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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.

Cancer clinical trials typically generate detailed patient toxicity data. The most common measure used to summarize patient toxicity is the maximum grade among all toxicities and it does not fully represent the toxicity burden experienced by patients. In this article, we study the mathematical and statistical properties of the toxicity index (TI), in an effort to address this deficiency. We introduce a total ordering, (T-rank), that allows us to fully rank the patients according to how frequently they exhibit toxicities, and show that TI is the only measure that preserves the T-rank among its competitors. Moreover, we propose a Poisson-Limit model for sparse toxicity data. Under this model, we develop a general two-sample test, which can be applied to any summary measure for detecting differences among two population of toxicity data. We derive the asymptotic power function of this class as well as the asymptotic relative efficiency (ARE) of the members of the class. We evaluate the ARE formula empirically and show that if the data are drawn from a random Poisson-Limit model, the TI is more efficient, with high probability, than the maximum and the average summary measures. Finally, we evaluate our method on clinical trial toxicity data and show that TI has a higher power in detecting the differences in toxicity profile among treatments. The results of this article can be applied beyond toxicity modeling, to any problem where one observes a sparse array of scores on subjects and a ranking based on extreme scores is desirable.

We present a cancer phase I clinical trial design of a combination of two drugs with the goal of estimating the maximum tolerated dose curve in the two-dimensional Cartesian plane. A parametric model is used to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re-parameterized in terms of the probabilities of toxicities at dose combinations corresponding to the minimum and maximum doses available in the trial and the interaction parameter. Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC), where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. The maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. Performance of the trial is studied by evaluating its design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD curve and under model misspecifications for the true dose-toxicity relationship. The method is further extended to accommodate discrete dose combinations and compared with previous approaches under several scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

We present a cancer phase I clinical trial design of a combination of two drugs with the goal of estimating the maximum tolerated dose curve in the two-dimensional Cartesian plane. A parametric model is used to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re-parameterized in terms of the probabilities of toxicities at dose combinations corresponding to the minimum and maximum doses available in the trial and the interaction parameter. Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC), where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. The maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. Performance of the trial is studied by evaluating its design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD curve and under model misspecifications for the true dose-toxicity relationship. The method is further extended to accommodate discrete dose combinations and compared with previous approaches under several scenarios. Copyright © 2016 John WileySons, Ltd.

We examine a large class of prior distributions to model the dose-response relationship in cancer phase I clinical trials. We parameterize the dose-toxicity model in terms of the maximum tolerated dose (MTD) gamma and the probability of dose limiting toxicity (DLT) at the initial dose rho(0). The MTD is estimated using the EWOC (escalation with overdose control) method of Babb et al. We show through simulations that a candidate joint prior for (rho0,gamma) with negative a priori correlation structure results in a safer trial than the one that assumes independent priors for these two parameters while keeping the efficiency of the estimate of the MTD essentially unchanged.