The traditional "3+3" sequential design provides us with a good basis in identification of maximum toxicity doses (MTD) in Phase I clinical trials. Its simplicity and reliability make the "3+3" design be attractive and popular for decades in oncology. This thesis employs the idea behind the "3+3" design and extends the discussion to accommodate more general situations in evaluating toxicities for a new experimental treatments in clinical trials when the proposed dose of interest is pre-determined. Based on the general family of "A+B" designs, a few flexible sequential designs with two different stopping rules are considered and studied in this paper. We demonstrate that some of these designs proposed here can improve the efficiency of the traditional "3+3" designs. The results and the findings may allow investigators to consider various choices of MTD and alternative toxicity rates for safety consideration more flexibly in Phase I trial.
