A bayesian strategy for evaluating treatments applicable only to a subset of patients

If we wish to evaluate the efficacy of a proposed treatment applicable only to a subset of the patient population, then a comparison of the results of the proposed treatment with historical experience may be misleading if the applicability of the proposed treatment is itself of prognostic value. We present a Bayesian strategy to estimate the response rate of patients eligible for the proposed treatment but who receive standard therapy; we can compare the results with the experimentally observed response rate of patients who receive the proposed therapy. I extend the approach to apply to time to event data that may be censored, such as time to disease progression. One can use the information obtained in this fashion to evaluate experimental designs for future trials of the proposed treatment.