Covariate adjustment in subgroup analyses of randomized clinical trials: A propensity score approach

Background: Subgroup analyses are frequently conducted in randomized clinical trials to assess evidence of heterogeneous treatment effect across patient subpopulations. Although randomization balances covariates within subgroups in expectation, chance imbalance may be amplified in small subgroups and adversely impact the precision of subgroup analyses. Covariate adjustment in overall analysis of randomized clinical trial is often conducted, via either analysis of covariance or propensity score weighting, but covariate adjustment for subgroup analysis has been rarely discussed. In this article, we develop propensity score weighting methodology for covariate adjustment to improve the precision and power of subgroup analyses in randomized clinical trials. Methods: We extend the propensity score weighting methodology to subgroup analyses by fitting a logistic regression propensity model with pre-specified covariate-subgroup interactions. We show that, by construction, overlap weighting exactly balances the covariates with interaction terms in each subgroup. Extensive simulations were performed to compare the operating characteristics of unadjusted estimator, different propensity score weighting estimators and the analysis of covariance estimator. We apply these methods to the Heart Failure: A Controlled Trial Investigating Outcomes of Exercise Training trial to evaluate the effect of exercise training on 6-min walk test in several pre-specified subgroups. Results: Standard errors of the adjusted estimators are smaller than those of the unadjusted estimator. The propensity score weighting estimator is as efficient as analysis of covariance, and is often more efficient when subgroup sample size is small (e.g. <125), and/or when outcome model is misspecified. The weighting estimators with full-interaction propensity model consistently outperform the standard main-effect propensity model. Conclusion: Propensity score weighting is a transparent and objective method to adjust chance imbalance of important covariates in subgroup analyses of randomized clinical trials. It is crucial to include the full covariate-subgroup interactions in the propensity score model.