In clinical trials, the responses of patients usually depend on the assigned treatment as well as some important covariates, which may cause heteroscedasticity in treatment responses. As clinical trials are generally designed to demonstrate efficacy for the overall population, they are usually not adequately powered for detecting interactions. To improve the power of interaction tests, this article develops two model-based adaptive randomization procedures for heteroscedasticity of treatment responses, and derives their limiting allocation proportions, which are generalizations of the Neyman allocation. Issues of hypothesis testing and sample size estimation are also addressed. Simulation studies show that compared with complete randomization, the two model-based randomization procedures have greater power to detect differences in systematic effects, main treatment effects and treatment-covariate interactions. In addition, the validity of limiting allocation proportion is also verified through simulations.
Keywords: Heteroscedasticity; generalized variance; limiting allocation proportion; power; systematic effects.