Microbiota and Dose Response: Evolving Paradigm of Health Triangle

SRA Dose‐Response and Microbial Risk Analysis Specialty Groups jointly sponsored symposia that addressed the intersections between the “microbiome revolution” and dose response. Invited speakers presented on innovations and advances in gut and nasal microbiota (normal microbial communities) in the first decade after the Human Microbiome Project began. The microbiota and their metabolites are now known to influence health and disease directly and indirectly, through modulation of innate and adaptive immune systems and barrier function. Disruption of healthy microbiota is often associated with changes in abundance and diversity of core microbial species (dysbiosis), caused by stressors including antibiotics, chemotherapy, and disease. Nucleic‐acid‐based metagenomic methods demonstrated that the dysbiotic host microbiota no longer provide normal colonization resistance to pathogens, a critical component of innate immunity of the superorganism. Diverse pathogens, probiotics, and prebiotics were considered in human and animal models (in vivo and in vitro ). Discussion included approaches for design of future microbial dose–response studies to account for the presence of the indigenous microbiota that provide normal colonization resistance , and the absence of the protective microbiota in dysbiosis. As NextGen risk analysis methodology advances with the “microbiome revolution,” a proposed new framework, the Health Triangle, may replace the old paradigm based on the Disease Triangle (focused on host, pathogen, and environment) and germophobia. Collaborative experimental designs are needed for testing hypotheses about causality in dose–response relationships for pathogens present in our environments that clearly compete in complex ecosystems with thousands of bacterial species dominating the healthy superorganism.     

Estimating Listeria monocytogenes Growth in Ready-to-Eat Chicken Salad Using a Challenge Test for Quantitative Microbial Risk Assessment

Currently, there is a growing preference for convenience food products, such as ready-to-eat (RTE) foods, associated with long refrigerated shelf-lives, not requiring a heat treatment prior to consumption. Because Listeria monocytogenes is able to grow at refrigeration temperatures, inconsistent temperatures during production, distribution, and at consumer's household may allow for the pathogen to thrive, reaching unsafe limits. L. monocytogenes is the causative agent of listeriosis, a rare but severe human illness, with high fatality rates, transmitted almost exclusively by food consumption. With the aim of assessing the quantitative microbial risk of L. monocytogenes in RTE chicken salads, a challenge test was performed. Salads were inoculated with a three-strain mixture of cold-adapted L. monocytogenes and stored at 4, 12, and 16 °C for eight days. Results revealed that the salad was able to support L. monocytogenes’ growth, even at refrigeration temperatures. The Baranyi primary model was fitted to microbiological data to estimate the pathogen's growth kinetic parameters. Temperature effect on the maximum specific growth rate (μ_max) was modeled using a square-root-type model. Storage temperature significantly influenced μ_max of L. monocytogenes (p < 0.05). These predicted growth models for L. monocytogenes were subsequently used to develop a quantitative microbial risk assessment, estimating a median number of 0.00008726 listeriosis cases per year linked to the consumption of these RTE salads. Sensitivity analysis considering different time–temperature scenarios indicated a very low median risk per portion (<−7 log), even if the assessed RTE chicken salad was kept in abuse storage conditions.     

Survival of Staphylococcus aureus ATCC 13565 in Intermediate Moisture Foods is Highly Variable

