A robust two-stage design identifying the optimal biological dose for phase I/II clinical trials

Yong Zang, J. Jack Lee

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We propose a robust two-stage design to identify the optimal biological dose for phase I/II clinical trials evaluating both toxicity and efficacy outcomes. In the first stage of dose finding, we use the Bayesian model averaging continual reassessment method to monitor the toxicity outcomes and adopt an isotonic regression method based on the efficacy outcomes to guide dose escalation. When the first stage ends, we use the Dirichlet-multinomial distribution to jointly model the toxicity and efficacy outcomes and pick the candidate doses based on a three-dimensional volume ratio. The selected candidate doses are then seamlessly advanced to the second stage for dose validation. Both toxicity and efficacy outcomes are continuously monitored so that any overly toxic and/or less efficacious dose can be dropped from the study as the trial continues. When the phase I/II trial ends, we select the optimal biological dose as the dose obtaining the minimal value of the volume ratio within the candidate set. An advantage of the proposed design is that it does not impose a monotonically increasing assumption on the shape of the dose–efficacy curve. We conduct extensive simulation studies to examine the operating characteristics of the proposed design. The simulation results show that the proposed design has desirable operating characteristics across different shapes of the underlying true dose–toxicity and dose–efficacy curves. The software to implement the proposed design is available upon request.

Original languageEnglish (US)
Pages (from-to)27-42
Number of pages16
JournalStatistics in Medicine
Issue number1
StatePublished - Jan 15 2017


  • Bayesian adaptive design
  • dose-finding
  • isotonic regression
  • optimal biological dose
  • phase I/II design

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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