Abstract B213: Toward better preclinical combination studies: Using constrained optimization techniques in combination dosage and study design.
Authors: Chen Andrew , Collins Sabrina , Mettetal Jerome , Manfredi Mark , Galvin Katherine , Shyu Wen Chyi , Ecsedy Jeffrey , Palani Santhosh , Chakravarty Arijit 
Published: August 2014

Abstract
Dose-limiting toxicities limit the potential of many oncology agents, including targeted therapies. Combination therapies provide a path forward for widening the dose-response window, particularly if efficacy combines in an additive or synergistic manner, while toxicity is subadditive or non-overlapping. Here, we model the efficacy and toxicity landscapes of two-drug combinations, and provide analytical and numerical methods to establish optimal combination study design.
Methods: The combined efficacy and toxicity of a pair of drugs were modeled from first principles using isobolograms as a sum of the single-agent PK/Efficacy (PK/E) relationships and a multiplicative combination term. 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. These analytical results were supported by graphical inspection as well as numerical estimation. We used a combination of simulated efficacy studies and analytical methods to identify the most efficient combination study designs.
Results: A combination of simple PK/E models was sufficient to describe a wide range of observed efficacy and toxicity isobolograms. The model uniquely determined the optimum combination dosage that provides maximal efficacy, and we found the single-agent conditions that can favor drug combination, namely: similar maximal efficacy (Emax) values, saturating relationships, weak sigmoidicity, and strong combination interaction effect. We analytically demonstrated that, for most scenarios, the optimal study design involves a diagonal escalation, resulting from the exploration of a fixed-dose combination with several ascending dose levels. We demonstrated via simulation that this diagonal escalation design depends only on the single-agent PK/E relationships, and not on the degree of interaction between the toxicities of the two agents. We ran an in vivo validation experiment using this diagonal escalation design, demonstrating its practical benefit in an experimental setting.
Conclusion: We demonstrate a modeling approach to combination therapy that solves for optimal dosing and study design. We found that a diagonal, constant-ratio escalation scheme was generally the most optimal for gathering combination information, and that the design depended only on the single-agent dose-response profiles. The combination information is critical for generating the efficacy and toxicity isoboles, which in turn allow us to predict the optimal combination dosage. The methods presented here can allow for the rapid and efficient translational assessment of the added benefit of a given combination in the clinical context.
Citation Information: Mol Cancer Ther 2013;12(11 Suppl):B213.
Citation Format: Andrew Chen, Sabrina Collins, Jerome Mettetal, Mark Manfredi, Katherine Galvin, Wen Chyi Shyu, Jeffrey Ecsedy, Santhosh Palani, Arijit Chakravarty. Toward better preclinical combination studies: Using constrained optimization techniques in combination dosage and study design. [abstract]. In: Proceedings of the AACR-NCI-EORTC International Conference: Molecular Targets and Cancer Therapeutics; 2013 Oct 19-23; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2013;12(11 Suppl):Abstract nr B213.