Moving beyond the conventional stratified analysis to estimate an overall treatment efficacy with the data from a comparative randomized clinical study.

For a two-group comparative study, a stratified inference procedure is routinely used to estimate an overall group contrast to increase the precision of the simple two-sample estimator. Unfortunately, most commonly used methods including the Cochran-Mantel-Haenszel statistic for a binary outcome and the stratified Cox procedure for the event time endpoint do not serve this purpose well. In fact, these procedures may be worse than their two-sample counterparts even when the observed treatment allocations are imbalanced across strata. Various procedures beyond the conventional stratified methods have been proposed to increase the precision of estimation when the naive estimator is consistent. In this paper, we are interested in the case when the treatment allocation proportions vary markedly across strata. We study the stochastic properties of the two-sample naive estimator conditional on the ancillary statistics, the observed treatment allocation proportions and/or the stratum sizes, and present a biased-adjusted estimator. This adjusted estimator is asymptotically equivalent to the augmentation estimators proposed under the unconditional setting. Moreover, this consistent estimation procedure is also equivalent to a rather simple procedure, which estimates the mean response of each treatment group first via a stratum-size weighted average and then constructs the group contrast estimate. This simple procedure is flexible and readily applicable to any target patient population by choosing appropriate stratum weights. All the proposals are illustrated with the data from a cardiovascular clinical trial, whose treatment allocations are imbalanced.