Design and Inference of clinical Trials with Continuous Covariates

Covariate-adaptive designs are widely used to balance covariates and maintain randomization in clinical trials. Restricted randomization procedures for discrete covariates and their asymptotic properties have been addressed in the literature. However, clinical trials can often contain continuous covariates. Simply discretizing or categorizing continuous covariates can result in lose of information. The state-of-the-art adaptive design with continuous covariates is still entirely based on simulation and to-date lacks a rigorous theoretical understanding. Therefore, conventional hypothesis testing for clinical trials using continuous covariates is still not well understood. In this dissertation, we establish a theoretical framework for hypothesis testing on clinical trials with continuous covariates randomized using adaptive designs. We test for treatment effects and significance of covariates under null and alternative hypotheses. To verify our framework, numerical simulations are conducted under a class of covariate-adaptive designs including, the p-value based method, the Su’s percentile method, the empirical cumulative-distribution method, the Kullback-Leibler divergence method, and the kernel-density method. For independent covariates we find that: (1) hypothesis testing that compares treatment effects has small Type I error, (2) hypothesis testing using adaptive designs outperforms complete randomization method in terms of power, and (3) testing for significance of covariates is still valid. For correlated covariates we prove and verify in simulations that treatment effects still have small Type I error, and estimators of continuous covariate coefficients are biased under covariate-adaptive designs. Furthermore, we adapt a minimization procedure to the kernel-density method for covariate-adaptive design, and show that our method out-performs other adaptive designs in balancing the distributions of continuous covariates across treatment groups in clinical trials.