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.

Accuracy and Safety of Novel Designs for Phase I Drug-Combination Oncology Trials*

Despite numerous innovative designs having been published for phase I drug-combination dose finding trials, their use in real applications is rather limited. As a working group under the American Statistical Association Biopharmaceutical Section, our goal is to identify the unique challenges associated with drug combination, share industry's experiences with combination trials, and investigate the pros and cons of the existing designs. Toward this goal, we review seven existing designs and distinguish them based on the criterion of whether their primary objectives are to find a single maximum tolerated dose (MTD) or the MTD contour (i.e., multiple MTDs). Numerical studies, based on either industry-specified fixed scenarios or randomly generated scenarios, are performed to assess their relative accuracy, safety, and ease of implementation. We show that the algorithm-based 3+3 design has poor performance and often fails to find the MTD. The performance of model-based combination trial designs is mixed: some demonstrate high accuracy of finding the MTD but poor safety, while others are safe but with compromised identification accuracy. In comparison, the model-assisted designs, such as BOIN and waterfall designs, have competitive and balanced performance in the accuracy of MTD identification and patient safety, and are also simple to implement, thus offering an attractive approach to designing phase I drug-combination trials. By taking into consideration the design's operating characteristics, ease of implementation and regulation, the need for advanced infrastructures, as well as the risk of regulatory acceptance, our paper offers practical guidance on the selection of a suitable dose-finding approach for designing future combination trials.

A nonparametric Bayesian method for dose finding in drug combinations cancer trials

We propose an adaptive design for early-phase drug-combination cancer trials with the goal of estimating the maximum tolerated dose (MTD). A nonparametric Bayesian model, using beta priors truncated to the set of partially ordered dose combinations, is used to describe the probability of dose limiting toxicity (DLT). Dose allocation between successive cohorts of patients is estimated using a modified continual reassessment scheme. The updated probabilities of DLT are calculated with a Gibbs sampler that employs a weighting mechanism to calibrate the influence of data vs the prior. At the end of the trial, we recommend one or more dose combinations as the MTD based on our proposed algorithm. We apply our method to a Phase I clinical trial of CB-839 and Gemcitabine that motivated this nonparametric design. The design operating characteristics indicate that our method is comparable with existing methods.

Dynamic ordering design for dose finding in drug-combination trials

Drug-combination studies have become increasingly popular in oncology. One of the critical concerns in phase I drug-combination trials is the uncertainty in toxicity evaluation. Most of the existing phase I designs aim to identify the maximum tolerated dose (MTD) by reducing the two-dimensional searching space to one dimension via a prespecified model or splitting the two-dimensional space into multiple one-dimensional subspaces based on the partially known toxicity order. Nevertheless, both strategies often lead to complicated trials which may either be sensitive to model assumptions or induce longer trial durations due to subtrial split. We develop two versions of dynamic ordering design (DOD) for dose finding in drug-combination trials, where the dose-finding problem is cast in the Bayesian model selection framework. The toxicity order of dose combinations is continuously updated via a two-dimensional pool-adjacent-violators algorithm, and then the dose assignment for each incoming cohort is selected based on the optimal model under the dynamic toxicity order. We conduct extensive simulation studies to evaluate the performance of DOD in comparison with four other commonly used designs under various scenarios. Simulation results show that the two versions of DOD possess competitive performances in terms of correct MTD selection as well as safety, and we apply both versions of DOD to two real oncology trials for illustration.