Case-only gene-environment interaction studies: when does association imply mechanistic interaction?

Case-only studies are often used to identify interactions between a genetic factor and an environmental factor under the assumption both factors are independent in the population. However, interpreting a statistical association between the genetic and the environmental factors among the cases, as evidence of a mechanistic gene-environment interaction, is not always warranted. Using a mechanistic approach based on the sufficient cause framework, we show association amongst cases can arise between the genetic and environmental factors when there is in fact no mechanistic gene-environment interaction. However, when it can be assumed the genetic and environmental factors themselves can never prevent the outcome, we show a positive association amongst cases implies a mechanistic gene-environment interaction. Without this assumption that the effects of the two factors are never preventive, a multiplicative interaction greater than two is needed to conclude the presence of a mechanistic interaction. We furthermore show these tests for mechanistic interaction can be extended to scenarios in which the genetic and environmental factors are negatively associated in the population rather than independent.