With the advancement of computer-based technology, progress in computation has enabled effective real-life application of sampling methods. This has led to the adoption of Bayesian models in clinical trials. To this end, this dissertation comprises three papers that develop and apply Bayesian parametric and nonparametric models for the planning and analysis of clinical trials. The first paper focuses on developing a statistical clustering method that clusters subjects across multiple groups through Bayesian nonparametric modeling. This method, named the Plaid Atoms Model (PAM), is built on the concept of “atom-skipping", which allows the model to stochastically assign zero weights to atoms in an infinite mixture. By implementing atom-skipping across different groups, PAM establishes a dependent clustering pattern, identifying both common and unique clusters among these groups. This approach furtherprovides interpretable posterior inference such as the posterior probability of cluster being unique to a single group or common across a subset of groups. The paper also discusses the theoretical properties of the proposed and related models. Minor extensions of the model for multivariate or count data are presented. Simulation studies and applications using real-world datasets illustrate the performance of the new models with comparison to existing models. The second paper delves into leveraging information from external data to augment the control arm of a current randomized clinical trial (RCT), aiming to borrow information while addressing potential heterogeneity in subpopulations between the external data and the current trial. To achieve this, we employ the PAM model introduced in the first paper. This method is used to identify overlapping and unique subpopulations across datasets, enabling us to limit information borrowing to those subpopulations common to both the external data and the current trial. This strategy establishes a Hybrid Control (HC) that results in a more precise estimation of treatment effects. Through simulation studies, we validate the robustness of the proposed method. Additionally, its application to an Atopic Dermatitis dataset shows the method’s improved treatment effect estimation. The third paper introduces a Bayesian Estimator of Sample Size (BESS) method and its application in oncology dose optimization clinical trials. BESS seeks a balance among three factors: Sample size, Evidence from observed data, and Confidence in posterior inference. It uses a simple logic of "given the evidence from data, with a specific sample size one is guaranteed to achieve a degree of confidence in the posterior inference." This approach contrasts with traditional sample size estimation (SSE), which typically relies on frequentist inference: BESS assumes a possible outcome from the observed data rather than utilizing the true parameters values in SSE method’s sample size calculation. As a result, BESS does not calibration sample size based on type I or II error rates but on posterior probabilities, offering a more interpretable statement for investigators. The proposed method can easily accommodates sample size re-estimation and the incorporation of prior information. We demonstrate its performance through case studies via oncology optimization trials. However, BESS can be applied in general hypothesis tests which we discuss at the end.