Risk ratios for contagious outcomes

Abstract

<jats:p>Epidemiologists commonly use the risk ratio to summarize the relationship between a binary covariate and outcome, even when outcomes may be dependent. 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. We exhibit analytically and by simulation the circumstances under which the risk ratio implies an effect whose direction is opposite that of the true effect of the covariate. In particular, the risk ratio can be greater than one even when the covariate reduces both individual-level susceptibility to infection, and transmissibility once infected. We explain these findings in the epidemiologic language of confounding and Simpson's paradox, underscoring the pitfalls of failing to account for transmission when outcomes are contagious.</jats:p>

Heterogeneous susceptibility to rotavirus infection and gastroenteritis in two birth cohort studies: Parameter estimation and epidemiological implications

“…Variation in susceptibility among individuals within and between studies—due to these or other unmeasured risk factors—is well known to influence estimates of vaccine efficacy and effectiveness [10–13]. Differential removal of highly-susceptible individuals to a partially-immune state constitutes a form of frailty bias or effect modification that may persist even in randomized studies [10,14,15]; we use the term bias here in reference to discrepancies between common measures of association, such as hazard ratios and risk ratios, and the per-exposure biological effect of immunity (from vaccination or natural infection) on infection and/or disease endpoints [16,17]. Demonstrations of the impact of variation in susceptibility have arisen in both experimental and theoretical studies [18,19].…”

Coughs, Colds and “Freshers’ Flu” Survey in the University of Cambridge, 2007-2008

“…Assuming equal response rates between those with and without symptoms might also not be valid, as having symptoms could conceivably make someone more motivated to contribute to the survey, or less if they feel ill and perhaps did not see the survey advertised. Furthermore, risk ratios and proportional hazards models are not built for the contagious nature of infectious diseases and the possible resulting dependence between individuals [34].…”

A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure

“…vaccine studies). 20,21,85 In all cases, the hierarchical causal models presented in this manuscript ensure that the parameter of interest is defined separately from the estimation approach and reflects the underlying scientific question. This is a distinct advantage of the Targeted Learning framework over other approaches that rely on parametric regressions to define the quantity estimated and thus the scientific question answered.…”