On the Importance of Covariate-by-Time Interactions in Longitudinal Linear Models

Linear regression models for repeated measures have been widely used in clinical trials to compare treatment effects on continuous outcome measures. These models often include baseline covariates to improve precision and adjust for potential confounding. However, a common misapplication arises when baseline variables are included in the model without incorporating interaction terms between each covariate and time. This modeling strategy implicitly assumes that the covariates have constant effects over time but, crucially, it fails to adjust the treatment-by-time interaction, which is typically the primary parameter of interest. As a result, the inclusion of baseline covariates in this way does not truly adjust the estimated treatment effect over time. To properly account for baseline differences in repeated measures models, interaction terms between each covariate and time should be taken into account and carefully treated. This approach ensures that baseline covariates can differentially influence the outcome at different time points, and thus appropriately adjust the estimated treatment effect. To demonstrate the practical implications of this issue, we analyzed real data from two randomized controlled trials (RCTs) and showed that including covariates without time interaction terms led to no change in the estimated treatment effect, whereas proper inclusion of interaction terms yielded different conclusions.