIDS/HIV incidence in the state of Alabama. Advantages in the Bayesian intervened approach are cited.