Traditional（frequentist）trial design may use information from previous studies only at the design stage.At the analysis stage,the data from previous studies is not part of,but considered as a complement to,the formal analysis.In contrast,the Bayesian trial design considers the prior information and the trial results as part of a continuous data stream.Inferences are being updated when the new data becomes available.These advances have resulted in an enormous increase in the popularity of Bayesian design.In this thesis,we proposed the three Bayesian adaptive designs for various early phase clinical trials.They are i)Bayesian basket trial design accounting for multiple cutoffs,ii)Bayesian adaptive design for biosimilar trials with time-to-event endpoints,and iii)Bayesian design for phase I/II cancer vaccine trials.Basket trial design enrolls patients with different cancer types but the same genetic mutation or biomarker to evaluate the treatment effect of targeted therapy.However,the explicit biomarker sometimes may not be clearly identified.In this thesis,we proposed a new Bayesian basket trial design to account for multiple cutoffs of ambiguous biomarkers and select the optimal cutoff window to maximize the benefit subpopulation.A two-stage design is proposed for the estimation.Secondly,we proposed threshold calibration and sample size determination to facilitate the design.Extensive simulations are conducted to demonstrate the operating characteristics of the two estimation methods in terms of the probability of correct selection of optimal cutoff window and probability of efficacy.We show the application of the proposed Bayesian adaptive basket trial design to explore the treatment effect of therapies with potential biomarker expression levels under three cancer types.A biosimilar drug is a biological product that is highly similar to and at the same time has no clinically meaningful difference from a licensed product in terms of safety,purity,and potency.Biosimilar study design is essential to demonstrate the equivalence between biosimilar drug and reference product.However,existing designs and assessment methods are primarily based on binary and continuous endpoints.We proposed a Bayesian adaptive design for biosimilarity trials with time-to-event endpoint.The features of the proposed design are twofold.First,we employ the calibrated power prior to precisely borrow relevant information from historical data for the reference drug.Second,we proposed a two-stage procedure using the Bayesian biosimilarity index to allow early stop and improve the efficiency.Extensive simulations are conducted to demonstrate the operating characteristics of the proposed method in contrast with some naive method.Sensitivity analysis and extension with respect to the assumptions are presented.We validate the design to a biosimilar trial for treating non-small-cell lung cancer.Therapeutic cancer vaccines are an active immunotherapy whose primary aim is to induce or enhance an adaptive antitumor immunity,such as T cells against tumor cells.The primary objective of the typical phase I designs for cytotoxic drugs are to identify the maximum tolerable dose under the assumption that the efficacy and toxicity monotonically increase with dose.As a result,typical dose finding designs are not suitable for therapeutic cancer vaccines.However,existing designs rely on the prespecified correlation between the toxicity and efficacy endpoints.We proposed a Bayesian design for cancer vaccine trial that incorporates the correlation information at each dose level.We demonstrate the proposed design by numerical study.In summary,the proposed Bayesian adaptive designs are well motivated by practical needs and shown to be more efficient than some existing designs from different perspectives.They can be further explored and extended to meet more challenges.