Bounds on sufficient-cause interaction

A common goal of epidemiologic research is to study how two exposures interact in causing a binary outcome. Sufficient-cause interaction is a special type of mechanistic interaction, which requires that two events (e.g. specific exposure levels from two risk factors) are necessary in order for the outcome to occur. Recently, tests have been derived to establish the presence of sufficient-cause interactions, for categorical exposures with at most three levels. In this paper we derive prevalence bounds, i.e. lower and upper bounds on the prevalence of subjects for which sufficient-cause interaction is present. The derived bounds hold for categorical exposures with arbitrary many levels. We apply the bounds to data from a study of gene-gene interaction in the development of Rheumatoid Arthritis. We provide an R-program to estimate the bounds from real data .