Unified implementation and comparison of Bayesian shrinkage methods for treatment effect estimation in subgroups

Abstract

Evaluating treatment effect heterogeneity across patient subgroups is a fundamental aspect of clinical trial analysis. These analyses have inherent limitations due to small sample sizes and the substantial number of subgroups investigated. There is a tendency to focus on extreme estimates, which may reflect random variation rather than true effects, potentially leading to spurious clinical conclusions. Statisticians in regulatory agencies and pharmaceutical companies have begun considering shrinkage methods grounded in Bayesian theory. These methods incorporate priors on treatment effect heterogeneity, which shrink subgroup estimates towards the overall treatment effect. Various shrinkage estimators have been proposed, yet it remains unclear which perform best. This work provides a unified presentation and software implementation of shrinkage methods. It also provides simulation comparisons of one-way and global shrinkage methods for two simulation set-ups. One-way models fit a separate shrinkage model for each subgrouping variable while global models include all subgroup indicators. Both can derive standardized subgroup-specific treatment effects. Across all simulation scenarios, shrinkage methods outperformed the standard subgroup estimator in terms of mean squared error. They were also more efficient in identifying a non-efficacious subgroup. Global shrinkage models tended to have smaller mean squared error and less dependence on hyperprior parameters than one-way models, but also exhibited slightly larger bias and worse frequentist coverage of credible intervals. For both models, hyperprior choices anchored in trial assumptions about the anticipated overall treatment effect size performed well. We conclude that some shrinkage is preferable to none and advocate routine inclusion of shrunken estimates in clinical forest plots to facilitate robust decision-making.