A Benchmark for Dose Finding Studies with Unknown Ordering

Mozgunov, Pavel and Paoletti, Xavier and Jaki, Thomas (2022) A Benchmark for Dose Finding Studies with Unknown Ordering. Biostatistics, 23 (3). pp. 721-737. ISSN 1465-4644

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Abstract

An important tool to evaluate the performance of a dose finding design is the non-parametric optimal benchmark that provides an upper bound on the performance of a design under a given scenario. A fundamental assumption of the benchmark is that the investigator can arrange doses in monotonically increasing toxicity order. While the benchmark can be still applied to combination studies in which not all dose combinations can be ordered, it does not account for the uncertainty in the ordering. In this work, we propose a generalization of the benchmark that accounts for this uncertainty and, as a result, provides a sharper upper bound on the performance. The benchmark assesses how probable the occurrence of each ordering is, given the complete information about each patient. The proposed approach can also be applied to trials with an arbitrary number of endpoints with discrete or continuous distributions. We illustrate the utility of the benchmark using recently proposed dose finding designs for Phase I combination trials with a binary toxicity endpoint and Phase I/II combination trials with binary toxicity and continuous efficacy endpoints.