Analyzing pre-post designs using the analysis of covariance models with and without the interaction term in a heterogeneous study population

Pre-post parallel group randomized designs have been frequently used to compare the effectiveness of competing treatment strategies and the ordinary least squares (OLS)-based analysis of covariance model (ANCOVA) is a routine analytic approach. In many scenarios, the associations between the baseline and the post-randomization scores could differ between the treatment and control arms, which justifies the inclusion of the treatment by baseline score interaction in ANCOVA. This heterogeneity may also cause heteroscedastic errors in ANCOVA. In this study, we compared the performances of the ANCOVA models with and without the interaction term in estimating the marginal treatment effect in a heterogeneous two-arm pre-post design. We explored the relationship between the two nested ANCOVA models from the perspective of an omitted variable bias problem and further revealed the reasons why the usual ANCOVA may fail in heterogeneous scenario through the discussion of the three types of variances associated with the ANCOVA estimators of the marginal treatment effect: the target unconditional variance, the conditional variance allowing unequal error variances, and the OLS conditional variance derived under the assumption of constant error variance. We demonstrated analytically and with simulations that the proposed heteroscadastic-consistent variance estimators provide valid unconditional inference for ANCOVA, and the ANCOVA interaction model is more powerful than the ANCOVA main effect model when a design is unbalanced.