Analysis of Covariance in Parallel-Group Clinical Trials with Pretreatment Baselines

Abstract

Analysis of covariance (ANCOVA) techniques are often employed in the analysis of clinical trials to try to account for the effects of varying pretreatment baseline values of an outcome variable on posttreatment measurements of the same variable. Baseline measurements of outcome variables are typically random variables, which violates the usual ANCOVA assumption that covariate values are fixed. Therefore, the usual ANCOVA hypothesis tests of treatment effects may be invalid, and the ANCOVA slope parameter estimator biased, for this application. We show, however, that if the pretreatment - posttreatment measurements have a bivariate normal distribution, then (i) the ANCOVA model with residual error independent of the covariate is a valid expression of the relationship between pretreatment and posttreatment measurements; (ii) the usual (fixed-covariate analysis) ANCOVA estimates of the slope parameter and treatment effect contrasts are unbiased; and (iii) the usual ANCOVA treatment effect contrast t-tests are valid significance tests for treatment effects. Moreover, as long as the magnitudes of the treatment effects do not depend on the "true" pretreatment value of the outcome variable, the true slope parameter must lie in the interval (0, 1) and the ANCOVA model has a clear interpretation as an adjustment (based on between- and within-subject variability) to an analysis of variance model applied to the posttreatment-pretreatment differences.