An expanded Fermi solution for microbial risk assessment Micha Peleg a, ⁎ , Mark D. Normand a , Joseph Horowitz b , Maria G. Corradini a a Department of Food Science, Chenoweth Laboratory, University of Massachusetts, Amherst, MA 01003, USA b Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA Received 20 January 2006; received in revised form 6 July 2006; accepted 31 July 2006 Abstract ‘Fermi solution’ refers to an estimate of a quantity of interest derived from a sequence of guesses about factors of which detailed knowledge is unavailable. When one makes such guesses, it is unlikely that the large majority of them will be either too high or too low. Most probably, some of the overestimates will be offset by some of the underestimates, and the final result will be often close to the correct value. The method has been popularized as recreational physics but it has also been applied in risk assessment, where the factors involved, but not their exact magnitudes, are known. The concept has potential application in certain types of food poisoning risk assessments, and in estimating the number victims of a bioterrorist attack on the food or water supply, where some guessing is inevitable because of the absence of accurate relevant data. We consider a version of the method in which ranges instead of single values are entered as the factors' estimates. For simplicity, the risk to be assessed is taken to be the product of the factors, and their true values are regarded as being uniformly distributed over their respective ranges. The risk itself is therefore construed as a random variable with a probability distribution whose parameters are explicitly determined by the individual factors' ranges and which can often be approximated by a lognormal distribution. The mode of this lognormal distribution is taken to be the “best guess” of the risk, and a credible interval is constructed with a specified level of “confidence”. The best guess and credible interval are shown to be robust against small perturbations of the ranges. Thus, even if the ranges are misspecified to some degree, assessments based on the best guess or credible interval will not be substantially altered. This can help to achieve consensus among assessors in situations where very little hard knowledge exists. The calculation procedure has been automated in software that has been made freely available over the Internet. The concept is demonstrated with two hypothetical problems: predicting the number of persons who would come down with acute food poisoning after consuming a contaminated dish, and estimating the number of daily salmonellosis cases in a large metropolitan area. © 2006 Elsevier B.V. All rights reserved. Keywords: Fermi solution; Food poisoning; Quantitative risk assessment (QRA); Microbial risk assessment (MRA); Bioterrorism; Epidemiology 1. Introduction Microbial risk assessment (MRA) and quantitative risk assessment (QRA) have been topics of extensive discussion in the food literature (e.g., Voysey and Brown, 2000; Brown and Stringer, 2002). They have also been the theme of numerous websites and conferences around the world. The most challenging task in quantitative MRA is the translation of knowledge about the organism's virulence and its life history into the probability of future outbreaks. Equally challenging is how to predict the severity of future food poisoning outbreaks or even that of one that has just started. The public health implications of the two kinds of situations are obvious. If both the probability and severity of a problem could be estimated with reasonable accuracy, then health authorities would be able to take measures to avoid it, or if not, at least to be prepared for its consequences. There are already some methods to estimate microbial risk even for complex situations, and programs to calculate the probability of a mishap that might be affected by as many as twenty factors. One such program has been used by Cassin et al. (1998a,b) to estimate the risk of E. coli O157:H7 in hamburgers. The calculation is based on Monte Carlo simulations using a set of distributions for each factor obtained from epidemiological and other data. The mathematical properties of the distributions that are often used are discussed by Vose (1998). Dose response curves, International Journal of Food Microbiology 113 (2007) 92 – 101 www.elsevier.com/locate/ijfoodmicro ⁎ Corresponding author. Tel.: +1 413 545 5852; fax: +1 413 545 1262. E-mail address: micha.peleg@foodsci.umass.edu (M. Peleg). 0168-1605/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijfoodmicro.2006.07.020