Efficiency study of estimators for a treatment effect in a pretest-posttest trial

Several possible methods, used to evaluate treatment effects in a randomize d pretest-posttest trial with two treatment groups are the two-sample t tes t, the paired t test, analysis of covariance I (ANCOVA I), the analysis of covariance II (ANCOVA W), and generalized estimating equations (GEE). The A NCOVA I includes treatment and baseline response as covariates in a linear model and ANCOVA H additionally includes an interaction term between the ba seline response and treatment indicator as a covariate. The parameters in t he ANCOVA I and ANCOVA H models are generally estimated using ordinary leas t squares. In this article, a semiparametric model, which makes no assumpti ons about the response distributions, is used. The asymptotic properties of the estimators derived from these five methods and their relative efficien cies are discussed under this semiparametric model. We show that all these methods yield consistent estimators for the treatment effect which have asy mptotically normal distributions under the semiparametric model. The GEE an d the ANCOVA H estimators are asymptotically equivalent and the most effici ent. The estimators from other three methods are less efficient except unde r some special conditions which are outlined in the article.