|
Abstract:
|
Covariate-adaptive randomization (CAR) has been widely used to balance the observed and unobserved covariates in clinical trials and other comparative studies. Several recent works, using a response model involving only the observed covariates, have built up the theoretical foundation for the statistical inference of CAR experiments. If the response is also related to some important unobserved covariate, whether these results are still valid is a question of great importance. In this article, we study the effect of unobserved covariates in the statistical inference of the treatment effect under complete randomization (CR), stratified permuted block (STR-PB), and CAR procedures such as Pocock and Simon's method, and Hu and Hu's method. First, we show that the estimate of treatment effect can be biased in general and describe the conditions under which the treatment effect is unbiased. Second, we derive the asymptotic distribution of the treatment effect and obtain valid statistical inference. The findings in this paper not only enrich our understanding of the effect of unobserved covariates in statistical inference under randomized experiments but also provide a new way to study the effect of unobserved covariates for many different problems.
|
