Semiparametric Inference for Covariate-Adaptive Randomization without Ad-hoc Discretization

Covariate-adaptive randomization has been frequently employed in clinical trials and other studies to ensure that important prognostic factors are balanced across treatment and control groups. However, most model-based studies on inference for covariate-adaptive randomization assume a correctly specified model and require discretization of the continuous covariates as a preliminary step; inference with a more flexible model for covariate-adaptive randomization directly applied to continuous covariates remains understudied. In this paper, we propose a covariate-adaptive randomization with an increasing dimension of the feature map under a partially linear model without discretization on the covariates, some or all of which are used for treatment balancing. We propose a framework to obtain valid and powerful inference for covariate-adaptive randomization when the true model is partially linear under three different working models: (i) a location-shift model that leads to the two-sample t-test, (ii) a linear model, and (iii) a partially linear model. Specifically, we obtain an explicit variance adjustment for each working model to perform asymptotically sharp inference. Through numerical studies, we show that the proposed approach often improves performance over the existing approaches for covariate-adaptive randomization based on discretization.