A case study of model‐based Bayesian dose response estimation

Abstract

A Bayesian nonlinear longitudinal Emax model for a binary endpoint was used to characterize the dose-response relationship for a new treatment of rheumatoid arthritis. The model includes prespecified parametric functions for the dependence of response on dose level and time. It was selected based on pharmacometric input about likely dose and time trends. The longitudinal model was useful for combining data collected at different doses and times from two different studies. The example illustrates the utility of more substantive parametric models to guide selection of doses outside the initial dosing range when designing an additional phase 2 study and for extrapolating shorter-term phase 2 dose response to longer-term phase 3 studies, as is often required for dosing decisions in drug development for chronic diseases. Comparison of the estimated dose response from the longitudinal model with a corresponding logistic regression model applied at a single time point also demonstrated improved precision. Specification of an informative prior distribution based on numerous sources of prior information is described. This was the most difficult step in the analysis and one that has limited the use of Bayesian methods in similar applications. Model fit was evaluated and the potential impact of some model deficiencies on the dosing decision was assessed. Analyses of the combined studies identified doses likely to achieve a targeted effect in larger and longer confirmatory trials.