The design of an optimal combination therapy can be thought of as a set of tradeoffs designed to maximize the efficacy of the combination for a given toxicity budget. As anticancer agents (even targeted ones) often have overlapping toxicities, an efficient approach to making efficacy-toxicity tradeoffs is critical. In this context, a major impediment is that the search space grows exponentially with each additional drug while in vivo studies have a fixed upper size limit.

Here, we model the efficacy and toxicity landscapes of multidrug cocktails, and describe an approach to visualize and design efficient studies for three-drug combinations. We further demonstrate the application of our approach in a practical drug development context by showing its impact on actual study design, and validation with in vivo datasets. As our approach relies on equations from first principles, it is in theory extensible to an arbitrary number of drugs, subject to the practical constraints of drug dosing.

First, we demonstrate an approach to visually determine the optimal dose combination for a three-drug combination with fully overlapping toxicity. Efficacy and toxicity isoboles visualized as surfaces in three-drug space demonstrate the optimal dose combination, which corresponds to the point of tangency between the MTD and efficacy isobole surfaces.

Next, we derive an analytical method to efficiently estimate this point with a minimum of data, and without using graphical methods (important for extending the work beyond three dimensions). The combined efficacy and toxicity of a three-drug combination were modeled from first principles using isobolograms as a sum of the single-agent PK/Efficacy (PK/E) relationships and four combination terms (three binary and one ternary) to account for potential interactions between the drugs. Borrowing from Microeconomic Utility Theory, we found the point of greatest efficacy along the Maximum Tolerated Dose (MTD) toxicity contour, which corresponds to the efficacy isobole tangentially intersecting the MTD contour. Through both analytical and numerical approaches, we determined the the single- and double-agent efficacy parameters uniquely determine the dose escalation path which provides the best estimate of combination efficacy. Simulated experiments demonstrate the optimal observation path up to MTD performs acceptably compared to a uniformly-gridded exposure space.

Finally, we demonstrate the application of this approach in a proposed experimental design for three-drug combinations, and validate it with experimental data.

While developing multi-drug cocktails poses many scientific and operational challenges, the approach presented here provides a straightforward route to preclinical testing and validation through the design of parsimonious studies that can explicitly define the contribution of each individual drug (and each two drug combination) to the overall efficacy and toxicity landscape of the cocktail.

Citation Format: Christopher J. Zopf, Andrew Chen, Santhosh Palani, Rachael Brake, Mark Manfredi, Jeffrey Ecsedy, Wen Chyi Shyu, Arijit Chakravarty. Rational dose optimization for multi-drug cocktails. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 791. doi:10.1158/1538-7445.AM2014-791