Abstract
In the analysis of observational studies, propensity score subclassification has been shown to be a powerful method for adjusting unbalanced covariates for the purpose of causal inferences. One practical difficulty in carrying out such an analysis is to obtain a correct variance estimate for inference, while reducing bias in the estimate of the treatment effect due to an imbalance in the measured covariates. In this paper, we propose a bootstrap procedure for the inferences concerning the average treatment effect; our bootstrap method is based on an extension of Efron's bias-corrected accelerated (BCa) bootstrap confidence interval to a two-sample problem. Unlike the currently available inference procedures based on propensity score subclassifications, the validity of the proposed method does not rely on a particular form of variance estimation. A brief simulation study is included to evaluate the operating characteristics of the proposed procedure. We conclude the paper by illustrating the new procedure through a clinical application comparing the renal effects of two non-steroidal anti-inammatory drugs (NSAIDs).
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