Abstract
Covariate-adaptive designs are often implemented to balance important covariates in clinical trials. However, the theoretical properties of conventional statistical methods are usually unknown under covariate-adaptive randomized clinical trials. In literature, most studies are based on simulations. In this dissertation, we provide theoretical foundation of statistical inference under covariate-adaptive designs based on linear models and generalized linear models.
In Chapter 2, we derive asymptotic distributions of the test statistics of testing both treatment effects and significance of covariates under null and alternative hypotheses in the linear model framework. Under a large class of covariate-adaptive designs, we find that: (i) the hypothesis testing to compare treatment effects is usually conservative in terms of small Type I error; (ii) the hypothesis testing to compare treatment effects is usually more powerful than complete randomization; and (iii) the hypothesis testing for significance of covariates is still valid. The class includes most of the covariate-adaptive designs in literature, for example, Pocock and Simon's marginal procedure (Pocock and Simon, 1975), stratified permuted block design, etc. Numerical studies are also conducted to assess their corresponding finite sample properties.
In Chapter 3, theoretical properties of hypothesis testing under linear models are studied based on more general assumptions. In particular, the assumption used in Chapter 2 that all covariates are independent of each other is relaxed in this chapter by taking into consideration of the correlation between covariates. Under such general assumptions, we prove that the hypothesis testing to compare treatment effects is still conservative, while the estimators of covariate coefficients are biased under covariate-adaptive designs.
Covariate-adaptive designs are often used in clinical trials where outcome is not continuous. In these scenarios, generalize linear models can be used to perform statistical inference. For example, logistic regression is used when outcome is a binary variable. In Chapter 4, we concentrate on hypothesis testing for treatment effects based on logistic regression under covariate-adaptive designs. We propose a framework to derive theoretical properties of test statistic for stratified covariate-adaptive designs and conclude that the Type I error is also conservative. Numerical studies are also carried out to study power for several tests.
