Supplementary material from "Risk ratios for contagious outcomes"

Investigations of transmissible diseases in clusters—households, villages or small groups—often report risk ratios. Epidemiologists have warned that risk ratios may be misleading when outcomes are contagious, but the nature of this error is poorly understood.

In this study, we assess the meaning of the risk ratio when outcomes are contagious. We provide a mathematical definition of infectious disease transmission within clusters, based on the canonical stochastic susceptible-infective model. From this characterization, we define the individual-level ratio of instantaneous infection risks as the inferential target, and evaluate the properties of the risk ratio as an approximation of this quantity.