Parametric empirical Bayes estimation for a class of extended log-linear regression models

This paper presents a fully parametric empirical Bayes approach for the analysis of count data, with emphasis on its application to environmental toxicity data. A hierarchical structure for the mean response is developed from a generalized linear model, based on a Poisson distribution. The linear predictor is embedded at the prior level of the hierarchy. This allows for enhanced flexibility when accounting for extra-Poisson variation, which is often displayed with count data from environmental bioassays. The model expands upon the traditional log-linear model in two different ways: (1) it extends the Poisson distributional assumption; and (2) it incorporates an extended family of link functions that includes the log link as a special case. The main advantage of this approach is that it combines relative computational simplicity with hierarchical modeling flexibility. In this paper, we emphasize the model's development and the practical issues related to the analysis. We describe an application of the proposed model to data from an environmental mutagenesis experiment. Copyright (C) 2000 John Wiley and Sons, Ltd.