Date of Award


Degree Name

Doctor of Philosophy (PhD)



Second Advisor


Third Advisor



Most of the research on Response-adaptive randomization(RAR) designs has been focused on clinical trials with a single endpoint. However modern clinical trials are often complex, with multiple competing objectives and multiple endpoints. We overcome the obstacles introduced by the large number of unknown parameters and the possible correlations between the multiple endpoints. We obtained the optimal allocation proportions for the following two optimization problems: (1) maximizing the power of the test of homogeneity with a xed sample size, and (2) minimizing the expected weighted number of failures with a fixed power. Further, we implemented these optimal allocations through response-adaptive randomization procedures. Our theoretical results provided the foundation for the implementation and further investigation of the procedure, and our numerical studies demonstrated its ability to achieve diverse objectives. Covariate adaptive randomization (CAR) designs including the stratified permuted block randomization design is a standard in clinical trials. It is well accepted through numerous numerical studies that the type I error rate would be conservative if not all the randomization covariates were included in the data analysis following CAR designs. But the theoretical investigation for clinical trials using CAR designs for randomization and time-to-event outcomes for data analysis is lacking in the literature. In this paper, we proposed the test statistics, and demonstrated the e ect of CAR designs on the type I error rate and power for such trials with simulations. We also proposed approaches to control the type I error rate. Numerical studies demonstrated our showed that our proposed methods successfully protected the type I error rate in these trials. These numerical results o ered practical guidance for future clinical trials employing CAR designs and survival analysis.