A continuous endpoint is recorded and then dichotomized as a responder based on whether it has exceeded some predefined cutoff. Of interest is the difference in responder proportions between treatment and control groups. Deyi et al. (1998) provide an early consideration of this problem and Uryniak et al. (2011) have recently offered an updated review. In this research, we use the totality of the continuous data, avoiding dichotomization, to make inference on binary endpoints. We assume that the underlying distributions of the response variables are normally distributed and explore the impact of leveraging this assumption to directly estimate the distribution of the difference between treatment and control responder proportions. In order to develop rules that have good frequentist characteristics we seek thresholds that guarantee type I error control. The performance of this Bayesian approach is contrasted with the Wald test for dichotomized data. When the common variance assumption is made (be it known or unknown) this Bayesian approach behaves nearly identically to the standard t-test (for the underlying continuous data) and as a result improves upon Wald test for dichotomized data.

Deyi, B., Kosinski, A., Snapinn, S. Power considerations when a continuous outcome variable is dichotomized. J Biopharm Stat. 1998 May;8(2):337-52.

Uryniak, T., Chan, I., Fedorov, V., Jiang, Q., Oppenheimer, L. , Snapinn, S., Teng, C., Zhang, J. Responder Analyses—A PhRMA Position Paper, 2011 Stat in Biopharm Research, 3:3, 476-487