Development and application of a dose–response model for Elizabethkingia spp

Elizabethkingia spp. are common environmental pathogens responsible for infections in more vulnerable populations. Although the exposure routes of concern are not well understood, some hospital-associated outbreaks have indicated possible waterborne transmission. In order to facilitate quantitative microbial risk assessment (QMRA) for Elizabethkingia spp., this study fit dose–response models to frog and mice datasets that evaluated intramuscular and intraperitoneal exposure to Elizabethkingia spp. The frog datasets could be pooled, and the exact beta-Poisson model was the best fitting model with optimized parameters α  = 0.52 and β = 86,351. Using the exact beta-Poisson model, the dose of Elizabethkingia miricola resulting in a 50% morbidity response (LD₅₀) was estimated to be approximately 237,000 CFU. The model developed herein was used to estimate the probability of infection for a hospital patient under a modeled exposure scenario involving a contaminated medical device and reported Elizabethkingia spp. concentrations isolated from hospital sinks after an outbreak. The median exposure dose was approximately 3 CFU/insertion event, and the corresponding median risk of infection was 3.4E-05. The median risk estimated in this case study was lower than the 3% attack rate observed in a previous outbreak, however, there are noted gaps pertaining to the possible concentrations of Elizabethkingia spp. in tap water and the most likely exposure routes. This is the first dose–response model developed for Elizabethkingia spp. thus enabling future risk assessments to help determine levels of risk and potential effective risk management strategies.     

Modeling the Dose Response Relationship of Waterborne Acanthamoeba

This study developed dose response models for determining the probability of eye or central nervous system infections from previously conducted studies using different strains of Acanthamoeba spp. The data were a result of animal experiments using mice and rats exposed corneally and intranasally to the pathogens. The corneal inoculations of Acanthamoeba isolate Ac 118 included varied amounts of Corynebacterium xerosis and were best fit by the exponential model. Virulence increased with higher levels of C. xerosis. The Acanthamoeba culbertsoni intranasal study with death as an endpoint of response was best fit by the beta‐Poisson model. The HN‐3 strain of A. castellanii was studied with an intranasal exposure and three different endpoints of response. For all three studies, the exponential model was the best fit. A model based on pooling data sets of the intranasal exposure and death endpoint resulted in an LD₅₀ of 19,357 amebae. The dose response models developed in this study are an important step towards characterizing the risk associated with free‐living amoeba like Acanthamoeba in drinking water distribution systems. Understanding the human health risk posed by free‐living amoeba will allow for quantitative microbial risk assessments that support building design decisions to minimize opportunities for pathogen growth and survival.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time‐to‐response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple‐dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time‐to‐death (TTD). Among the models developed, the best‐fitting survival model (baseline model) is an exponential dose–response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose–response functions and use the assumption that, in a multiple‐dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high‐dose rabbit data sets. More accurate survival models depend upon future development of dose–response data sets specifically designed to assess potential multiple‐dose effects on response and time‐to‐response. The process used in this article to develop the best‐fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host–pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen‐specific empirically‐derived parameters.     

Demonstrating the Benefits of Predictive Bayesian Dose–Response Relationships Using Six Exposure Studies of Cryptosporidium parvum

A conventional dose–response function can be refitted as additional data become available. A predictive dose–response function in contrast does not require a curve-fitting step, only additional data and presents the unconditional probabilities of illness, reflecting the level of information it contains. In contrast, the predictive Bayesian dose–response function becomes progressively less conservative as more information is included. This investigation evaluated the potential for using predictive Bayesian methods to develop a dose–response for human infection that improves on existing models, to show how predictive Bayesian statistical methods can utilize additional data, and expand the Bayesian methods for a broad audience including those concerned about an oversimplification of dose–response curve use in quantitative microbial risk assessment (QMRA). This study used a dose–response relationship incorporating six separate data sets for Cryptosporidium parvum. A Pareto II distribution with known priors was applied to one of the six data sets to calibrate the model, while the others were used for subsequent updating. While epidemiological principles indicate that local variations, host susceptibility, and organism strain virulence may vary, the six data sets all appear to be well characterized using the Bayesian approach. The adaptable model was applied to an existing data set for Campylobacter jejuni for model validation purposes, which yielded results that demonstrate the ability to analyze a dose–response function with limited data using and update those relationships with new data. An analysis of the goodness of fit compared to the beta-Poisson methods also demonstrated correlation between the predictive Bayesian model and the data.     

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.     

