Assessment of evidence against homogeneity in exhaustive subgroup treatment effect plots

Exhaustive subgroup treatment effect plots are constructed by displaying all subgroup treatment effects of interest against subgroup sample size, providing a useful overview of the observed treatment effect heterogeneity in a clinical trial. As in any exploratory subgroup analysis, however, the observed estimates suffer from small sample sizes and multiplicity issues. To facilitate more interpretable exploratory assessments, this paper introduces a computationally efficient method to generate homogeneity regions within exhaustive subgroup treatment effect plots. Using the Doubly Robust (DR) learner, pseudo-outcomes are used to estimate subgroup effects and derive reference distributions, quantifying how surprising observed heterogeneity is under a homogeneous effects model. Explicit formulas are derived for the homogeneity region and different methods for calculation of the critical values are compared. The method is illustrated with a cardiovascular trial and evaluated via simulation, showing well-calibrated inference and improved performance over standard approaches using simple differences of observed group means.

💡 Research Summary

This paper addresses a persistent challenge in exploratory subgroup analysis of clinical trials: how to interpret the myriad of treatment‑effect estimates that arise when every possible subgroup is displayed in an “exhaustive subgroup treatment‑effect plot”. While such plots give a comprehensive visual picture of heterogeneity, they traditionally lack any formal statistical inference, leaving investigators to rely on subjective impressions that are vulnerable to small‑sample noise and multiplicity.

The authors propose a computationally efficient framework that overlays statistically calibrated “homogeneity regions” on these plots. The key methodological innovation is the use of the doubly‑robust (DR) learner to construct individual pseudo‑outcomes (φi) for each patient. The DR learner combines an estimated propensity score π(x)=P(A=1|X=x) with outcome regression models μ0(x) and μ1(x) to produce φi = μ1(Xi)−μ0(Xi) + (Ai−π(Xi))/