Evaluating the performance of copula models in phase I-II clinical trials under model misspecification

Kristen Cunanan, Joseph S. Koopmeiners

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21 Scopus citations


Background: Traditionally, phase I oncology trials are designed to determine the maximum tolerated dose (MTD), defined as the highest dose with an acceptable probability of dose limiting toxicities(DLT), of a new treatment via a dose escalation study. An alternate approach is to jointly model toxicity and efficacy and allow dose escalation to depend on a pre-specified efficacy/toxicity tradeoff in a phase I-II design. Several phase I-II trial designs have been discussed in the literature; while these model-based designs are attractive in their performance, they are potentially vulnerable to model misspecification. Methods. Phase I-II designs often rely on copula models to specify the joint distribution of toxicity and efficacy, which include an additional correlation parameter that can be difficult to estimate. We compare and contrast three models for the joint probability of toxicity and efficacy, including two copula models that have been proposed for use in phase I-II clinical trials and a simple model that assumes the two outcomes are independent. We evaluate the performance of the various models through simulation both when the models are correct and under model misspecification. Results: Both models exhibited similar performance, as measured by the probability of correctly identifying the optimal dose and the number of subjects treated at the optimal dose, regardless of whether the data were generated from the correct or incorrect copula, even when there is substantial correlation between the two outcomes. Similar results were observed for a simple model that assumes independence, even in the presence of strong correlation. Further simulation results indicate that estimating the correlation parameter in copula models is difficult with the sample sizes used in Phase I-II clinical trials. Conclusions: Our simulation results indicate that the operating characteristics of phase I-II clinical trials are robust to misspecification of the copula model but that a simple model that assumes independence performs just as well due to difficulty in estimating the copula model correlation parameters from binary data.

Original languageEnglish (US)
Article number51
JournalBMC Medical Research Methodology
Issue number1
StatePublished - Apr 14 2014

Bibliographical note

Funding Information:
This research was partially supported by a research grant from Medtronic, Inc. and a grant-in-aid of research, artistry and scholarship from the University of Minnesota. The authors would also like to thank the Associate Editor and two Referees for their helpful comments, which improved the manuscript.


  • Bayesian Adaptive Design
  • Copula models
  • Phase I-II


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