Statistical inference on the relative risk following covariate-adaptive randomization

Covariate-adaptive randomization (CAR) is widely adopted in clinical trials to ensure balanced treatment allocations across key baseline covariates. Although much research has focused on analyzing average treatment effects, the inference of relative risk under CAR experiments has been less thoroughly explored. In this study, we examine a covariate-adjusted estimate of relative risk and investigate the properties of its associated hypothesis tests under CAR. We first derive the theoretical properties of the covariate-adjusted relative risk for a broad class of CAR procedures. Our findings indicate that conventional tests for relative risk tend to be conservative, leading to reduced type I error rates. To mitigate this issue, we introduce model-based and model-robust methods that enhance the estimation of standard errors. We demonstrate the validity and usage of model-robust and model-based adjusted tests. Extensive numerical studies have been conducted to demonstrate our theoretical findings and the favorable properties of the proposed adjustment methods.