In comparing two treatments via a randomized clinical trial, the analysis of covari- ance 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 estima- tion counterpart. Unfortunately when the ANCOVA model is not correctly specified, the resulting estimator is generally not consistent especially when the model is nonlin- ear. Recently various nonparametric alternatives, such as the augmentation methods, to ANCOVA 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 paper, 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 condi- tional inference principle via relevant ancillary statistics from the observed covariates. This estimator is shown to be asymptotically equivalent to an augmentation estimator under the conditional setting. We utilize the data from a clinical trial for evaluating a combination treatment of cardiovascular diseases to illustrate our findings.



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