Missing Data and Adaptive Designs in Clinical Studies

For the past decades, the use of adaptive designs in clinical research and development based on accrued data has become very popular due to its flexibility, efficiency and ethics. This dissertation addresses two practical considerations, missing data and continuous covariates, for the proper implementation of adaptive randomization designs. First, missing data are commonly encountered in clinical trials, which may produce biased parameter estimates and mislead the patient allocations to undesirable targets. Consequently, it may impair the ethical benefits and efficiency of an adaptive design. In this dissertation, we propose likelihood-based inferences to sequentially analyze missing data to ensure the target allocation proportion be consistently estimated and approached. In Chapter 2, we show that doubly-adaptive biased coin design (DBCD) is robust to missing responses if the missingness solely depends on the treatment. When the missingness of responses depends on covariates, we propose factorized likelihood to incorporate the information of covariates, and establish the strong consistency and asymptotic normality of DBCD with missing data. In Chapter 3, we define a new allocation function for covariate-adjusted response-adaptive (CARA) design with missing covariates. We propose using EM by the method of weights to iteratively obtain the maximum likelihood parameter estimates of the allocation function in the presence of missing covariates and responses. With the new allocation function, we establish the strong consistency and asymptotic normality of CARA design. Furthermore, we derive the asymptotic results of CARA allocation proportion for any given observed covariate vector. Thebalanceofimportantbaselinecovariatesisessentialforconvincingtreatment comparisons. In clinical studies, continuous covariates are typically discretized in order to be included in the randomization scheme. But breakdown of continuous iii covariates into subcategories often changes the nature of the covariates and makes distributional balance unattainable. In Chapter 4, we propose balancing continuous covariates based on kernel density estimations, which keeps the continuity of the covariates. Numerical studies show that the proposed Kernel-Minimization can achieve distributional balance of both continuous and categorical covariates, while also keeping the group size well balanced. It is also shown that Kernel-Minimization is less predictable than stratified permuted block design and minimization.

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