Frequentist propensity score approach is a well-developed statistical methodology to control confounding bias and population heterogeneity in the observation studies. Unlike its heavy reliance on model selection and validation, the Bayesian framework naturally considers the modelling uncertainty in the propensity scores and allows incorporation of prior information accumulated from real world practice, expert opinion or previous research. Non-Medical Switching (NMS) is the switching of a patient who is stabilized on originator treatment to a regulatory approved biosimilar treatment for reasons other than efficacy and safety. To study the clinical impact on NMS, a randomized controlled trial with concurrent comparison between switchers and continuers is practically impossible. Using a simulation case study, we discuss a two-step Bayesian Propensity Score Approach with Bayesian Model Averaging (Kaplan & Chen, 2012, 2014) that can be used as a sensitivity analysis in additional to frequentist approach. Practical consideration and its application to more general real-world studies will be given.