Title: Risk ratios for contagious outcomes,
Abstract: The risk ratio is a popular tool for summarizing the relationship between a
binary covariate and outcome, even when outcomes may be dependent.
Investigations of infectious disease outcomes in cohort studies of individuals
embedded within 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 and severity of this
error is not well understood. In this study, we assess the epidemiologic
meaning of the risk ratio when outcomes are contagious. We first give a
structural definition of infectious disease transmission within clusters, based
on the canonical susceptible-infective epidemic model. From this standard
characterization, we define the individual-level ratio of instantaneous risks
(hazard ratio) as the inferential target, and evaluate the properties of the
risk ratio as an estimate of this quantity. We exhibit analytically and by
simulation the circumstances under which the risk ratio implies an effect whose
direction is opposite that of the true individual-level hazard ratio. In
particular, the risk ratio can be greater than one even when the covariate of
interest reduces both individual-level susceptibility to infection, and
transmissibility once infected. We explain these findings in the epidemiologic
language of confounding and relate the direction bias to Simpson's paradox.