Asynergistic Regression Based on Maximized Rank Correlation

Abstract

The property of synergy and its detection are discussed. A response surface is said to possess synergy if it is monotone in each argument and its level curves are convex. Detecting this is useful in the study of combination drug therapies, where the goal is enhanced response with diminished side effect. One way to detect synergy is to fit a surface with linear level curves under the assumption of asynergy and observe the residuals. We explore an algorithm to accomplish this asynergistic regression via a reduction in dimensionality and connections to semiparametric monotonic linear index models (Cavanagh and Sherman, 1998). We see that the asynergistic model is a generalized version of the monotonic linear index model where the linear level curves are not restricted to be parallel.

Keywords:

• Dose-response
• Drug interactions
• Monotonic index models
• Synergy

Mathematics Subject Classification:

• 62G08

Notes

¹The terms “additive, dose-additive, zero-interactive, and noninteractive” have also been used, but we believe that additivity and interaction are mathematically unrelated concepts and the language should be kept apart.