Staphylococcus aureus is a gram-positive, enterotoxin-producing coccus. It is a hardy organism and known to survive over a wide range of water activities, pH values, and temperatures. The objective of this study was to model the survival or gradual inactivation of S. aureus ATCC 13565 in intermediate moisture foods (IMFs). Various initial concentrations (approximately 10(1), 10(2), 10(3), and 10(4) CFU/g) were used to inoculate three different IMFs (beefsteak, bread, and chicken pockets). Viable counts were determined up to 60 days using tryptic soy agar. Inoculum size did not influence the survival or gradual inactivation of S. aureus in these foods. The rate of change (increase or decrease) in log CFU/day was calculated for every consecutive pair of data points and by linear regression for each inactivation curve. Both consecutive pair and linear regression rates of change were fit to logistic distributions (with parameters alpha and beta) for each food. Based on the distribution parameters, survival or gradual inactivation of S. aureus was predicted by computer simulation. The simulations indicated an overall decline in S. aureus population over time, although a small fraction of samples in the consecutive pair simulation showed a slight population increase even after 60 days, consistent with the observed data. Simulation results were compared to predictions from other computer models. The models of Stewart et al., were fail-safe, predicting the possibility of significant growth only after > 3,000 days. The USDA pathogen modeling program predictions were found to be fail-dangerous, predicting declines at least four times faster than observed.     

Consumer Phase Risk Assessment for Listeria monocytogenes in Deli Meats

The foodborne disease risk associated with the pathogen Listeria monocytogenes has been the subject of recent efforts in quantitative microbial risk assessment. Building upon one of these efforts undertaken jointly by the U.S. Food and Drug Administration and the U.S. Department of Agriculture (USDA), the purpose of this work was to expand on the consumer phase of the risk assessment to focus on handling practices in the home. One-dimensional Monte Carlo simulation was used to model variability in growth and cross-contamination of L. monocytogenes during food storage and preparation of deli meats. Simulations approximated that 0.3% of the servings were contaminated with >10(4) CFU/g of L. monocytogenes at the time of consumption. The estimated mean risk associated with the consumption of deli meats for the intermediate-age population was approximately 7 deaths per 10(11) servings. Food handling in homes increased the estimated mean mortality by 10(6)-fold. Of all the home food-handling practices modeled, inadequate storage, particularly refrigeration temperatures, provided the greatest contribution to increased risk. The impact of cross-contamination in the home was considerably less. Adherence to USDA Food Safety and Inspection Service recommendations for consumer handling of ready-to-eat foods substantially reduces the risk of listeriosis.     

Modeling Microbial Growth Within Food Safety Risk Assessments

Risk estimates for food-borne infection will usually depend heavily on numbers of microorganisms present on the food at the time of consumption. As these data are seldom available directly, attention has turned to predictive microbiology as a means of inferring exposure at consumption. Codex guidelines recommend that microbiological risk assessment should explicitly consider the dynamics of microbiological growth, survival, and death in foods. This article describes predictive models and resources for modeling microbial growth in foods, and their utility and limitations in food safety risk assessment. We also aim to identify tools, data, and knowledge sources, and to provide an understanding of the microbial ecology of foods so that users can recognize model limits, avoid modeling unrealistic scenarios, and thus be able to appreciate the levels of confidence they can have in the outputs of predictive microbiology models. The microbial ecology of foods is complex. Developing reliable risk assessments involving microbial growth in foods will require the skills of both microbial ecologists and mathematical modelers. Simplifying assumptions will need to be made, but because of the potential for apparently small errors in growth rate to translate into very large errors in the estimate of risk, the validity of those assumptions should be carefully assessed. Quantitative estimates of absolute microbial risk within narrow confidence intervals do not yet appear to be possible. Nevertheless, the expression of microbial ecology knowledge in "predictive microbiology" models does allow decision support using the tools of risk assessment.     

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.     

Validation of Quantitative Microbial Risk Assessment Using Epidemiological Data from Outbreaks of Waterborne Gastrointestinal Disease

