Identifying the source of food-borne disease outbreaks: An application of Bayesian variable selection

Abstract

Early identification of contaminated food products is crucial in reducing health burdens of food-borne disease outbreaks. Analytic case-control studies are primarily used in this identification stage by comparing exposures in cases and controls using logistic regression. Standard epidemiological analysis practice is not formally defined and the combination of currently applied methods is subject to issues such as response misclassification, missing values, multiple testing problems and small sample estimation problems resulting in biased and possibly misleading results. In this paper, we develop a formal Bayesian variable selection method to account for misclassified responses and missing covariates, which are common complications in food-borne outbreak investigations. We illustrate the implementation and performance of our method on a Salmonella Thompson outbreak in the Netherlands in 2012. Our method is shown to perform better than the standard logistic regression approach with respect to earlier identification of contaminated food products. It also allows relatively easy implementation of otherwise complex methodological issues.

Keywords: Bayesian variable selection; food-borne disease outbreaks; misclassification; missing value imputation; spike and slab prior.

Figure 1.

Generalization of logistic regression as illustrated by Rousseeuw and Christmann.

Figure 2.

Spike (black curve) and slab (grey curve) prior distribution as used in the stochastic search variable selection procedure. ε indicates the threshold for practical significance.

Figure 3.

Posterior percentiles of regression coefficients and corresponding one-sided posterior inclusion probabilities, $P({\beta }_j>0.05|\text{Data})$, in the analysis of subsets of the Salmonella Thompson data mimicking the available data at different time points during the outbreak.

Figure 4.

Odds ratios plotted over time comparing three Bayesian methods with standard and Lasso logistic regression for four potential sources of the Dutch Salmonella Thompson 2012 outbreak.