Investigating the Source of a Disease Outbreak Based on Risk Estimation: A Simulation Study Comparing Risk Estimates Obtained From Logistic and Poisson Regression Applied to a Dichotomous Outcome

Background: In epidemiologic investigations of disease outbreaks, multivariable regression techniques with adjustment for confounding can be applied to assess the association between exposure and outcome. Traditionally, logistic regression has been used in analyses of case-control studies to determine the odds ratio (OR) as the effect measure. For rare outcomes (incidence of 5% to 10%), an adjusted OR can be used to approximate the risk ratio (RR). However, concern has been raised about using logistic regression to estimate RR because how closely the calculated OR approximates the RR depends largely on the outcome rate. The literature shows that when the incidence of outcomes exceeds 10%, ORs greatly overestimate RRs. Consequently, in addition to logistic regression, other regression methods to accurately estimate adjusted RRs have been explored. One method of interest is Poisson regression with robust standard errors. This generalized linear model estimates RR directly vs logistic regression that determines OR. The purpose of this study was to empirically compare risk estimates obtained from logistic regression and Poisson regression with robust standard errors in terms of effect size and determination of the most likely source in the analysis of a series of simulated single-source disease outbreak scenarios. Methods: We created a prototype dataset to simulate a foodborne outbreak following a public event with 14 food exposures and a 52.0% overall attack rate. Regression methods, including binary logistic regression and Poisson regression with robust standard errors, were applied to analyze the dataset. To further examine how these two models led to different conclusions of the potential outbreak source, a series of 5 additional scenarios with decreasing attack rates were simulated and analyzed using both regression models. Results: For each of the explanatory variables—sex, age, and food types—in both univariable and multivariable models, the ORs obtained from logistic regression were estimated further from 1.0 than their corresponding RRs estimated by Poisson regression with robust standard errors. In the simulated scenarios, the Poisson regression models demonstrated greater consistency in the identification of one food type as the most likely outbreak source. Conclusion: Poisson regression with robust standard errors proved to be a decisive and consistent method to estimate risk associated with a single source in an outbreak when the cohort data collection design was used.