A comparison of microbial dose–response models fitted to human data

A Generalized QMRA Beta-Poisson Dose-Response Model

Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, K_min , is not fixed, but a random variable following a geometric distribution with parameter 0<r*≤1. The single-hit beta-Poisson model, PI(d|α,β), is a special case of the generalized model with K_min = 1 (which implies r*=1). The generalized beta-Poisson model is based on a conceptual model with greater detail in the dose-response mechanism. Since a maximum likelihood solution is not easily available, a likelihood-free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median r* estimates produced fall short of meeting the required condition of r* = 1 for single-hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single-hit assumption for characterizing the dose-response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three-parameter generalized model provides a possibility to investigate the mechanism of a dose-response process in greater detail than is possible under a single-hit model.

Heterogeneity: a major factor influencing microbial exposure and risk assessment

Microbial risk assessment is dependent on several biological and environmental factors that affect both the exposure characteristics to the biological agents and the mechanisms of pathogenicity involved in the pathogen-host relationship. Many exposure assessment studies still focus on the location parameters of the probability distribution representing the concentration of the pathogens and/or toxin. However, the mean or median by themselves are insufficient to evaluate the adverse effects that are associated with a given level of exposure. Therefore, the effects on the risk of disease of a number of factors, including the shape parameters characterizing the distribution patterns of the pathogen in their environment, were investigated. The statistical models, which were developed to provide a better understanding of the factors influencing the risk, highlight the role of heterogeneity and its consequences on the commonly used risk assessment paradigm. Indeed, the heterogeneity characterizing the spatial and temporal distribution of the pathogen and/or the toxin contained in the water or food consumed is shown to be a major factor that may influence the magnitude of the risk dramatically. In general, the risk diminishes with higher levels of heterogeneity. This scheme is totally inverted in the presence of a threshold in the dose-response relationship, since heterogeneity will then have a tremendous impact, namely, by magnifying the risk when the mean concentration of pathogens is below the threshold. Moreover, the approach of this article may be useful for risk ranking analysis, regarding different exposure conditions, and may also lead to improved water and food quality guidelines.

Selection of process conditions by risk assessment for apple juice pasteurization by UV-heat treatments at moderate temperatures

The effect of bactericidal UV-C treatments (254 nm) on Escherichia coli O157:H7 suspended in apple juice increased synergistically with temperature up to a threshold value. The optimum UV-C treatment temperature was 55 °C, yielding a 58.9% synergistic lethal effect. Under these treatment conditions, the UV-heat (UV-H55 °C) lethal variability achieving 5-log reductions had a logistic distribution (α = 37.92, β = 1.10). Using this distribution, UV-H55 °C doses to achieve the required juice safety goal with 95, 99, and 99.9% confidence were 41.17, 42.97, and 46.00 J/ml, respectively, i.e., doses higher than the 37.58 J/ml estimated by a deterministic procedure. The public health impact of these results is that the larger UV-H55 °C dose required for achieving 5-log reductions with 95, 99, and 99.9% confidence would reduce the probability of hemolytic uremic syndrome in children by 76.3, 88.6, and 96.9%, respectively. This study illustrates the importance of including the effect of data variability when selecting operational parameters for novel and conventional preservation processes to achieve high food safety standards with the desired confidence level.

Model uncertainty and model averaging in the estimation of infectious doses for microbial pathogens

Food-borne infection is caused by intake of foods or beverages contaminated with microbial pathogens. Dose-response modeling is used to estimate exposure levels of pathogens associated with specific risks of infection or illness. When a single dose-response model is used and confidence limits on infectious doses are calculated, only data uncertainty is captured. We propose a method to estimate the lower confidence limit on an infectious dose by including model uncertainty and separating it from data uncertainty. The infectious dose is estimated by a weighted average of effective dose estimates from a set of dose-response models via a Kullback information criterion. The confidence interval for the infectious dose is constructed by the delta method, where data uncertainty is addressed by a bootstrap method. To evaluate the actual coverage probabilities of the lower confidence limit, a Monte Carlo simulation study is conducted under sublinear, linear, and superlinear dose-response shapes that can be commonly found in real data sets. Our model-averaging method achieves coverage close to nominal in almost all cases, thus providing a useful and efficient tool for accurate calculation of lower confidence limits on infectious doses.

