Bayesian hierarchical models for multi-way subgroup problems
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*Gene Anthony Pennello, FDA/CDRH 


Estimates of treatment effects within subgroups tend to have too much variation relative to the true treatment effects, hampering clinical interpretation. To remove this unwanted random variation, Bayesian hierarchical models can be used to pull or shrink the within-subgroup estimates toward the overall estimate, with the degree of shrinkage depending on variation between to variation within the subgroups. Most presentations on Bayesian hierarchical models consider the simple one-way model of unstructured subgroups. However, subgroups may be defined by the levels of more than one factor (e.g., age, sex, ethnicity). The factors may be additive or may interact in their modification of treatment effect. In this talk, Bayesian hierarchical models for multi-factor subgroup problems will be presented that exploit factor structure. The Bayesian posterior mean of the difference in treatment effect between subgroups will be shown to be an intuitive linear combination of marginal and interaction contrasts that are shrunk according to evidence for main factor and interaction effects, respectively. An advantage of using such models is that a difference between subgroups defined by two levels of one factor is adjusted for any imbalance between treatment arms in other factors as well as for unwanted random variation due to multiplicity. Time permitting, we also consider Bayesian hierarchical models to extrapolate from adult to pediatric use of a medical product while adjusting for differences in covariate distributions between the two subpopulations. Bayesian hierarchical models rely on the assumption that subgroups are related by exchangeability, that is, any ordering of the subgroup-specific treatment effects is equally plausible. Application of this assumption should be done with care, as it can be conservative or anti-conservative, depending on study objectives.