Estimating rates of change in randomized clinical trials

This article deals with the extension of the pretest-posttest clinical trial to the longitudinal data setting. We assume that a baseline (or pretest) measurement is taken on all individuals, who are then randomized, without regard to baseline values, to a treatment group. Repeated measurements are taken postrandomization at specified times. Our objective is to estimate the average rate of change (or slope) in the experimental groups and the differences in the slopes. Our focus is on the optimal use of the baseline measurements in the analysis. We contrast two different approaches:--a multivariate one that regards the entire vector of responses (including the baseline) as random outcomes and a univariate one that uses each individual's least squares slope as an outcome. Our multivariate approach is essentially a generalization of Stanek's Seemingly Unrelated Regression (SUR) estimator for the pretest-posttest design. The multivariate approach is natural to apply in this setting, and optimal if the assumed model is correct. However, the most efficient estimator requires assuming that the baseline mean parameters are the same for all experimental groups. Although this assumption is reasonable in the randomized setting, the resulting multivariate estimator uses postrandomization data as a covariate; if the assumed linear model is not correct, this can lead to distortions in the estimated treatment effect. We propose instead a reduced form multivariate estimator that may be somewhat less efficient, but protects against model misspecification.