A Comparison of Regulatory Implications of Traditional and Exact Two-Stage Dose–Response Models

We compare the regulatory implications of applying the traditional (linearized) and exact two-stage dose–response models to animal carcinogenic data. We analyze dose–response data from six studies, representing five different substances, and we determine the goodness-of-fit of each model as well as the 95% confidence lower limit of the dose corresponding to a target excess risk of 10^–5 (the target risk dose TRD). For the two concave datasets, we find that the exact model gives a substantially better fit to the data than the traditional model, and that the exact model gives a TRD that is an order of magnitude lower than that given by the traditional model. In the other cases, the exact model gives a fit equivalent to or better than the traditional model. We also show that although the exact two-stage model may exhibit dose–response concavity at moderate dose levels, it is always linear or sublinear, and never supralinear, in the low-dose limit. Because regulatory concern is almost always confined to the low-dose region extrapolation, supralinear behavior seems not to be of regulatory concern in the exact two-stage model. Finally, we find that when performing this low-dose extrapolation in cases of dose–response concavity, extrapolating the model fit leads to a more conservative TRD than taking a linear extrapolation from 10% excess risk. We conclude with a set of recommendations.     

Dose‐Response Model of Coxiella burnetii (Q Fever)

Q fever is a zoonotic disease caused by the intracellular gram‐negative bacterium Coxiella burnetii (C. burnetii), which only multiplies within the phagolysosomal vacuoles. Q fever may manifest as acute or chronic disease. The acute form is generally not fatal and manifestes as self‐controlled febrile illness. Chronic Q fever is usually characterized by endocarditis. Many animal models, including humans, have been studied for Q fever infection through various exposure routes. The studies considered different endpoints including death for animal models and clinical signs for human infection. In this article, animal experimental data available in the open literature were fit to suitable dose‐response models using maximum likelihood estimation. Research results for tests of severe combined immunodeficient mice inoculated intraperitoneally (i.p.) with C. burnetii were best estimated with the Beta‐Poisson dose‐response model. Similar inoculation (i.p.) trial outcomes conducted on C57BL/6J mice were best fit by an exponential model, whereas those tests run on C57BL/10ScN mice were optimally represented by a Beta‐Poisson dose‐response model.     

Development of an Interspecies Nested Dose‐Response Model for Mycobacterium avium subspecies paratuberculosis

Mycobacterium avium subspecies paratuberculosis (MAP) causes chronic inflammation of the intestines in humans, ruminants, and other species. It is the causative agent of Johne's disease in cattle, and has been implicated as the causative agent of Crohn's disease in humans. To date, no quantitative microbial risk assessment (QMRA) for MAP utilizing a dose‐response function exists. The objective of this study is to develop a nested dose‐response model for infection from oral exposure to MAP utilizing data from the peer‐reviewed literature. Four studies amenable to dose‐response modeling were identified in the literature search and optimized to the one‐parameter exponential or two‐parameter beta‐Poisson dose‐response models. A nesting analysis was performed on all permutations of the candidate data sets to determine the acceptability of pooling data sets across host species. Three of four data sets exhibited goodness of fit to at least one model. All three data sets exhibited good fit to the beta‐Poisson model, and one data set exhibited goodness of fit, and best fit, to the exponential model. Two data sets were successfully nested using the beta‐Poisson model with parameters α = 0.0978 and N₅₀ = 2.70 × 10² CFU. These data sets were derived from sheep and red deer host species, indicating successful interspecies nesting, and demonstrate the highly infective nature of MAP. The nested dose‐response model described should be used for future QMRA research regarding oral exposure to MAP.     

Development of Dose‐Response Models to Predict the Relationship for Human Toxoplasma gondii Infection Associated with Meat Consumption

Toxoplasma gondii is a protozoan parasite that is responsible for approximately 24% of deaths attributed to foodborne pathogens in the United States. It is thought that a substantial portion of human T. gondii infections is acquired through the consumption of meats. The dose‐response relationship for human exposures to T. gondii‐infected meat is unknown because no human data are available. The goal of this study was to develop and validate dose‐response models based on animal studies, and to compute scaling factors so that animal‐derived models can predict T. gondii infection in humans. Relevant studies in literature were collected and appropriate studies were selected based on animal species, stage, genotype of T. gondii, and route of infection. Data were pooled and fitted to four sigmoidal‐shaped mathematical models, and model parameters were estimated using maximum likelihood estimation. Data from a mouse study were selected to develop the dose‐response relationship. Exponential and beta‐Poisson models, which predicted similar responses, were selected as reasonable dose‐response models based on their simplicity, biological plausibility, and goodness fit. A confidence interval of the parameter was determined by constructing 10,000 bootstrap samples. Scaling factors were computed by matching the predicted infection cases with the epidemiological data. Mouse‐derived models were validated against data for the dose‐infection relationship in rats. A human dose‐response model was developed as P (d) = 1–exp (–0.0015 × 0.005 × d) or P (d) = 1–(1 + d × 0.003 / 582.414)^?1.479. Both models predict the human response after consuming T. gondii‐infected meats, and provide an enhanced risk characterization in a quantitative microbial risk assessment model for this pathogen.     

