Infectious Dose of Listeria monocytogenes in Outbreak Linked to Ice Cream, United States, 2015

Listeriosis can occur in susceptible populations when products with low-level contamination are distributed widely.

where Xp is the number of cases and mp is the number of persons in the subpopulation p and the distribution of the dose only has to be known. Moreover, because r is usually very small for L. monocytogenes, 1 − (1 − ) ≈ . Under this limit, the equation simplifies to where ̅ is the mean number dose ingested in the population. From (Eq. 3), r can be then evaluated as where ̂ is the estimated number of L. monocytogenes ingested by the population.
To better characterize variability in L. monocytogenes dose-response, Pouillot et al. (5) used a log-normal distribution to describe ri, rather than a constant, that is log 10 ( )~normal( , ), with negligible probability that r >1. During an outbreak, σp characterize only the within subpopulation variability in susceptibility because strain virulence variability can be neglected (5,6). Following assumptions used in Pouillot et al. (5) and Food and Drug Administration/Food Safety and Inspection Service (6), we considered a high variability in susceptibility within the overall population (90% of the individual variability in r may be contained within a range of 2.9 log10, leading to σ = 0.82 log10), a medium variability in susceptibility within the pregnant women population and the older adult populations (90% of the individual variability in r may be contained within a range of 1.8 log10, leading to σ = 0.55 log10), and a low variability in susceptibility in the highly susceptible population (90% of the individual variability in r may be contained within a range of 0.8 log10, leading to σ = 0.24 log10). With an assumption of a log-normal distribution of ri, (Eq. 1) cannot be simplified and the equation should be integrated numerically over the distribution of ri and di. Integrations were performed using R software (7).

Derivation of the Contamination Level Distributions
Briefly, 2,320 samples of ice cream product 1 (80 g each), 295 samples of product 2 (70 g), and 96 samples of product 3 (160 g) were microbiologically tested. L. monocytogenes cells were enumerated in these products by using the most probable number (MPN) method from dilution assay results. Microbiological methods and summary statistics are described in Chen et al, (8) and Burall et al (unpub. data).
Product 1 samples were collected from 7 lots. All tested products from the 5 first lots were contaminated (2,020 positive samples of 2,020 tested). After the first reports of contaminated products, the production line was reportedly cleaned and overhauled in factory 1 on January 30, 2015 (9). Ninety-six percent (287 positive samples of 300) of products tested from 2 later lots, manufactured after the cleaning, were contaminated. L. monocytogenes contamination levels were extremely homogeneous among products within boxes, boxes within lots, and across lots (8). The observed mean concentration of L. monocytogenes in product 1 before the cleaning of the line was 9 MPN/g of product.
From the experimental design (8) and from the raw results, we characterize in this study the variability in L. monocytogenes levels across lots (lot to lot; data from 5 lots), across boxes within a lot (box to box; 8-53 boxes tested per lot), and across servings within a box (serving to serving; 10-20 servings tested per box). We restricted the analysis to lots manufactured before cleaning and overhauling of the production line. To evaluate the lot-to-lot, box-to-box within lots, and serving-to-serving within box variability, a hierarchical Bayesian framework was Ninety-five samples of product 3 from 5 lots manufactured before the cleaning of the manufacturing line were tested. Forty-three (45%) were positive for L. monocytogenes. The mean L. monocytogenes contamination level for positive samples was lower, estimated to 0.12 MPN/g and the standard deviation to 0.14 MPN/g).
For product 1, from the Bayesian model, the mean of the log10 concentrations is estimated 0.70 log10 CFU/g, with an interlot variability of 0.21 log10 CFU/g, an interbox variability of 0.14 log10 CFU/g, and an intrabox variability of 0.33 log10 CFU/g (Technical Appendix Table 1). The lot-to-lot variation is not known as precisely as the other levels of variability because fewer lots than boxes or products were examined.
From these results, we simulated the production of the manufacturing line using the empirical posterior distributions from the Bayesian analysis (Technical Appendix Figure). Under the model (assuming that the 5 lots are representative of all lots), Table 1 Table 1).
The credible interval are much larger than those obtained for product 1, reflecting the wider variability and the lower number of tested samples. The mean dose for one 70-g serving of product 2 (the serving size of this product) was estimated as 310 cfu (95% credible interval [CrI] 55-11,000 CFU). Table 1 in the main text provides additional estimates for various quantiles in the distribution.
Because the number of tested samples for product 3 was low (n = 95), we did not derive a distribution for this product but considered that, as observed in the tested sample, 45% of these product 3 were contaminated and that the average concentration of L. monocytogenes in contaminated products 3 was 0.12 L. monocytogenes cells per gram.
In further estimation of the prevalence of contaminated products, 100% will be used for product 1 and product 1 like, 80% for product 2 and product 2 like, and 45% for product 3.

Estimation of the Proportion of Ice Cream Eaten by Various Subpopulations
Demographic data were estimated from data provided by the Centers for Disease Control and Prevention (10) and by the US Census Bureau (11). Per capita consumption of ice cream for pregnant women and for the overall population were estimated by using the FARE software