Bayesian models for subgroup analysis in clinical trials

Abstract

Background: In a pharmaceutical drug development setting, possible interactions between the treatment and particular baseline clinical or demographic factors are often of interest. However, the subgroup analysis required to investigate such associations remains controversial. Concerns with classical hypothesis testing approaches to the problem include low power, multiple testing, and the possibility of data dredging.

Purpose: As an alternative to hypothesis testing, the use of shrinkage estimation techniques is investigated in the context of an exploratory post hoc subgroup analysis. A range of models that have been suggested in the literature are reviewed. Building on this, we explore a general modeling strategy, considering various options for shrinkage of effect estimates. This is applied to a case-study, in which evidence was available from seven-phase II-III clinical trials examining a novel therapy, and also to two artificial datasets with the same structure.

Methods: Emphasis is placed on hierarchical modeling techniques, adopted within a Bayesian framework using freely available software. A range of possible subgroup model structures are applied, each incorporating shrinkage estimation techniques.

Results: The investigation of the case-study showed little evidence of subgroup effects. Because inferences appeared to be consistent across a range of well-supported models, and model diagnostic checks showed no obvious problems, it seemed this conclusion was robust. It is reassuring that the structured shrinkage techniques appeared to work well in a situation where deeper inspection of the data suggested little evidence of subgroup effects.

Limitations: The post hoc examination of subgroups should be seen as an exploratory analysis, used to help make better informed decisions regarding potential future studies examining specific subgroups. To a certain extent, the degree of understanding provided by such assessments will be limited by the quality and quantity of available data.

Conclusions: In light of recent interest by health authorities into the use of subgroup analysis in the context of drug development, it appears that Bayesian approaches involving shrinkage techniques could play an important role in this area. Hopefully, the developments outlined here provide useful methodology for tackling such a problem, in-turn leading to better informed decisions regarding subgroups.