The assumptions underlying quantitative microbial risk assessment (QMRA) are simple and biologically plausible, but QMRA predictions have never been validated for many pathogens. The objective of this study was to validate QMRA predictions against epidemiological measurements from outbreaks of waterborne gastrointestinal disease. I screened 2,000 papers and identified 12 outbreaks with the necessary data: disease rates measured using epidemiological methods and pathogen concentrations measured in the source water. Eight of the 12 outbreaks were caused by Cryptosporidium, three by Giardia, and one by norovirus. Disease rates varied from 5.5 × 10^?6 to 1.1 × 10^?2 cases/person‐day, and reported pathogen concentrations varied from 1.2 × 10^?4 to 8.6 × 10² per liter. I used these concentrations with single‐hit dose–response models for all three pathogens to conduct QMRA, producing both point and interval predictions of disease rates for each outbreak. Comparison of QMRA predictions to epidemiological measurements showed good agreement; interval predictions contained measured disease rates for 9 of 12 outbreaks, with point predictions off by factors of 1.0–120 (median = 4.8). Furthermore, 11 outbreaks occurred at mean doses of less than 1 pathogen per exposure. Measured disease rates for these outbreaks were clearly consistent with a single‐hit model, and not with a “two‐hit” threshold model. These results demonstrate the validity of QMRA for predicting disease rates due to Cryptosporidium and Giardia.     

Risk Assessment of Human Listeriosis from Semisoft Cheeses Made from Raw Sheep's Milk in Lazio and Tuscany (Italy)

Semisoft cheese made from raw sheep's milk is traditionally and economically important in southern Europe. However, raw milk cheese is also a known vehicle of human listeriosis and contamination of sheep cheese with Listeria monocytogenes has been reported. In the present study, we have developed and applied a quantitative risk assessment model, based on available evidence and challenge testing, to estimate risk of invasive listeriosis due to consumption of an artisanal sheep cheese made with raw milk collected from a single flock in central Italy. In the model, contamination of milk may originate from the farm environment or from mastitic animals, with potential growth of the pathogen in bulk milk and during cheese ripening. Based on the 48‐day challenge test of a local semisoft raw sheep's milk cheese we found limited growth only during the initial phase of ripening (24 hours) and no growth or limited decline during the following ripening period. In our simulation, in the baseline scenario, 2.2% of cheese servings are estimated to have at least 1 colony forming unit (CFU) per gram. Of these, 15.1% would be above the current E.U. limit of 100 CFU/g (5.2% would exceed 1,000 CFU/g). Risk of invasive listeriosis per random serving is estimated in the 10^?12 range (mean) for healthy adults, and in the 10^?10 range (mean) for vulnerable populations. When small flocks (10–36 animals) are combined with the presence of a sheep with undetected subclinical mastitis, risk of listeriosis increases and such flocks may represent a public health risk.     

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.     

The Discrete Weibull Distribution: An Alternative for Correlated Counts with Confirmation for Microbial Counts in Water

Distributions of pathogen counts in treated water over time are highly skewed, power‐law‐like, and discrete. Over long periods of record, a long tail is observed, which can strongly determine the long‐term mean pathogen count and associated health effects. Such distributions have been modeled with the Poisson lognormal (PLN) computed (not closed‐form) distribution, and a new discrete growth distribution (DGD), also computed, recently proposed and demonstrated for microbial counts in water (Risk Analysis 29, 841–856). In this article, an error in the original theoretical development of the DGD is pointed out, and the approach is shown to support the closed‐form discrete Weibull (DW). Furthermore, an information‐theoretic derivation of the DGD is presented, explaining the fit shown for it to the original nine empirical and three simulated (n = 1,000) long‐term waterborne microbial count data sets. Both developments result from a theory of multiplicative growth of outcome size from correlated, entropy‐forced cause magnitudes. The predicted DW and DGD are first borne out in simulations of continuous and discrete correlated growth processes, respectively. Then the DW and DGD are each demonstrated to fit 10 of the original 12 data sets, passing the chi‐square goodness‐of‐fit test (α= 0.05, overall p = 0.1184). The PLN was not demonstrated, fitting only 4 of 12 data sets (p = 1.6 × 10^?8), explained by cause magnitude correlation. Results bear out predictions of monotonically decreasing distributions, and suggest use of the DW for inhomogeneous counts correlated in time or space. A formula for computing the DW mean is presented.     

