Mathematical Properties of Incremental Effect Additivity and Other Synergy Theories

TL;DR

This paper explores the mathematical properties of Incremental Effect Additivity, a synergy theory for multi-component mixtures, demonstrating its advantages over traditional methods and analyzing its theoretical foundations and practical implications.

Contribution

It provides a detailed mathematical analysis of Incremental Effect Additivity, highlighting its properties, advantages, and limitations compared to other synergy theories like Simple Effect Additivity.

Findings

Incremental Effect Additivity circumvents non-linearity issues in dose-effect relations.

Theorems and propositions characterize when mixture effects lie between single-agent effects.

Application demonstrated on cosmic ray mixture toxicity simulations.

Abstract

Synergy theories for multi-component agent mixtures use 1-agent dose-effect relations, assumed known from analyzing previous 1-agent experiments, to calculate baseline Neither-Synergy-Nor-Antagonism mixture dose-effect relations. The most commonly used synergy theory, Simple Effect Additivity, is not self-consistent mathematically. Many nonlinear alternatives have been suggested, almost all of which require an assumption that effects increase monotonically as dose increases. We here emphasize the recently introduced Incremental Effect Additivity synergy theory and briefly discuss Loewe Additivity. By utilizing the fact that, when dose increments approach zero, dose-effect relations approach linearity, Incremental Effect Additivity theory to some extent circumvents the non-linearity of dose-effect relations that plague Simple Effect Additivity calculations. We study mathematical properties of Incremental Effect Additivity that are relevant to practical implementation of this synergy theory and hold whatever particular area of biology, medicine, toxicology or pharmacology is involved. However, as yet Incremental Effect Additivity synergy theory has only been applied to mixture experiments simulating the toxic galactic cosmic ray mixture encountered during voyages in interplanetary space. Our main results are theorems, propositions, examples and counterexamples revealing various properties of Incremental Effect Additivity synergy theory including whether or not Neither-Synergy-Nor-Antagonism dose-effect relations lie between 1-agent dose-effect relations. These results are amply illustrated with figures.