The impacts of unobserved covariates on covariate-adaptive randomized experiments

Abstract

Covariate-adaptive randomization (CAR) is commonly implemented in clinical trials to balance observed covariates. Recent studies have demonstrated the advantages of CAR procedures in balancing covariates and improving the subsequent statistical analysis. Covariate balance is crucial, but it is not a panacea for the valid statistical inferences. If the response to a treatment interacts with some unobserved covariates, the conclusion drawn from a CAR experiment may be affected, and thus, be inconsistent with other evidence. This paper aims to demonstrate the relationships between unobserved covariates and the analysis of treatment and covariate effects in CAR experiments. We first derive the asymptotic properties of the statistical methods based on a linear model framework with interactions between the treatment and an unobserved covariate. We also provide sufficient conditions for the identifiability of the treatment and covariate effects. Our results theoretically explain how inconsistent estimations are generated in CAR experiments when some important covariates are unobserved. Under these sufficient conditions, we show that the tests for the treatment and covariate effects can have reduced Type I errors under CAR procedures. A residual-based adjusted test is proposed to recover the Type I error when the effect can be correctly estimated. Numerical studies are conducted to evaluate the performance of our proposed procedure and theoretical findings.