Mixed Models for Repeated Measures Should Include Time-by-Covariate Interactions to Assure Power Gains and Robustness Against Dropout Bias Relative to Complete-Case ANCOVA

In randomized trials with continuous-valued outcomes, the goal is often to estimate the difference in average outcomes between two treatment groups. However, the outcome in some trials is longitudinal, meaning that multiple measurements of the same outcome are taken over time for each subject. The target of inference in this case is often still the difference in averages at a given timepoint. One way to analyze these data is to ignore the measurements at intermediate timepoints and proceed with a standard covariate-adjusted analysis (e.g., ANCOVA) with the complete cases. However, it is generally thought that exploiting information from intermediate timepoints using mixed models for repeated measures (MMRM) (a) increases power and (b) more naturally "handles" missing data. Here, we prove that neither of these conclusions is entirely correct when baseline covariates are adjusted for without including time-by-covariate interactions. We back these claims up with simulations. MMRM provides benefits over complete-cases ANCOVA in many cases, but covariate-time interaction terms should always be included to guarantee the best results.