Unified Implementation and Comparison of Bayesian Shrinkage Methods for Treatment Effect Estimation in Subgroups

Evaluating treatment effect heterogeneity across patient subgroups is a fundamental aspect of clinical trial analysis. Yet, these analyses have inherent limitations due to small sample sizes and the substantial number of subgroups investigated. There is also a tendency to focus on extreme estimates, which may reflect random variation rather than true effects, potentially leading to spurious clinical conclusions. In recent years, statisticians in regulatory agencies and pharmaceutical companies have begun considering shrinkage methods grounded in Bayesian statistical theory. These methods incorporate priors on treatment effect heterogeneity, which operationally shrink raw subgroup treatment effect estimates towards the overall treatment effect. Various shrinkage estimators and priors have been proposed, yet it remains unclear which methods perform best. This work provides a unified presentation and software implementation for continuous, binary, count, and time-to-event endpoints in the R package bonsaiforest2. It also provides simulation comparisons of one-way and global shrinkage methods for two distinct simulation set-ups. One-way models fit a separate shrinkage model for each subgrouping variable, whereas global models fit a model including all subgroup indicators at once. Both can derive standardized subgroup-specific treatment effects. Across all simulation scenarios, shrinkage methods outperformed the standard subgroup estimator without shrinkage 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 associated credible intervals. For both models, hyperprior choices anchored in trial assumptions about the anticipated size of the overall treatment effect performed well. We conclude that some degree of shrinkage is preferable to none and advocate for the routine inclusion of shrunken estimates in clinical forest plots to facilitate more robust decision-making.