The main goal of a Phase I cancer clinical trial is to identify the maximum tolerated dose (MTD) of a new drug having acceptable dose-limiting toxicity (DLT). Two main model-based designs are continual reassessment method (CRM) (O'Quigley et al., 1990) and escalation with overdose control (EWOC) (Babb et al., 1998). Most of the designs are based on the binary toxic outcome. The occurrence of DLT is assessed over a predefined time window, and complete follow-up of the current patient is required

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... to fit the model. Information is lost by categorizing time to DLT to a binary variable and might lead to a poor estimate of MTD. Trials might have to suspend accrual to obtain complete data and lead to long trial durations and complicate administrative burdens. Some methods have been proposed to incorporate the time-to-DLT using a weight function, such as TITE-CRM by Cheung and Chappell (2000) and TITE-EWOC by Mauguen et al. (2011). A better approach would be to model the time-to-DLT data directly for patients who will experience the DLT and to separate these patients from those who will never experience the DLT given a specific dose. This approach can be based on the well-studied cure model, a type of mixture model. This mixture model seems to be more appropriate for dose finding in Phase I cancer studies when time-to-DLT is incorporated. In this thesis, we will develop a Bayesian design framework based ii on cure model approach to incorporate the time-to-DLT and will extend the current model-based designs such as CRM, EWOC or the hybrid design (Chu et al., 2009) to incorporate the time-to-DLT event. We will call such design as CATE design for Cure rate model Approach for Time-to-DLT Event. To evaluate performance of CATE designs, extensive simulation studies had been conducted, and the results shows that CATE designs outperform the existing designs for phase I cancer clinical trials. iii