Identifying Treatment Effect Heterogeneity with Bayesian Hierarchical Adjustable Random Partition in Adaptive Enrichment Trials

TL;DR

The Bayesian Hierarchical Adjustable Random Partition (BHARP) model is proposed, a self-contained framework that applies a finite mixture model with an unknown number of components to explore the partition space accounting for model uncertainty.

Abstract

Treatment effect heterogeneity refers to the systematic variation in treatment effects across subgroups. There is an increasing need for clinical trials that aim to investigate treatment effect heterogeneity and estimate subgroup-specific responses. While several statistical methods have been proposed to address this problem, existing partitioning-based methods often depend on auxiliary analysis, overlook model uncertainty, or impose inflexible borrowing strength. We propose the Bayesian Hierarchical Adjustable Random Partition (BHARP) model, a self-contained framework that applies a finite mixture model with an unknown number of components to explore the partition space accounting for model uncertainty. The BHARP model jointly estimates subgroup-specific effects and the heterogeneity patterns, and adjusts the borrowing strengths based on within-cluster cohesion without requiring manual calibration. Posterior sampling is performed via a custom reversible-jump Markov chain Monte Carlo sampler tailored to partitioning-based information borrowing in clinical trials. Simulation studies across a range of treatment effect heterogeneity patterns show that the BHARP model achieves better accuracy and precision compared to conventional and advanced methods. We showcase the utilities of the BHARP model in the context of a multi-arm adaptive enrichment trial investigating physical activity interventions in patients with type 2 diabetes.

Figures (4)

• Figure 1: Average co-clustering probability for BHARP. Darker colors indicate stronger evidence that a pair of subgroups belongs to the same component. The true TEH structures are: Scenario A,B {1,...,10}; Scenario C--G {1,...,7}{8,9,10}; Scenario H--J {1,...,5}{6,...,10}; Scenario K {1,2,3,4}{5,6,7}{8,9,10}; Scenario L{1,...,7}{8,9}{10}. Subgroups 7,8 in Scenario G and 5,6 in Scenario J contain reduced sample sizes.
• Figure 2: Root mean squared error (RMSE) of posterior median estimates of the BHARP model comparing with the BLAST, BHM, and IND methods. Gray shading indicates true effect sizes of subgroups. Scenarios B,D,F,G,I and J include within-cluster variances. Subgroups 7,8 in Scenario G and 5,6 in Scenario J contain reduced sample sizes.
• Figure 3: Network plots of co-clustering probabilities estimated by BHARP model. Thickness and color of edges represent the average co-clustering probability between subgroup pairs.
• Figure 4: RMSE and IQR summarizing the estimation performance of BHARP, BHM, and IND models. Shaded regions indicate the underlying true effect-size levels.