An adaptive multi-stage phase I dose-finding design incorporating continuous efficacy and toxicity data from multiple treatment cycles

J Biopharm Stat. 2019;29(2):271-286. doi: 10.1080/10543406.2018.1535497. Epub 2018 Nov 7.


Phase I designs traditionally use the dose-limiting toxicity (DLT), a binary endpoint from the first treatment cycle, to identify the maximum-tolerated dose (MTD) assuming a monotonically increasing relationship between dose and efficacy. In this article, we establish a general framework for a multi-stage adaptive design where we jointly model a continuous efficacy outcome and continuous/quasi-continuous toxicity endpoints from multiple treatment cycles. The normalized Total Toxicity Profile (nTTP) is used as an illustration for quasi-continuous toxicity endpoints, and we replace DLT with nTTP to take into account multiple grades and types of toxicities. In addition, the proposed design accommodates non-monotone dose-efficacy relationships, and longitudinal toxicity data in effort to capture the adverse events from multiple cycles. Stage 1 of our design uses toxicity data to perform dose-escalation and identify a set of initially allowable (safe) doses; stage 2 of our design incorporates an efficacy outcome to update the set of allowable doses for each new cohort and randomizes the new cohort of patients to the allowable doses with emphasis towards those with higher predicted efficacy. Stage 3 uses all data from all treated patients at the end of the trial to make final recommendations. Simulations showed that the design had a high probability of making the correct dose selection and good overdose control across various dose-efficacy and dose-toxicity scenarios. In addition, the proposed design allows for early termination when all doses are too toxic. To our best knowledge, the proposed dual-endpoint dose-finding design is the first such study to incorporate multiple cycles of toxicities and a continuous efficacy outcome.

Keywords: Adaptive design; bayesian method; dose-finding; joint modeling; phase I clinical trial; toxicity-efficacy dual endpoint.

MeSH terms

  • Algorithms
  • Antineoplastic Agents / administration & dosage*
  • Antineoplastic Agents / therapeutic use
  • Antineoplastic Agents / toxicity
  • Bayes Theorem
  • Clinical Trials, Phase I as Topic / methods*
  • Clinical Trials, Phase I as Topic / statistics & numerical data
  • Computer Simulation
  • Dose-Response Relationship, Drug
  • Drug-Related Side Effects and Adverse Reactions* / epidemiology
  • Drug-Related Side Effects and Adverse Reactions* / etiology
  • Humans
  • Longitudinal Studies
  • Maximum Tolerated Dose
  • Models, Statistical*
  • Research Design / statistics & numerical data*
  • Treatment Outcome*


  • Antineoplastic Agents