Risk/Benefit Assessments of Human Diseases: Optimum Dose for Intervention

A simple procedure is proposed in order to quantify the tradeoff between a loss suffered from an illness due to exposure to a microbial pathogen and a loss due to a toxic effect, perhaps a different illness, induced by a disinfectant employed to reduce the microbial exposure. Estimates of these two types of risk as a function of disinfectant dose and their associated relative losses provide information for the estimation of the optimum dose of disinfectant that minimizes the total expected loss. The estimates of the optimum dose and expected relative total loss were similar regardless of whether the beta-Poisson, log-logistic, or extreme value function was used to model the risk of illness due to exposure to a microbial pathogen. This is because the optimum dose of the disinfectant and resultant expected minimum loss depend upon the estimated slope (first derivative) of the models at low levels of risk, which appear to be similar for these three models at low levels of risk. Similarly, the choice among these three models does not appear critical for estimating the slope at low levels of risk for the toxic effect induced by the use of a disinfectant. For the proposed procedure to estimate the optimum disinfectant dose, it is not necessary to have absolute values for the losses due to microbial-induced or disinfectant-induced illness, but only relative losses are required. All aspects of the problem are amenable to sensitivity analyses. The issue of risk/benefit tradeoffs, more appropriately called risk/risk tradeoffs, does not appear to be an insurmountable problem.     

Incorporating Time‐Dose‐Response into Legionella Outbreak Models

A novel method was used to incorporate in vivo host–pathogen dynamics into a new robust outbreak model for legionellosis. Dose‐response and time‐dose‐response (TDR) models were generated for Legionella longbeachae exposure to mice via the intratracheal route using a maximum likelihood estimation approach. The best‐fit TDR model was then incorporated into two L. pneumophila outbreak models: an outbreak that occurred at a spa in Japan, and one that occurred in a Melbourne aquarium. The best‐fit TDR from the murine dosing study was the beta‐Poisson with exponential‐reciprocal dependency model, which had a minimized deviance of 32.9. This model was tested against other incubation distributions in the Japan outbreak, and performed consistently well, with reported deviances ranging from 32 to 35. In the case of the Melbourne outbreak, the exponential model with exponential dependency was tested against non‐time‐dependent distributions to explore the performance of the time‐dependent model with the lowest number of parameters. This model reported low minimized deviances around 8 for the Weibull, gamma, and lognormal exposure distribution cases. This work shows that the incorporation of a time factor into outbreak distributions provides models with acceptable fits that can provide insight into the in vivo dynamics of the host‐pathogen system.     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

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 LD₅₀ increases with aerosol size for aerosols at and above 4.5 μm. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD₅₀ when aerosol size is increased from 1 μm to 12 μm. 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.     

Dose‐Response Models Incorporating Aerosol Size Dependency for Francisella tularensis

The effect of bioaerosol size was incorporated into predictive dose‐response models for the effects of inhaled aerosols of Francisella tularensis (the causative agent of tularemia) on rhesus monkeys and guinea pigs with bioaerosol diameters ranging between 1.0 and 24 μm. Aerosol‐size‐dependent models were formulated as modification of the exponential and β‐Poisson dose‐response models and model parameters were estimated using maximum likelihood methods and multiple data sets of quantal dose‐response data for which aerosol sizes of inhaled doses were known. Analysis of F. tularensis dose‐response data was best fit by an exponential dose‐response model with a power function including the particle diameter size substituting for the rate parameter k scaling the applied dose. There were differences in the pathogen's aerosol‐size‐dependence equation and models that better represent the observed dose‐response results than the estimate derived from applying the model developed by the International Commission on Radiological Protection (ICRP, 1994) that relies on differential regional lung deposition for human particle exposure.     

