Extensions of the mTPI and TEQR designs to include non-monotone efficacy in addition to toxicity for optimal dose determination for early phase immunotherapy oncology trials.

With the emergence of immunotherapy and other novel therapies, the traditional assumption that the efficacy of the study drug increases monotonically with dose levels is not always true. Therefore, dose-finding methods evaluating only toxicity data may not be adequate. In this paper, we have first compared the Modified Toxicity Probability Interval (mTPI) and Toxicity Equivalence Range (TEQR) dose-finding oncology designs for safety with identical stopping rules; we have then extended both designs to include efficacy in addition to safety - we determine the optimal dose for safety and efficacy using these designs by applying isotonic regression to the observed toxicity and efficacy rates, once the early phase trial is completed. We consider multiple types of underlying dose response curves, i.e., monotonically increasing, plateau, or umbrella-shaped. We conduct simulation studies to investigate the operating characteristics of the two proposed designs and compare them to existing designs. We found that the extended mTPI design selects the optimal dose for safety and efficacy more accurately than the other designs for most of the scenarios considered.