An expert panel report of a proposed scientific model demonstrating the effectiveness of antibacterial handwash products

In 2005, a US Food and Drug Administration Nonprescription Drug Advisory Committee (NDAC) review of consumer antiseptic handwash product studies concluded that the data regarding existing products failed to demonstrate any association between specific log reductions of bacteria achieved by antiseptic handwashing and reduction of infection. The NDAC recommended that consumer antibacterial handwashing products should demonstrate a reduction in infection compared with non-antibacterial handwash products. In response to the NDAC review, a consumer product industry-sponsored expert panel meeting was held in October 2007 to review new methods for assessing the efficacy of antibacterial handwashes. The expert panel reviewed a newly proposed model for linking the effectiveness of antibacterial handwashing to infection reduction and made recommendations for conducting future studies designed to demonstrate the efficacy of antibacterial handwash formulations. The panel concluded that using the surrogate infection model to demonstrate efficacy has a sound scientific basis, that the use of Shigella flexneri as a test organism coupled with a modified hand contamination procedure is supported by published data, and that the model represents a realistic test for the efficacy of consumer antibacterial handwash products. This article summarizes the expert panel's deliberations, conclusions, and recommendations.

Benchmark dose analysis for Bacillus anthracis inhalation exposures in the nonhuman primate

There is considerable variability in the published lethality values for inhalation exposures of Bacillus anthracis. The lack of consensus on an acceptable dose-response relationship poses a significant challenge in the development of risk-based management approaches for use following a terrorist release of B. anthracis spores. This article reviewed available B. anthracis dose-response modeling and literature for the nonhuman primate, evaluated the use of the U.S. Environmental Protection Agency's Benchmark Dose Software (BMDS) to fit mathematical dose-response models to these data, and reported results of the benchmark dose analysis of suitable data sets. The BMDS was found to be a useful tool to evaluate dose-response relationships in microbial data, including that from B. anthracis exposure. An evaluation of the sources of variability identified in the published lethality data and the corresponding BMDS-derived lethality values found that varying levels of physical characterization of the spore product, differing receptor-specific exposure assumptions, choice of dose metrics, and the selected statistical methods all contributed to differences in lethality estimates. Recognition of these contributors to variability could ultimately facilitate agreement on a B. anthracis dose-response relationship through provision of a common description of necessary study considerations for acceptable dose-response data sets.

Dose-response models for inhalation of Bacillus anthracis spores: interspecies comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD(50) increases with aerosol size for aerosols at and above 4.5 mum. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD(50) when aerosol size is increased from 1 mum to 12 mum. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.

Determination of quantitative food consumption levels for use in microbial risk assessments: cheddar cheese as an example

Microbial risk assessment (MRA) is becoming increasingly used in the management of food safety because it can be used to quantify risks and help rank intervention strategies. The exposure assessment components of the assessments have become complex with many aspects of the contamination, survival, and growth of a pathogen in a food being taken into consideration. Insufficient consumption data constitutes an important data gap and consequently one of many sources of uncertainty in MRA even though the effects of uncertainty are smaller than those affecting bacterial concentration in foods. Therefore, food consumption data also play an important role in exposure assessment of MRA. In the United States, there are large-scale, nationwide sets of consumption data available for use in MRA, i.e., the National Health and Nutrition Examination Survey (NHANES). Newly released dietary interview data in the NHANES 2001 to 2002 survey show that it has been redesigned and that the data were sufficiently updated from previous versions to have more value for MRAs. We propose a model that can effectively use the new data sets and be incorporated into MRAs, using as an example consumption of Cheddar cheese/American-type cheese. This model included the prevalence of food eaten as well as the amount and frequency. We determined the amount of Cheddar/American cheese consumed per day with probability distribution (e.g., lognormal distribution). These could be further determined by gender, age, pregnancy, and combination food type, which we plan to do in the future. The frequency of the range of serving numbers for Cheddar/American cheese consumed per person per day and prevalence as the proportion of a population (e.g., survey respondents) eating a certain food in a day are also presented. Unlike traditional published mean values, the results of this model provide probability distribution intakes that can be compared with mean and median intakes. This allows values in the upper percentiles to be considered for inclusion in MRAs. We believe this simulation model can be adapted with different variables applicable to different foods, pathogens, and specific health risk population groups.

Model averaging using the Kullback information criterion in estimating effective doses for microbial infection and illness

Since the National Food Safety Initiative of 1997, risk assessment has been an important issue in food safety areas. Microbial risk assessment is a systematic process for describing and quantifying a potential to cause adverse health effects associated with exposure to microorganisms. Various dose-response models for estimating microbial risks have been investigated. We have considered four two-parameter models and four three-parameter models in order to evaluate variability among the models for microbial risk assessment using infectivity and illness data from studies with human volunteers exposed to a variety of microbial pathogens. Model variability is measured in terms of estimated ED01s and ED10s, with the view that these effective dose levels correspond to the lower and upper limits of the 1% to 10% risk range generally recommended for establishing benchmark doses in risk assessment. Parameters of the statistical models are estimated using the maximum likelihood method. In this article a weighted average of effective dose estimates from eight two- and three-parameter dose-response models, with weights determined by the Kullback information criterion, is proposed to address model uncertainties in microbial risk assessment. The proposed procedures for incorporating model uncertainties and making inferences are illustrated with human infection/illness dose-response data sets.