Application of the Central Limit Theorem in microbial risk assessment: High number of servings reduces the Coefficient of Variation of food-borne burden-of-illness

Abstract

The Central Limit Theorem (CLT) is proposed as a means of understanding microbial risk in foods from a Public Health perspective. One variant of the CLT states that as the number of random variables, each with a finite mean and variance, increases (→∞), the distribution of the sum (or mean) of those variables approximates a normal distribution. On the basis of the CLT, the hypothesis introduced by this paper states that the Coefficient of Variation (CV) of the annual number of food-borne illness cases decreases as a result of a larger number of exposures (or servings) (n). Second-order Monte-Carlo analysis and classical statistics were used to support the hypothesis, based on existing risk models on Listeria monocytogenes in deli meat products focused on elderly people in the United States. Likewise, the hypothesis was tested on epidemiological data of annual incidence of salmonellosis and listeriosis in different countries (i.e. different n). Although different sources of error affected the accuracy of the results, both the Monte-Carlo analysis (in silico) and epidemiological data (in vivo), especially for salmonellosis, demonstrated that the CV of the annual number of cases decreased as n increased as stated by the CLT. Furthermore, results from this work showed that classical statistical methods can be helpful to provide reliable risk estimates based on simple and well-established statistical principles.