# Optimal Benchmark for Evaluating Drug-Combination Dose-Finding Clinical Trials

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## Abstract

Numerous dose-finding methods have been proposed for drug-combination trials. A head-to-head comparison of the performance of these designs is difficult and often not very meaningful because different designs use different models and decision rules that often require judicious calibration to obtain good small-sample performance. It is desirable to have a general benchmark that can be used to evaluate the absolute performance of combination dose-finding designs. In this article, we propose an optimal nonparametric benchmark for evaluating drug-combination dose-finding methods, which provides an upper bound of accuracy beyond which further improvements are generally not achievable without making parametric assumptions of the dose-toxicity relationship. Our method is based on a new concept called critical information, which provides an upper bound on the information that we could possibly learn from patients while explicitly accounting for the partial order of the dose combinations, a fundamental feature of drug-combination trials. Our numerical study shows that the proposed benchmark provides a sharp upper bound that is useful for evaluating the performance of combination dose-finding designs.

## Keywords

Combination trials Dose finding Partial order Optimal benchmark Upper limit## Supplementary material

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