Interaction in the Effects

Abstract

Genetic interactions have been increasingly appreciated as an essential component in the development and progression of complex diseases. Detection of interaction can reveal functional relationships between genes and pathways. It is generally agreed to regard factors as interacting when one modifies directly or indirectly the effect of the other, or when their joint effect is surprisingly unexpected when compared with their individual effects. A quantitative definition of interaction has then two components: an effect measure (phenotype), and a neutrality function that predicts the effect of non-interacting factors (ex. gene mutations). Interaction is then defined as departure of the combined factor effects from the expected neutral effect. A pragmatically insufficient resolution of the concept of interaction has largely subsided, mainly because of the open arbitrariness in the definition of models for neutral effect. In genetic epidemiology for example, four distinct quantitative definition of neutral effect are in common usage (Product, Additive, Log, and Min), and the choice has shown to have profound practical consequences. In particular to determine which combinations of genetic alterations interact to produce cancer phenotypes remains a challenge, in spite of the unprecedent rate at which cancer mutations are uncovered. ? Starting from very basic principles and based on minimal elementary conditions, we derived a model of no-interaction or neutral effect uniquely determined. The model departs from previous proposals, and is generally applicable independently of mechanistic details involved in each scenario. We assess and discuss its validity on two examples of a disease process with causal mechanism assumed to be known.