Optimal designs for identifying effective doses in drug combination studies

TL;DR

This paper develops an optimal design framework for accurately identifying effective dose combinations in drug studies, improving precision over traditional methods by focusing on contour line estimation.

Contribution

It introduces a novel design criterion targeting the estimation of effective dose contours, with theoretical development and practical demonstration in nonlinear dose-response models.

Findings

Optimal design reduces confidence band width for dose contours

Proposed method outperforms ray and factorial designs

Effective in a real oncological dose combination case study

Abstract

We consider the optimal design problem for identifying effective dose combinations within drug combination studies where the effect of the combination of two drugs is investigated. Drug combination studies are becoming increasingly important as they investigate potential interaction effects rather than the individual impacts of the drugs. In this situation, identifying effective dose combinations that yield a prespecified effect is of special interest. If nonlinear surface models are used to describe the dose combination-response relationship, these effective dose combinations result in specific contour lines of the fitted response model. We propose a novel design criterion that targets the precise estimation of these effective dose combinations. In particular, an optimal design minimizes the width of the confidence band of the contour lines of interest. Optimal design theory is developed for this problem, including equivalence theorems and efficiency bounds. The performance of the optimal design is illustrated in different examples modeling dose combination data by various nonlinear surface models. It is demonstrated that the proposed optimal design for identifying effective dose combinations yields a more precise estimation of the effective dose combinations than ray or factorial designs, which are commonly used in practice. This particularly holds true for a case study motivated by data from an oncological dose combination study.