Adaptive Designs Utilizing Covariates for Precision Medicine and Their Statistical Inference Open Access
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Precision medicine takes account of individual characteristics for disease treatment and prevention. To develop precision medicine, more covariates of patients are under consideration in clinical trials. Based on different roles played in clinical studies, covariates can be categorized into two types: (1) prognostic covariates, which are used to balance treatment allocations for a simple treatment comparison, and (2) predictive covariates, which are used to select a suitable treatment based on efficiency and ethics. In the literature, covariate-adaptive designs have been proposed to deal with prognostic covariates, while covariate-adjusted response-adaptive designs utilize information of predictive covariates. Theoretical properties of statistical inference under these two procedures are provided based on linear models in Chapter 2 and Chapter 3. We show that, when the covariate, which is used in the randomization procedure, is excluded from the working model of inference, the hypothesis testing to compare treatment effects under CARA designs is not always valid, depending on the unknown parameters in the employed model and the choice of the allocation function. While, under covariate-adaptive designs, the hypothesis testing is usually conservative when prognostic covariates, which are balanced in randomization, are omitted in statistical inference. In Chapter 4, we propose a general framework of new CARA designs, which can incorporate both prognostic and predictive covariates in the randomization procedure simultaneously. Similar problems of hypothesis testing are studied under new designs when prognostic covariates are excluded from the final analysis. Some mild conditions for imbalances and target allocation proportions need to be satisfied to derive asymptotic properties of test statistics. It is proved that the test for comparing treatment effects is usually conservative under new designs. One possible solution to this problem is the bootstrap method. New CARA designs have advantages leading to improvement on average outcomes, but still allowing high power. Continuous covariates are often used in clinical trials. In Chapter 5, the discrete assumption for prognostic covariates is relaxed and similar inference problems are studied under the CAR design and the new CARA design. Asymptotic distributions of test statistics are obtained under both the null and alternative hypotheses. We show that the tests for comparing treatment effects are conservative under both designs when prognostic covariates are omitted for statistical inference regardless of whether they are discrete or continuous.
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