On the use of G-computation in small randomized controlled trials with many covariates

Abstract: In contemporary randomized controlled trials (RCTs), the number of patients is often small relative to the number of baseline covariates collected. In such settings, maximum likelihood estimators of conditional treatment effects in generalized linear models, along with their standard errors, may exhibit substantial bias. This study examines whether similar bias arises in G-computation estimators of marginal treatment effects, which are known for their robustness to model misspecification when applied with canonical GLMs. We develop theoretical insights, drawing on recent literature on G-computation under proportional asymptotic regimes, in which the number of covariates grows with the sample size. Specifically, we characterize the bias of the standard G-computation estimator and the leave-one-out G-computation estimator under such high-dimensional settings. Monte Carlo simulations using linear and logistic outcome models are conducted to evaluate practical remedies for G-computation estimators, including covariate selection, cross-fitting, leave-one-out cross-fitting, and small sample corrections to standard errors. Further insights are derived from a re-analysis of the BestAIR trial data. Our findings provide guidance for the application of G-computation in modern RCTs, particularly when addressing challenges posed by limited sample size. \textbf{Keywords:} Covariate adjustment, covariate selection, high-dimensional, proportional asymptotics, targeted learning, cross-fitting.