Abstract: There is an urgent need to evaluate new therapies in a time-sensitive and cost-effective manner. We propose the adaptive seamless phase II/III clinical trials with covariate adaptive randomization (CAR) to satisfy this need. CAR is one of the most popular designs in randomized controlled trials, enhancing covariance balance and ensuring valid treatment comparisons. However, it has several challenges: (1) the type I error rate of the commonly used Student's t-test following CAR can be inflated because of the seamless trials, but can also be decreased using CAR; (2) the complicated allocation mechanism induced by CAR causes extra difficulties to derive the asymptotic properties of a test procedure; and (3) previous theoretical studies of seamless trials rely mainly on the assumption of complete randomization, a procedure rarely used in real trials. We establish a theoretical foundation for adaptive seamless phase II/III trials with CAR. We also propose an approach that is easy to implement in order to control the type I error rate and improve the power when using Student's t-test. This important step will promote the application of this procedure.

Key words and phrases: Adaptive design, type I error, power.