Risk Analysis, Vol. 33, No. 3, 2013 DOI: 10.1111/risa.12017 Letter to the Editor Regarding “The Economic Efficiency of Sampling Size: The Case of Beef Trim” Mark R. Powell, 1 * Maarten Nauta, 2 Don Schaffner, 3 and Marcel Zwietering 4 Ferrier and Buzby (1) are to be commended for advancing efforts to integrate risk assessment and cost-benefit analysis and for presenting a frame- work for the economic design of microbiological food safety sampling. Microbiological food safety sam- pling has often been based on conventions that re- flect generally accepted practices established over 30 years ago. (2,3) Therefore, the focus of their re- search represents a welcome advance in the de- sign of effective food safety measures. However, the model developed by Ferrier and Buzby to identify the economically efficient sample size for lot accep- tance sampling of beef trim for E. coli O157:H7 suf- fers from a number of errors that render the results unreliable. The most fundamental error in Ferrier and Buzby’s model is a specification error in character- izing the prevalence of E. coli O157:H7 in portions (servings or sample units) drawn from a lot of beef trimmings (typically a 1 metric ton (MT) “combo bin”). Ferrier and Buzby treat prevalence of contam- ination as independent of portion size, applying the same probability distribution to both sample units and servings. This constitutes a fundamental error in calculating microbial prevalence, which is the proba- bility of one or more organisms occurring in a well- defined mass, volume, or surface area. The process of randomly drawing portions (e.g., containers, serv- ings, or sample units) from a larger body of material 1 U.S. Department of Agriculture, ORACBA, DC, USA. 2 Division of Food Microbiology and Risk Assessment, Technical University of Denmark, Denmark. 3 Department of Food Science, Rutgers University, NJ, USA. 4 Laboratory of Food Microbiology, WUR, Wageningen, the Netherlands. ∗ Address correspondence to Mark R. Powell, U.S. Department of Agriculture, ORACBA, 1400 Independence Ave., SW Rm 5248 SAG, Washington, DC 20250, USA; mpowell@oce.usda.gov. such as a volume of manufactured beef trim is a Pois- son process. (4) The number of organisms (x) in a por- tion can take any number of count values: x = 0, 1, 2, ... In a Poisson process, prevalence (p) = P(x = 1, 2, ...) = 1– P(x = 0). A Poisson process may be homogeneous or nonhomogeneous. (5) The Pois- son distribution, which assumes a homogeneous (stationary) mean, is a specific case arising from a Poisson process. The Poisson parameter also may be nonhomogeneous, changing over time or space, giv- ing rise to a discrete mixture distribution. The num- ber of organisms present in each portion depends on the size of the portion (in terms of mass, vol- ume, or surface area) and the microbial concentra- tion distribution in the larger body of material. (4,6,7) For example, the microbial concentration may fol- low a lognormal distribution, yielding a nonhomoge- neous Poisson-lognormal mixture distribution for the number of organisms in a portion. (4,8) Other things being equal, the larger the portion, the higher the prevalence. For example, the probability of detecting at least one organism by sampling the entire surface area of a beef carcass is greater than the probability of detecting at least one organism by sampling a 3 square inch area from the same carcass. As the sam- pling surface area increases, P(x = 0) decreases. Ferrier and Buzby model the expected damages (negative benefits (B)) from a lot of beef trim as follows: 5 B ( n| L, x,μ p ,σ 2 p ) =-r ×D×S( L |x) ×  1 0 p × (1 - p) n × g ( p|μ p ,σ 2 p ) dp, (1) where r = the proportion of contaminated beef trim lots; D = damages per contaminated 100 g serving; 5 The negative benefits equation used in the simulations by Ferrier and Buzby is their Eq. (14). 350 0272-4332/13/0100-0350$22.00/1 C  2013 Society for Risk Analysis