This thesis focuses on the design, statistical operating characteristics and interpretation of early phase oncology clinical trials. Anti-cancer drugs are generally highly toxic and it is imperative to deliver a dose to the patient that is low enough to be safe but high enough to produce a clinically meaningful response. Thus, a study of dose limiting toxicities (DLTs) and a determination of the maximum tolerated dose (MTD) of a drug that can be used in later phase trials is the focus of most Phase I oncology trials. We first comprehensively compare the statistical operating characteristics of various early phase oncology designs, finding that all the designs examined select the MTD more accurately when there is a clear separation between the true DLT rate at the MTD and the rates at the dose levels immediately above and below. Among the rule-based designs studied, we found that the 3+3 design under-doses a large percentage of patients and is not accurate in selecting the MTD for all the cases considered. The 5+5 a design picks the MTD as accurately as the model based designs for the true DLT rates generated using the chosen log-logistic and linear dose-toxicity curves, but requires enrolling a larger number of patients. The model based designs examined, mTPI, TEQR, BOIN, CRM and EWOC designs, perform well on the whole, assign the maximum percentage of patients to the MTD, and pick the MTD fairly accurately. However, the limited sample size of these Phase I oncology trials makes it difficult to accurately predict the MTD. Hence, we next study the effect of sample size and cohort size on the accuracy of dose selection in early phase oncology designs, finding that an adequate sample size is crucial. We then propose some integrated Phase 1/2 oncology designs, namely the 20+20 accelerated titration design and extensions of the mTPI and TEQR designs, that consider both toxicity and efficacy in dose selection, utilizing a larger sample size. We demonstrate that these designs provide an improvement over the existing early phase designs. / 2019-12-01T00:00:00Z