Bayesian hierarchical EMAX model for dose-response in early phase efficacy clinical trials

Byron J. Gajewski, Caitlyn Meinzer, Scott M. Berry, Gaylan L. Rockswold, William G. Barsan, Frederick K. Korley, Renee’ H. Martin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A primary goal of a phase II dose-ranging trial is to identify a correct dose before moving forward to a phase III confirmatory trial. A correct dose is one that is actually better than control. A popular model in phase II is an independent model that puts no structure on the dose-response relationship. Unfortunately, the independent model does not efficiently use information from related doses. One very successful alternate model improves power using a pre-specified dose-response structure. Past research indicates that EMAX models are broadly successful and therefore attractive for designing dose-response trials. However, there may be instances of slight risk of nonmonotone trends that need to be addressed when planning a clinical trial design. We propose to add hierarchical parameters to the EMAX model. The added layer allows information about the treatment effect in one dose to be “borrowed” when estimating the treatment effect in another dose. This is referred to as the hierarchical EMAX model. Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, and it has a fixed schedule for randomization. The second design is Bayesian but adaptive, and it uses response adaptive randomization. In this article, a randomized trial of patients with severe traumatic brain injury is provided as a motivating example.

Original languageEnglish (US)
Pages (from-to)3123-3138
Number of pages16
JournalStatistics in Medicine
Issue number17
StatePublished - Jul 30 2019


  • EMAX
  • dosing design, Bayesian models
  • hierarchical models
  • logistic

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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