Hexavalent Chromium and Lung Cancer in the Chromate Industry: A Quantitative Risk Assessment

The purpose of this investigation was to estimate excess lifetime risk of lung cancer death resulting from occupational exposure to hexavalent-chromium-containing dusts and mists. The mortality experience in a previously studied cohort of 2,357 chromate chemical production workers with 122 lung cancer deaths was analyzed with Poisson regression methods. Extensive records of air samples evaluated for water-soluble total hexavalent chromium were available for the entire employment history of this cohort. Six different models of exposure-response for hexavalent chromium were evaluated by comparing deviances and inspection of cubic splines. Smoking (pack-years) imputed from cigarette use at hire was included in the model. Lifetime risks of lung cancer death from exposure to hexavalent chromium (assuming up to 45 years of exposure) were estimated using an actuarial calculation that accounts for competing causes of death. A linear relative rate model gave a good and readily interpretable fit to the data. The estimated rate ratio for 1 mg/m3-yr of cumulative exposure to hexavalent chromium (as CrO3), with a lag of five years, was RR=2.44 (95% CI=1.54-3.83). The excess lifetime risk of lung cancer death from exposure to hexavalent chromium at the current OSHA permissible exposure limit (PEL) (0.10 mg/m3) was estimated to be 255 per 1,000 (95% CI: 109-416). This estimate is comparable to previous estimates by U.S. EPA, California EPA, and OSHA using different occupational data. Our analysis predicts that current occupational standards for hexavalent chromium permit a lifetime excess risk of dying of lung cancer that exceeds 1 in 10, which is consistent with previous risk assessments.     

Outbreak-Based Giardia Dose–Response Model Using Bayesian Hierarchical Markov Chain Monte Carlo Analysis

Giardia is a zoonotic gastrointestinal parasite responsible for a substantial global public health burden, and quantitative microbial risk assessment (QMRA) is often used to forecast and manage this burden. QMRA requires dose–response models to extrapolate available dose–response data, but the existing model for Giardia ignores valuable dose–response information, particularly data from several well-documented waterborne outbreaks of giardiasis. The current study updates Giardia dose–response modeling by synthesizing all available data from outbreaks and experimental studies using a Bayesian random effects dose–response model. For outbreaks, mean doses (D) and the degree of spatial and temporal aggregation among cysts were estimated using exposure assessment implemented via two-dimensional Monte Carlo simulation, while potential overreporting of outbreak cases was handled using published overreporting factors and censored binomial regression. Parameter estimation was by Markov chain Monte Carlo simulation and indicated that a typical exponential dose–response parameter for Giardia is r = 1.6 × 10⁻² [3.7 × 10⁻³, 6.2 × 10⁻²] (posterior median [95% credible interval]), while a typical morbidity ratio is m = 3.8 × 10⁻¹ [2.3 × 10⁻¹, 5.5 × 10⁻¹]. Corresponding (logistic-scale) variance components were σ_r = 5.2 × 10⁻¹ [1.1 × 10⁻¹, 9.6 × 10⁻¹] and σ_m = 9.3 × 10⁻¹ [7.0 × 10⁻², 2.8 × 10⁰], indicating substantial variation in the Giardia dose–response relationship. Compared to the existing Giardia dose–response model, the current study provides more representative estimation of uncertainty in r and novel quantification of its natural variability. Several options for incorporating variability in r (and m) into QMRA predictions are discussed, including incorporation via Monte Carlo simulation as well as evaluation of the current study's model using the approximate beta-Poisson.     

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.     

Dose-Response and Risk Assessment of Airborne Hexavalent Chromium and Lung Cancer Mortality

This study evaluates the dose-response relationship for inhalation exposure to hexavalent chromium [Cr(VI)] and lung cancer mortality for workers of a chromate production facility, and provides estimates of the carcinogenic potency. The data were analyzed using relative risk and additive risk dose-response models implemented with both Poisson and Cox regression. Potential confounding by birth cohort and smoking prevalence were also assessed. Lifetime cumulative exposure and highest monthly exposure were the dose metrics evaluated. The estimated lifetime additional risk of lung cancer mortality associated with 45 years of occupational exposure to 1 microg/m3 Cr(VI) (occupational exposure unit risk) was 0.00205 (90%CI: 0.00134, 0.00291) for the relative risk model and 0.00216 (90%CI: 0.00143, 0.00302) for the additive risk model assuming a linear dose response for cumulative exposure with a five-year lag. Extrapolating these findings to a continuous (e.g., environmental) exposure scenario yielded an environmental unit risk of 0.00978 (90%CI: 0.00640, 0.0138) for the relative risk model [e.g., a cancer slope factor of 34 (mg/kg-day)-1] and 0.0125 (90%CI: 0.00833, 0.0175) for the additive risk model. The relative risk model is preferred because it is more consistent with the expected trend for lung cancer risk with age. Based on statistical tests for exposure-related trend, there was no statistically significant increased lung cancer risk below lifetime cumulative occupational exposures of 1.0 mg-yr/m3, and no excess risk for workers whose highest average monthly exposure did not exceed the current Permissible Exposure Limit (52 microg/m3). It is acknowledged that this study had limited power to detect increases at these low exposure levels. These cancer potency estimates are comparable to those developed by U.S. regulatory agencies and should be useful for assessing the potential cancer hazard associated with inhaled Cr(VI).