Meta-Analysis of Food Safety Information Based on a Combination of a Relational Database and a Predictive Modeling Tool

The management of microbial risk in food products requires the ability to predict growth kinetics of pathogenic microorganisms in the event of contamination and growth initiation. Useful data for assessing these issues may be found in the literature or from experimental results. However, the large number and variety of data make further development difficult. Statistical techniques, such as meta-analysis, are then useful to realize synthesis of a set of distinct but similar experiences. Moreover, predictive modeling tools can be employed to complete the analysis and help the food safety manager to interpret the data. In this article, a protocol to perform a meta-analysis of the outcome of a relational database, associated with quantitative microbiology models, is presented. The methodology is illustrated with the effect of temperature on pathogenic Escherichia coli and Listeria monocytogenes, growing in culture medium, beef meat, and milk products. Using a database and predictive models, simulations of growth in a given product subjected to various temperature scenarios can be produced. It is then possible to compare food products for a given microorganism, according to its growth ability in these products, and to compare the behavior of bacteria in a given foodstuff. These results can assist decisions for a variety of questions on food safety.     

An Agent‐Based Model for Pathogen Persistence and Cross‐Contamination Dynamics in a Food Facility

We used an agent‐based modeling (ABM) framework and developed a mathematical model to explain the complex dynamics of microbial persistence and spread within a food facility and to aid risk managers in identifying effective mitigation options. The model explicitly considered personal hygiene practices by food handlers as well as their activities and simulated a spatially explicit dynamic system representing complex interaction patterns among food handlers, facility environment, and foods. To demonstrate the utility of the model in a decision‐making context, we created a hypothetical case study and used it to compare different risk mitigation strategies for reducing contamination and spread of Listeria monocytogenes in a food facility. Model results indicated that areas with no direct contact with foods (e.g., loading dock and restroom) can serve as contamination niches and recontaminate areas that have direct contact with food products. Furthermore, food handlers’ behaviors, including, for example, hygiene and sanitation practices, can impact the persistence of microbial contamination in the facility environment and the spread of contamination to prepared foods. Using this case study, we also demonstrated benefits of an ABM framework for addressing food safety in a complex system in which emergent system‐level responses are predicted using a bottom‐up approach that observes individual agents (e.g., food handlers) and their behaviors. Our model can be applied to a wide variety of pathogens, food commodities, and activity patterns to evaluate efficacy of food‐safety management practices and quantify contamination reductions associated with proposed mitigation strategies in food facilities.     

A New Theoretical Discrete Growth Distribution with Verification for Microbial Counts in Water

Living microbes are discrete, not homogeneously distributed in environmental media, and the form of the distribution of their counts in drinking water has not been well established. However, this count may "scale" or range over orders of magnitude over time, in which case data representing the tail of the distribution, and governing the mean, would be represented only in impractically long data records. In the absence of such data, knowledge of the general form of the full distribution could be used to estimate the true mean accounting for low-probability, high-consequence count events and provide a basis for a general environmental dose-response function. In this article, a new theoretical discrete growth distribution (DGD) is proposed for discrete counts in environmental media and other discrete growth systems. The term growth refers not to microbial growth but to a general abiotic first-order growth/decay of outcome sizes in many complex systems. The emergence and stability of the DGD in such systems, defined in simultaneous work, are also described. The DGD is then initially verified versus 12 of 12 simulated long-term drinking water and short-term treated and untreated water microbial count data sets. The alternative Poisson lognormal (PLN) distribution was rejected for 2 (17%) of the 12 data sets with 95% confidence and, like other competitive distributions, was not found stable (in simultaneous work). Sample averages are compared with means assessed from the fitted DGD, with varying results. Broader validation of the DGD for discrete counts arising as outcomes of mathematical growth systems is suggested.     

