Robust alternatives to ANCOVA for estimating the treatment effect via a randomized comparative study

In comparing two treatments via a randomized clinical trial, the analysis of covariance (ANCOVA) technique is often utilized to estimate an overall treatment effect. The ANCOVA is generally perceived as a more efficient procedure than its simple two sample estimation counterpart. Unfortunately, when the ANCOVA model is nonlinear, the resulting estimator is generally not consistent. Recently, various nonparametric alternatives to the ANCOVA, such as the augmentation methods, have been proposed to estimate the treatment effect by adjusting the covariates. However, the properties of these alternatives have not been studied in the presence of treatment allocation imbalance. In this article, we take a different approach to explore how to improve the precision of the naive two-sample estimate even when the observed distributions of baseline covariates between two groups are dissimilar. Specifically, we derive a bias-adjusted estimation procedure constructed from a conditional inference principle via relevant ancillary statistics from the observed covariates. This estimator is shown to be asymptotically equivalent to an augmentation estimator under the unconditional setting. We utilize the data from a clinical trial for evaluating a combination treatment of cardiovascular diseases to illustrate our findings.