Flexible use of copula-type model for dose-finding in drug combination clinical trials

Identification of the maximum tolerated dose combination (MTDC) of cancer drugs is an important objective in phase I oncology trials. Numerous dose-finding designs for drug combination have been proposed over the years. Copula-type models exhibit distinctive advantages in this task over other models used in existing competitive designs. For example, their application enables the consideration of dose-limiting toxicities attributable to one of two agents. However, if a particular combination therapy demonstrates extremely synergistic toxicity, copula-type models are liable to induce biases in toxicity probability estimators due to the associated Fréchet-Hoeffding bounds. Consequently, the dose-finding performance may be worse than those of other competitive designs. The objective of this study is to improve the performance of dose-finding designs based on copula-type models while maintaining their advantageous properties. We propose an extension of the parameter space of the interaction term in copula-type models. This releases the Fréchet-Hoeffding bounds, making the estimation of toxicity probabilities more flexible. Numerical examples in various scenarios demonstrate that the performance (e.g., the percentage of correct MTDC selection) of the proposed method is better than those exhibited by existing copula-type models and comparable with those of other competitive designs, irrespective of the existence of extreme synergistic toxicity. The results obtained in this study could motivate the real-world application of the proposed method in cases requiring the utilization of the properties of copula-type models.