Semiparametric Efficient Estimation of Treatment Effect in a Pretest-Posttest Study with Missing Data

Inference on treatment effect in a pretest–posttest study is a routine objective in medicine, public health, and other fields, and a number of approaches have been advocated. Typically, subjects are randomized to two treatments, the response is measured at baseline and a prespecified follow–up time, and interest focuses on the effect of treatment on follow—up mean response. Covariate information at baseline and in the intervening period until follow—up may also be collected. Missing posttest response for some subjects is routine, and disregarding these missing cases can lead to biased and inefficient inference. Despite the widespread popularity of this design, a consensus on an appropriate method of analysis when no data are missing, let alone on an accepted practice for taking account of missing follow—up response, does not exist. We take a semiparametric perspective, making no assumptions about the distributions of baseline and posttest responses. Exploiting the work of Robins et al. (1994), we characterize the class of all consistent estimators for treatment effect, identify the efficient member of this class, and propose practical procedures for implementation. The result is a unified framework for handling pretest—posttest inferences when follow—up response may be missing at random that allows the analyst to incorporate baseline and intervening information so as to improve efficiency of inference. Simulation studies and application to data from an HIV clinical trial illustrate the utility of the approach.