Predictive Bayesian Microbial Dose-Response Assessment Based on Suggested Self-Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose-response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence-based approaches. However, the method uses knowledge of the conditional dose-response form, and this form is not well established for the illness endpoint. A conditional parametric dose-response function for gastroenteric illness is proposed here based on simple numerical models of self-organized host-pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self-organized critical value of wellness. A generalized beta-Poisson illness dose-response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose-response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 x 10(-7) oocysts/exposure (e.g., 2.5 x 10(-7) oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson-distributed pathogen counts. This estimate should be revised to account for non-Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.     

The Impact of Cytochrome P450 2E1-Dependent Metabolic Variance on a Risk-Relevant Pharmacokinetic Outcome in Humans

Risk assessments include assumptions about sensitive subpopulations, such as the fraction of the general population that is sensitive and the extent that biochemical or physiological attributes influence sensitivity. Uncertainty factors (UF) account for both pharmacokinetic (PK) and pharmacodynamic (PD) components, allowing the inclusion of risk-relevant information to replace default assumptions about PK and PD variance (uncertainty). Large numbers of human organ donor samples and recent advances in methods to extrapolate in vitro enzyme expression and activity data to the intact human enable the investigation of the impact of PK variability on human susceptibility. The hepatotoxicity of trichloroethylene (TCE) is mediated by acid metabolites formed by cytochrome P450 2E1 (CYP2E1) oxidation, and differences in the CYP2E1 expression are hypothesized to affect susceptibility to TCE's liver injury. This study was designed specifically to examine the contribution of statistically quantified variance in enzyme content and activity on the risk of hepatotoxic injury among adult humans. We combined data sets describing (1) the microsomal protein content of human liver, (2) the CYP2E1 content of human liver microsomal protein, and (3) the in vitro Vmax for TCE oxidation by humans. The 5th and 95th percentiles of the resulting distribution (TCE oxidized per minute per gram liver) differed by approximately sixfold. These values were converted to mg TCE oxidized/h/kg body mass and incorporated in a human PBPK model. Simulations of 8-hour inhalation exposure to 50 ppm and oral exposure to 5 micro g TCE/L in 2 L drinking water showed that the amount of TCE oxidized in the liver differs by 2% or less under extreme values of CYP2E1 expression and activity (here, selected as the 5th and 95th percentiles of the resulting distribution). This indicates that differences in enzyme expression and TCE oxidation among the central 90% of the adult human population account for approximately 2% of the difference in production of the risk-relevant PK outcome for TCE-mediated liver injury. Integration of in vitro metabolism information into physiological models may reduce the uncertainties associated with risk contributions of differences in enzyme expression and the UF that represent PK variability.     

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.     

A Probabilistic Framework for the Reference Dose (Probabilistic RfD)

Determining the probabilistic limits for the uncertainty factors used in the derivation of the Reference Dose (RfD) is an important step toward the goal of characterizing the risk of noncarcinogenic effects from exposure to environmental pollutants. If uncertainty factors are seen, individually, as "upper bounds" on the dose-scaling factor for sources of uncertainty, then determining comparable upper bounds for combinations of uncertainty factors can be accomplished by treating uncertainty factors as distributions, which can be combined by probabilistic techniques. This paper presents a conceptual approach to probabilistic uncertainty factors based on the definition and use of RfDs by the US. EPA. The approach does not attempt to distinguish one uncertainty factor from another based on empirical data or biological mechanisms but rather uses a simple displaced lognormal distribution as a generic representation of all uncertainty factors. Monte Carlo analyses show that the upper bounds for combinations of this distribution can vary by factors of two to four when compared to the fixed-value uncertainty factor approach. The probabilistic approach is demonstrated in the comparison of Hazard Quotients based on RfDs with differing number of uncertainty factors.     

An Approach for Modeling Noncancer Dose Responses with an Emphasis on Uncertainty

This paper presents an approach for characterizing the probability of adverse effects occurring in a population exposed to dose rates in excess of the Reference Dose (RfD). The approach uses a linear threshold (hockey stick) model of response and is based on the current system of uncertainty factors used in setting RfDs. The approach requires generally available toxicological estimates such as No-Observed-Adverse-Effect Levels (NOAELs) or Benchmark Doses and doses at which adverse effects are observed in 50% of the test animals (ED₅₀s). In this approach, Monte Carlo analysis is used to characterize the uncertainty in the dose response slope based on the range and magnitude of the key sources of uncertainty in setting protective doses. The method does not require information on the shape of the dose response curve for specific chemicals, but is amenable to the inclusion of such data. The approach is applied to four compounds to produce estimates of response rates for dose rates greater than the RfD