Testing for subgroup treatment effect consistency in the Cox model

2026-08-03

AI Summary

This study addresses the limitation of conventional interaction tests in assessing whether treatment effect differences across subgroups are clinically negligible, which hinders reliable extrapolation of overall efficacy to specific subpopulations. Within the Cox proportional hazards framework, the authors reformulate subgroup treatment effect consistency as an equivalence testing problem, developing methods based on (weighted) treatment–subgroup interaction coefficients to evaluate consistency both between complementary subgroups and between each subgroup and the overall population. They propose a novel normal-parameter optimal equivalence test that maintains asymptotic validity while substantially improving statistical power. Simulation studies demonstrate superior performance over traditional two-one-sided-tests (TOST), and the method is successfully applied to real data from the CANTOS cardiovascular outcomes trial.

Abstract

An overall treatment effect in a clinical trial may inadequately represent particular patient subgroups, creating uncertainty about whether a population-level efficacy conclusion can legitimately be transferred to them. Conventional interaction tests only investigate whether subgroup-specific treatment effects are exactly equal or not, but cannot detect whether the differences are small enough to be clinically negligible. We develop a formal framework for assessing subgroup treatment effect consistency for time-to-event outcomes within the Cox proportional hazards model. Consistency is formulated as an equivalence problem based on the (weighted) treatment-by-subgroup interaction coefficient. We consider detecting consistency between two complementary subgroups and consistency of subgroup-specific treatment effects with the overall treatment effect. For each setting, we develop a conventional two one-sided tests procedure (TOST) and a new test motivated by optimal equivalence testing for normally distributed parameters. We prove the asymptotic validity of all procedures and show empirically that the new tests are more powerful than their TOST counterparts. Finally, we apply the new methodology to a case study motivated by the CANTOS cardiovascular outcomes trial.

Problem

• subgroup consistency
• treatment effect
• Cox model
• equivalence testing
• clinical trial

Innovation

• subgroup consistency
• equivalence testing
• Cox model
• treatment effect heterogeneity
• optimal TOST