Bayesian three-stage a-optimal design for generalized linear models

Abstract

Bayesian sequential designs are increasingly receiving attention in recent years, especially in clinical trials and biomedical research. Bayesian sequential design process can utilize the available prior information of the unknown parameters so that a better design can be achieved. In this paper, a hybrid computational method, which consists of the combination of a rough global optima search and a more precise local optima search, is proposed to efficiently search for the Bayesian A-optimal designs for multi-variable generalized linear models. Specifically, Poisson regression models and logistic regression models are investigated. Designs are examined for a range of prior distributions and the equivalence theorem is used to verify the design optimality. Design efficiency for various models were examined. Furthermore, the idea of the Bayesian sequential design is introduced and the Bayesian three-stage A-optimal design approach is introduced for generalized linear models. With the incorporation of the first stage data information into the second stage, the second stage data information into the third stage, the three-stage design procedure improved the design efficiency and produce more accurate and robust designs. The Bayesian three-stage A-optimal designs for Poisson and logistic regression models are evaluated based on simulation studies. The Bayesian three-stage A-optimal design is superior to the two-stage A-optimal design approach in terms of design optimality and efficiency criteria.