Dose--schedule finding in phase I/II clinical trials using a Bayesian isotonic transformation

Abstract

A dose-schedule-finding trial is a new type of oncology trial in which investigators aim to find a combination of dose and treatment schedule that has a large probability of efficacy yet a relatively small probability of toxicity. We demonstrate that a major difference between traditional dose-finding and dose-schedule-finding trials is that while the toxicity probabilities follow a simple nondecreasing order in dose-finding trials, those of dose-schedule-finding trials may adhere to a matrix order. We show that the success of a dose-schedule-finding method requires careful statistical modeling and a sensible dose-schedule allocation scheme. We propose a Bayesian hierarchical model that jointly models the unordered probabilities of toxicity and efficacy and apply a Bayesian isotonic transformation to the posterior samples of the toxicity probabilities, so that the transformed posterior samples adhere to the matrix-order constraints. On the basis of the joint posterior distribution of the order-constrained toxicity probabilities and the unordered efficacy probabilities, we develop a dose-schedule-finding algorithm that sequentially allocates patients to the best dose-schedule combination under certain criteria. We illustrate our methodology through its application to a clinical trial in leukemia and compare it with two alternative approaches.

Figure 1

Scenarios in the simulation study for the leukemia trial: —— schedule 1; . . . . . . schedule 2. There are five doses (horizontal axis) in each schedule. The vertical axis is the joint probability of efficacy without toxicity. Points marked by black triangles correspond to the target dose-schedule combinations, at which the probability of toxicity does not exceed 0.3 and the probability of efficacy is at least 0.3.

Figure 2

Summary operating characteristics based on the simulations: —— two-dimensional BIT design . . . . . . one-dimensional BIT design – – – CRM+AR design. The top two plots are the selection percentages of the target dose-schedule combinations and the numbers of patients treated (averaged across 1000 simulated trials) at these combinations. The bottom two plots are the overall observed toxicity and response rates, calculated by dividing the total numbers of patients who experienced toxicity and efficacy, respectively, by the total numbers of patients treated in the 1000 simulated trials.