Clinical trials with a hybrid control arm, a control arm constructed from a combination of randomized patients and real-world data on patients receiving usual care in standard clinical practice, have the potential to decrease the cost of randomized trials. However, due to stringent trial inclusion criteria and differences in care quality between trials and community practice, randomized control patients will likely have superior outcomes compared to their real-world counterparts. We propose a new method for analyses of trials with a hybrid control arm that efficiently controls bias and type I error. Under our proposed approach, each real-world subject is weighted by a function of the propensity score reflecting their similarity to the randomized controls while randomized subjects receive full weight. This weighting allows for real-world patients that more closely resemble randomized controls to have a larger contribution to the likelihood while dissimilar subjects are discounted. Estimates of the treatment effect are obtained via Bayesian inference. We compare our approach to existing approaches via simulations and apply these methods to a study using EHR data.