2D (2 Dimensional) TEQR design for Determining the optimal Dose for safety and efficacy

Designs, such as the Eff-Tox, OBD (optimal biological dose), STEIN (simple efficacy toxicity interval), and TEPI (toxicity efficacy probability interval) designs, have been proposed to determine the optimal dose of a new oncology drug using both efficacy and toxicity. The goal of these designs is to select the optimal drug dose for further phase trials more accurately than dose finding designs that only consider toxicity, such as the 3 + 3, TEQR (toxicity equivalence range), mTPI (modified toxicity probability interval), and EWOC (escalation with overdose control) designs. We propose a new frequentist design for optimal dose selection, the 2D TEQR design, that is easier to understand and simpler to implement than the TEPI, Eff-Tox, STEIN and OBD designs, as it is based on the empirical or observed toxicity and efficacy rates and does not require specialized computations. We compare the performance of this new design with those of the TEPI, STEIN, Eff-Tox and OBD Isotonic designs. Although for the same sample size and cohort size, the frequentist 2D TEQR design is less accurate than the Bayesian TEPI design and also the STEIN design in selecting the optimal dose, the accuracy of optimal dose selection of the 2D TEQR design can be increased, in many cases, with a moderate increase in cohort size. The 2D TEQR design is as accurate as or more accurate than the Eff-Tox design in optimal dose selection, and better than the OBD Isotonic design, unless there is a clear peak in the true response rates, in which case the OBD Isotonic design performs better than the other designs.