A Bayesian quasi-likelihood design for identifying the minimum effective dose and maximum utility dose in dose-ranging studies

Most existing dose-ranging study designs focus on assessing the dose–efficacy relationship and identifying the minimum effective dose. There is an increasing interest in optimizing the dose based on the benefit–risk tradeoff. We propose a Bayesian quasi-likelihood dose-ranging design that jointly considers safety and efficacy to simultaneously identify the minimum effective dose and the maximum utility dose to optimize the benefit–risk tradeoff. The binary toxicity endpoint is modeled using a beta-binomial model. The efficacy endpoint is modeled using the quasi-likelihood approach to accommodate various types of data (e.g. binary, ordinal or continuous) without imposing any parametric assumptions on the dose–response curve. Our design utilizes a utility function as a measure of benefit–risk tradeoff and adaptively assign patients to doses based on the doses’ likelihood of being the minimum effective dose and maximum utility dose. The design takes a group-sequential approach. At each interim, the doses that are deemed overly toxic or futile are dropped. At the end of the trial, we use posterior probability criteria to assess the strength of the dose–response relationship for establishing the proof-of-concept. If the proof-of-concept is established, we identify the minimum effective dose and maximum utility dose. Our simulation study shows that compared with some existing designs, the Bayesian quasi-likelihood dose-ranging design is robust and yields competitive performance in establishing proof-of-concept and selecting the minimum effective dose. Moreover, it includes an additional feature for further maximum utility dose selection.