Bayesian nonparametric inference on the dose level with specified response rate

The richness of nonparametric Bayesian models has attracted many different applications. Its application in dose-finding studies has been hindered due to lack of methodologies on the nonparametric Bayesian inference on percentiles. The primary interest in dose-finding studies focuses inference on the unknown toxicity or efficacy dose level corresponding to a prespecified rate. This paper shows how this problem may generally be handled by deriving inference on percentiles of a distribution following a Dirichlet process prior. In particular, theoretical results are derived to obtain the nonparametric Bayesian inference of the unknown dose level. This is followed by a description of the numerical implementation of that theory. The method also allows efficient estimation of the entire potency curve. Finally, the usefulness of the approach is demonstrated via an experimental data example.