Model-based optimal randomization procedure for treatment-covariate interaction tests

Linear models are extensively used in the analysis of clinical trials. However, required model assumptions (e.g. homoscedasticity) may not be satisfied in practice, resulting in low power of treatment-covariate interaction tests. Various interaction tests have been proposed to improve the efficiency of detecting differences in treatment-covariate interactions. Aiming to fundamentally improve the power of treatment-covariate interaction tests, for heteroscedasticity of treatment responses, we develop a model-based optimal randomization procedure, referred to as model-based Neyman allocation (MNA) in this article. The derived limiting allocation proportion indicates that the procedure MNA is a generalization of response-adaptive randomization targeting Neyman allocation (RAR-NA). In theory, we demonstrate that the procedure MNA can maximize the power of treatment-covariate interaction tests. The issue of sample size estimation is also addressed. Simulation studies show, in the framework of the heteroscedastic linear model, compared with Pocock and Simon's minimization method and RAR-NA, the procedure MNA has the greatest power of tests for both systematic effects and treatment-covariate interactions, even under model misspecification. Finally, the efficiency of the procedure MNA is illustrated by a hypothetical case study based on a real schizophrenia clinical trial.