  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.
