Bayesian isotonic regression dose-response model

Understanding dose-response relationship is a crucial step in drug development. There are a few parametric methods to estimate dose-response curves, such as the E_max model and the logistic model. These parametric models are easy to interpret and, hence, are widely used. However, these models often require the inclusion of patients on high-dose levels; otherwise, the model parameters cannot be reliably estimated. To have robust estimation, nonparametric models are used. However, these models are not able to estimate certain important clinical parameters, such as ED₅₀ and E_max. Furthermore, in many therapeutic areas, dose-response curves can be assumed as nondecreasing functions. This creates an additional challenge for nonparametric methods. In this paper, we propose a new Bayesian isotonic regression dose-response (BIRD) which features advantages from both parametric and nonparametric models. The ED₅₀ and E_max can be derived from this model. Simulations are provided to evaluate the BIRD model performance against two parametric models. We apply this model to a dataset from a diabetes dose-finding study.