Placebo response, an apparent improvement in the clinical condition of patients randomly assigned to the placebo treatment, is a major issue in clinical trials on psychiatric and pain disorders. Properly addressing the placebo response is critical to an accurate assessment of the efficacy of a therapeutic agent. The Sequential Parallel Comparison Design (SPCD) is one approach for addressing the placebo response. A SPCD trial runs in two stages, re-randomizing placebo patients in the second stage. Analysis pools the data from both stages. In this thesis, we propose a Bayesian approach for analyzing SPCD data. Our primary proposed model overcomes some of the limitations of existing methods and offers greater flexibility in performing the analysis. We find that our model is either on par or, under certain conditions, better, in preserving the type I error and minimizing mean square error than existing methods. We further develop our model in two ways. First, through prior specification we provide three approaches to model the relationship between the treatment effects from the two stages, as opposed to arbitrarily specifying the relationship as was done in previous studies. Under proper specification these approaches have greater statistical power than the initial analysis and give accurate estimates of this relationship. Second, we revise the model to treat the placebo response as a continuous rather than a binary characteristic. The binary classification, which groups patients into “placebo-responders” or “placebo non-responders”, can lead to misclassification, which can adversely impact the estimate of the treatment effect. As an alternative, we propose to view the placebo response in each patient as an unknown continuous characteristic. This characteristic is estimated and then used to measure the contribution (or the weight) of each patient to the treatment effect. Building upon this idea, we propose two different models which weight the contribution of placebo patients to the estimated second stage treatment effect. We show that this method is more robust against the potential misclassification of responders than previous methods. We demonstrate our methodology using data from the ADAPT-A SPCD trial.