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Efficiency Study of Estimators for a Treatment Effect in a Pretest–Posttest Trial

Several possible methods used to evaluate treatment effects in a randomized pretest–posttest trial with two treatment groups are the two-sample t test, the paired t test, analysis of covariance I (ANCOVA I), the analysis of covariance II (ANCOVA II), and generalized estimating equations (GEE). The ANCOVA I includes treatment and baseline response as covariates in a linear model and ANCOVA II additionally includes an interaction term between the baseline response and treatment indicator as a covariate. The parameters in the ANCOVAI and ANCOVAII models are generally estimated using ordinary least squares. In this article, a semiparametric model, which makes no assumptions about the response distributions, is used. The asymptotic properties of the estimators derived from these five methods and their relative efficiencies are discussed under this semiparametric model. We show that all these methods yield consistent estimators for the treatment effect which have asymptotically normal distributions under the semiparametric model. The GEE and the ANCOVA II estimators are asymptotically equivalent and the most efficient. The estimators from other three methods are less efficient except under some special conditions which are outlined in the article.