Risk ratios for contagious outcomes

TL;DR

This paper investigates how the commonly used risk ratio can be misleading in contagious outcomes, often implying effects opposite to the true individual-level hazard ratio, especially in clustered infectious disease studies.

Contribution

It provides a structural definition of infectious transmission, analyzes the bias of risk ratios, and explains the conditions under which they misrepresent true effects.

Findings

Risk ratios can be greater than one even when the covariate reduces susceptibility and transmissibility.

The bias is related to confounding and Simpson's paradox in infectious disease contexts.

Analytical and simulation results demonstrate when risk ratios are misleading.

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.