Conditional estimation and inference to address observed covariate imbalance in randomized clinical trials

Background: Baseline covariate imbalance (between treatment groups) is a common problem in randomized clinical trials which often raises questions about the validity of trial results. Answering these questions requires careful consideration of the statistical implications of covariate imbalance. The possibility of having covariate imbalance contributes to the marginal variance of an unadjusted treatment difference estimator, which can be reduced by making appropriate adjustments. Actual observed imbalance introduces a conditional bias into an unadjusted estimator, which may increase the conditional size of an unadjusted test. Methods: This article provides conditional estimation and inference procedures to address the conditional bias due to observed imbalance. Interestingly, it is possible to use the same adjusted treatment difference estimator to address the marginal variance issue and the conditional bias issue associated with covariate imbalance. Its marginal variance estimator tends to be conservative for conditional inference, and we propose a conditionally appropriate variance estimator. We also provide an estimator of the conditional bias in an unadjusted treatment difference estimator, together with a conditional variance estimator. Results: The proposed methodology is illustrated with real data from a stroke trial and evaluated in simulation experiments based on the same trial. The simulation results show that covariate imbalance can result in a substantial conditional bias and that the proposed methods deal with the conditional bias quite effectively. Discussion: We recommend that the proposed methodology be used routinely to address the observed covariate imbalance in randomized clinical trials.