Risk ranking of food categories associated with Salmonella enterica contamination in the central region of Mexico

To prevent and control foodborne diseases, there is a fundamental need to identify the foods that are most likely to cause illness. The goal of this study was to rank 25 commonly consumed food products associated with Salmonella enterica contamination in the Central Region of Mexico. A multicriteria decision analysis (MCDA) framework was developed to obtain an S. enterica risk score for each food product based on four criteria: probability of exposure to S. enterica through domestic food consumption (Se); S. enterica growth potential during home storage (Sg); per capita consumption (Pcc); and food attribution of S. enterica outbreak (So). Risk scores were calculated by the equation Se*W₁+Sg*W₂+Pcc*W₃+So*W₄, where each criterion was assigned a normalized value (1–5) and the relative weights (W) were defined by 22 experts’ opinion. Se had the largest effect on the risk score being the criterion with the highest weight (35%; IC95% 20%–60%), followed by So (24%; 5%–50%), Sg (23%; 10%–40%), and Pcc (18%; 10%–35%). The results identified chicken (4.4 ± 0.6), pork (4.2 ± 0.6), and beef (4.2 ± 0.5) as the highest risk foods, followed by seed fruits (3.6 ± 0.5), tropical fruits (3.4 ± 0.4), and dried fruits and nuts (3.4 ± 0.5), while the food products with the lowest risk were yogurt (2.1 ± 0.3), chorizo (2.1 ± 0.4), and cream (2.0 ± 0.3). Approaches with expert-based weighting and equal weighting showed good correlation (R² = 0.96) and did not show significant differences among the ranking order in the top 20 tier. This study can help risk managers select interventions and develop targeted surveillance programs against S. enterica in high-risk food products.     

Modeling Individual Cell Lag Time Distributions for Listeria monocytogenes

The food industry faces two paradoxical demands: on the one hand, foods need to be microbiologically safe for consumption and on the other hand, consumers want fresh, minimally processed foods. To meet these demands, more insight into the mechanisms of microbial growth is needed, which includes, among others, the microbial lag phase. This is the time needed by bacterial cells to adapt to a new environment (for example, after food product contamination) before starting an exponential growth regime. Since food products are often contaminated with low amounts of pathogenic microorganisms, it is important to know the distribution of these individual cell lag times to make accurate predictions concerning food safety. More precisely, cells with the shortest lag times (i.e., appearing in the left tail of the distribution) are largely decisive for the outgrowth of the population. In this study, an integrated modeling approach is proposed and applied to an existing data set of individual cell lag time measurements of Listeria monocytogenes. In a first step, a logistic modeling approach is applied to predict the fraction of zero-lag cells (which start growing immediately) as a function of temperature, pH, and water activity. For the nonzero-lag cells, the mean and variance of the lag time distribution are modeled with a hyperbolic-type model structure. This mean and variance allow identification of the parameters of a two-parameter Weibull distribution, representing the nonzero-lag cell lag time distribution. The integration of the developed models allows prediction of a global distribution of individual cell lag times for any combination of environmental conditions in the interpolation domain of the original temperature, pH, and water activity settings. The global fitting quality of the model is quantified using several measures indicating that the model gives accurate predictions, erring slightly on the fail-safe side when predicting the shortest lag times.     

Time-Dose-Response Models for Microbial Risk Assessment

While microbial risk assessment (MRA) has been used for over 25 years, traditional dose-response analysis has only predicted the overall risk of adverse consequences from exposure to a given dose. An important issue for consequence assessment from bioterrorist and other microbiological exposure is the distribution of cases over time due to the initial exposure. In this study, the classical exponential and beta-Poisson dose-response models were modified to include exponential-power dependency of time post inoculation (TPI) or its simplified form, exponential-reciprocal dependency of TPI, to quantify the time of onset of an effect presumably associated with the kinetics of in vivo bacterial growth. Using the maximum likelihood estimation approach, the resulting time-dose-response models were found capable of providing statistically acceptable fits to all tested pooled animal survival dose-response data. These new models can consequently describe the development of animal infectious response over time and represent observed responses fairly accurately. This is the first study showing that a time-dose-response model can be developed for describing infections initiated by various pathogens. It provides an advanced approach for future MRA frameworks.     

