Bayesian dose-finding designs for combination of molecularly targeted agents assuming partial stochastic ordering

Abstract

Molecularly targeted agent (MTA) combination therapy is in the early stages of development. When using a fixed dose of one agent in combinations of MTAs, toxicity and efficacy do not necessarily increase with an increasing dose of the other agent. Thus, in dose-finding trials for combinations of MTAs, interest may lie in identifying the optimal biological dose combinations (OBDCs), defined as the lowest dose combinations (in a certain sense) that are safe and have the highest efficacy level meeting a prespecified target. The limited existing designs for these trials use parametric dose-efficacy and dose-toxicity models. Motivated by a phase I/II clinical trial of a combination of two MTAs in patients with pancreatic, endometrial, or colorectal cancer, we propose Bayesian dose-finding designs to identify the OBDCs without parametric model assumptions. The proposed approach is based only on partial stochastic ordering assumptions for the effects of the combined MTAs and uses isotonic regression to estimate partially stochastically ordered marginal posterior distributions of the efficacy and toxicity probabilities. We demonstrate that our proposed method appropriately accounts for the partial ordering constraints, including potential plateaus on the dose-response surfaces, and is computationally efficient. We develop a dose-combination-finding algorithm to identify the OBDCs. We use simulations to compare the proposed designs with an alternative design based on Bayesian isotonic regression transformation and a design based on parametric change-point dose-toxicity and dose-efficacy models and demonstrate desirable operating characteristics of the proposed designs.

Keywords: Bayesian isotonic regression transformation; dose-efficacy surface; dose-toxicity surface; matrix ordering; plateau; post processing.

Figure 1

An illustration of dose combinations.

Figure 2

The top three panels are posterior densities of the efficacy probability when two out of three and one out of three responses are observed at combinations (1,1) and (1,2), respectively. The bottom three panels are the corresponding posterior densities when one out of three and two out of three responses are observed at combinations (1,1) and (1,2), respectively. The solid and dotted curves are the density curves at combinations (1,1) and (1,2), respectively. The vertical lines indicate the posterior means, with black representing unconstrained and blue and red representing constrained posterior means, and the solid and dotted lines correspond to combinations (1,1) and (1,2), respectively. The blue solid and red dotted lines overlap on the top right panel; the black and blue solid lines overlap and the black and red dotted lines overlap on the bottom right panel. BIT, Bayesian isotonic regression transformation; PSO II, partial stochastic ordering using sample sizes as weights.