This dissertation, "Bayesian Adaptive Methods for Phase I Clinical Trials" by Ruitao, Lin, 林瑞涛, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The primary objective of phase I dose-finding trials is to determine the maximum tolerated dose (MTD), which is typically defined as the dose with the dose-limiting toxicity probability closest to the target toxicity probability. The American Society of Clinical Oncology (ASCO) recently published an update of the ASCO policy statement to call for new phase I trial designs to allow for more efficient escalation to the therapeutic dose levels in order to cope with the changing landscape in cancer research. In this thesis, innovative and robust designs for single- or multiple-agent phase I dose-finding trials are studied. To enhance robustness and efficiency, two nonparametric methods are proposed to locate the MTD in single-agent phase I clinical trials without imposing any parametric assumption on the underlying distribution of the toxicity curve. First, a uniformly most powerful Bayesian interval (UMPBI) design is developed for dose finding, where the optimal interval is determined by the rejection region of the uniformly most powerful Bayesian test. UMPBI is easy to implement and can be nicely interpreted. Compared with existing interval designs, the proposed UMPBI design exhibits a unique feature of convergence to the MTD. Next, a nonparametric overdose control (NOC) method is proposed by casting dose finding in a Bayesian model selection framework. Each dose assignment under NOC is determined such that the posterior probability of overdosing is controlled. In addition, NOC is incorporated with a fractional imputation method to deal with late-onset toxicity outcomes. Both of the UMPBI and NOC designs are flexible, as well as possessing sound theoretical support and desirable numerical performance. In the era of precision medicine, combination therapy is playing an increasingly important role in drug development. However, drug combinations often lead to a high-dimensional dose searching space compared to conventional single-agent dose finding, especially when three or more drugs are combined for treatment. Most of the current dose-finding designs aim to quantify the toxicity probability space using certain prespecified yet complicated models. Not only do these models characterize each individual drug's toxicity profile, but they also need to quantify their interaction effects, which often leads to multi-parameter models. In order to stabilize the current practice of dose finding in drug-combination trials with limited sample sizes, a random walk Bayesian optimal interval (RW-BOIN) design and a Bootstrap aggregating continual reassessment method (Bagging CRM) are proposed. RW-BOIN is built on the basis of the single-agent BOIN design, and it can be utilized to tackle high-dimensional dose-finding problems. A convergence theorem is established to ensure the validity of RW-BOIN. On the other hand, Bagging CRM implements a dimension reduction technique and some ensemble methods in machine learning, so that the toxicity probability space can be stably reduced to a one-dimensional searching line. Simulation studies show that both RW-BOIN and Bagging CRM have comparative and robust operating characteristics compared with existing approaches under various dose-toxicity scenarios. All of the proposed methods are exemplified with real phase I dose-finding trials. Subjects: Bayesian statistical decision theory Clinical trials - Statistical methods