Nonparametric ANCOVA for longitudinal outcomes in a randomized clinical trial

The analysis of covariance (ANCOVA) is a commonly used method for correcting bias and improving accuracy in estimating the average treatment effect in randomized clinical trials. In this paper, we focus on using ANCOVA for longitudinal outcomes, where mixed effects regression is the standard approach. The effectiveness of ANCOVA depends on the regression model specification, including how the baseline covariates were used. Unlike traditional methods, we do not assume that the mixed effects model is correctly specified, making our approach nonparametric in nature. We investigate the optimal ANCOVA approach for longitudinal outcomes and show that appropriate covariate adjustment can greatly improve the precision of treatment effect estimates. Unfortunately, determining the optimal ANCOVA adjustment is challenging because it relies on the relationship between longitudinal outcomes and baseline covariates, which is typically unknown. We propose to use cross fitting procedure to estimate the conditional expectation of longitudinal outcomes given baseline covariates to guide the specification of ANCOVA. We provide theoretical derivations and empirical evidence from numerical studies to demonstrate the superiority of our proposed nonparametric ANCOVA method over traditional ANCOVA approaches. Our approach is robust, flexible, and can be easily implemented in practice to improve the accuracy and reliability of treatment effect estimates in clinical trials.