Hierarchical Bayes approach for subgroup analysis

In clinical data analysis, both treatment effect estimation and consistency assessment are important for a better understanding of the drug efficacy for the benefit of subjects in individual subgroups. The linear mixed-effects model has been used for subgroup analysis to describe treatment differences among subgroups with great flexibility. The hierarchical Bayes approach has been applied to linear mixed-effects model to derive the posterior distributions of overall and subgroup treatment effects. In this article, we discuss the prior selection for variance components in hierarchical Bayes, estimation and decision making of the overall treatment effect, as well as consistency assessment of the treatment effects across the subgroups based on the posterior predictive p-value. Decision procedures are suggested using either the posterior probability or the Bayes factor. These decision procedures and their properties are illustrated using a simulated example with normally distributed response and repeated measurements.