Analyzing pre-post randomized studies with one post-randomization score using repeated measures and ANCOVA models.

The analysis of covariance (ANCOVA) or repeated measures (RM) models are often used to compare the treatment effect between different arms in pre-post randomized studies. ANCOVA adjusts the baseline score as a covariate in regression models. RM treats both the baseline and post-randomization scores as outcome variables. We aim to establish the underlying connections between ANCOVA and a constrained RM ("cRM"). We start with the interrelated concepts in a pre-post randomized designs: homogeneous vs. heterogeneous study populations, the marginal vs. the conditional treatment effect, and homogeneity vs. heterogeneity of treatment effect. We then demonstrate the asymptotic equivalence between the ANCOVA and cRM estimators for the marginal treatment effect and discuss the conditions under which ANCOVA needs to include a baseline score by treatment interaction term. In particular, an ANCOVA interaction model with a mean centered baseline score can assess both the marginal treatment effect and the heterogeneity in the conditional treatment effect. However, the ordinary least squares (OLS)-based inference is not valid for unconditional inference because this interaction model typically has heteroskedastic errors, and ordinary least squares treats the sample mean of the baseline score as a known parameter. We propose a bootstrap and a heteroskedasticity consistent variance estimator for heteroskedastic ANCOVA. Our simulation studies demonstrate that the proposed methods provide valid inferences for testing both the marginal treatment effect and the heterogeneity of treatment effect using an ANCOVA interaction model. We used an acupuncture headache trial to elucidate the proposed approaches.