Abstract
Adjustment for prognostic baseline variables can reduce bias due to covariate imbalance and increase efficiency in randomized trials. While the use of covariate adjustment in late-phase trials is justified by favorable large-sample properties, it is seldom used in small, early-phase studies, due to uncertainty in which variables are prognostic and the potential for precision loss, type I error rate inflation, and undercoverage of confidence intervals. To address this problem, we consider adjustment for a valid negative control outcome (NCO), or an auxiliary post-randomization outcome believed to be completely unaffected by treatment but more highly correlated with the primary outcome than baseline covariates. We articulate the assumptions that permit adjustment for NCOs without producing post-randomization selection bias, and describe plausible data-generating models where NCO adjustment can improve upon adjustment for baseline covariates alone. In numerical experiments, we illustrate performance and provide practical recommendations regarding model selection and finite-sample variance corrections. We apply our methods to the reanalysis of two early-phase vaccine trials in HIV exposed uninfected (HEU) infants, where we demonstrate that adjustment for auxiliary post-baseline immunological parameters can enhance the precision of vaccine effect estimates relative to standard approaches that avoid adjustment or adjust for baseline covariates alone.