Comparison of Six Dose-Response Models for Use with Food-Borne Pathogens

Food-related illness in the United States is estimated to affect over six million people per year and cost the economy several billion dollars. These illnesses and costs could be reduced if minimum infectious doses were established and used as the basis of regulations and monitoring. However, standard methodologies for dose-response assessment are not yet formulated for microbial risk assessment. The objective of this study was to compare dose-response models for food-borne pathogens and determine which models were most appropriate for a range of pathogens. The statistical models proposed in the literature and chosen for comparison purposes were log-normal, log-logistic, exponential, -Poisson and Weibull-Gamma. These were fit to four data sets also taken from published literature, Shigella flexneri, Shigella dysenteriae,Campylobacter jejuni, and Salmonella typhosa, using the method of maximum likelihood. The Weibull-gamma, the only model with three parameters, was also the only model capable of fitting all the data sets examined using the maximum likelihood estimation for comparisons. Infectious doses were also calculated using each model. Within any given data set, the infectious dose estimated to affect one percent of the population ranged from one order of magnitude to as much as nine orders of magnitude, illustrating the differences in extrapolation of the dose response models. More data are needed to compare models and examine extrapolation from high to low doses for food-borne pathogens.     

A model of retail outlet selection for beef

Multinomial logit models were used to explain consumer outlet selection when buying beef, specifically roasts, steaks, ground beef, and other types of beef. Outlets were grouped into supermarkets, butchers, warehouses, supercenters, and others, and the probability of selecting each outlet type over a range of demographic and other variables was tested. The models were estimated from household data, with 198,682 observations used in the estimation. Empirical results showed that the type of beef purchased and the size of the purchase played an important role in the choice of outlet. Furthermore, the increase in mobility seen when consumers buy larger unit cuts could not be fully explained by price discounting. Implications for the potential growth of each outlet type are discussed.     

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single‐Hit Dose‐Response Models

Dose‐response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi‐mechanistic models known as single‐hit models, such as the exponential and the exact beta‐Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single‐hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so‐called single‐hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single‐hit models. Further analysis of the model framework is facilitated by formulating the single‐hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single‐hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model‐consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model‐consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model‐consistent expression for the mean per‐exposure dose that produces the correct total risk from repeated exposures is developed.     

Growth and Heat Resistance Kinetic Variation Among Various Isolates of Salmonella and its Application to Risk Assessment

The abilities of cells of a particular type of bacteria to leave lag phase and begin the process of dividing or surviving heat treatment can depend on the serotypes or strains of the bacteria. This article reports an investigation of serotype-specific differences in growth and heat resistance kinetics of clinical and food isolates of Salmonella. Growth kinetics at 19 degrees C and 37 degrees C were examined in brain heart infusion broth and heat resistance kinetics for 60 degrees C were examined in beef gravy using a submerged coil heating apparatus. Estimates of the parameters of the growth curves suggests a small between-serotype variance of the growth kinetics. However, for inactivation, the results suggest a significant between-serotype effect on the asymptotic D-values, with an estimated between-serotype CV of about 20%. In microbial risk assessment, predictive microbiology is used to estimate growth and inactivation of pathogens. Often the data used for estimating the growth or inactivation kinetics are based on measurements on a cocktail--a mixture of approximately equal proportions of several serotypes or strains of the pathogen being studied. The expected growth or inactivation rates derived from data using cocktails are biased, reflecting the characteristics of the fastest growing or most heat resistant serotype of the cocktail. In this article, an adjustment to decrease this possible bias in a risk assessment is offered. The article also presents discussion of the effect on estimating growth when stochastic assumptions are incorporated in the model. In particular, equations describing the variation of relative growth are derived, accounting for the stochastic variations of the division of cells. For small numbers of cells, the expected value of the relative growth is not an appropriate "representative" value for actual relative growths that might occur.