Mike Messner

Risk assessment for Cryptosporidium: A hierarchical Bayesian analysis of human dose response data

Three dose-response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID50) using a simple cumulative percent endpoint method (Reed and Muench, 1938). ID50s were derived using two definitions of infection: one as subjects having oocysts detected in stool by direct fluorescence assay, and the other by a clinical finding of diarrhea with or without detected oocysts (Chappell et al., 1998; Okhuysen et al., 1999). In the present study, the data were analyzed using the broader definition of infection (i.e., presence of oocysts in stool and/or diarrheal illness characteristic of cryptosporidiosis). Maximum likelihood dose-response parameter estimates for UCP, IOWA, and TAMU were 2980, 190, and 17.5, respectively. Based on these estimates, the ID50s of the three respective isolates were 2066, 132, and 12.1. The three oocyst isolates were considered representative of a larger population of human-infecting strains and analyzed as combined data using a hierarchical Bayesian model. Hyperparameters defined the distribution of dose-response parameters for the population of strains. Output from Markov Chain Monte Carlo analysis described posterior distributions for the hyperparameters and for the parameters of the IOWA, TAMU, and UCP strains. Point estimates of dose-response parameters produced by this analysis were similar to the maximum likelihood estimates. Finally, the utility of these results for probabilistic risk assessment was evaluated. The risk of infection from single oocyst doses was derived for a mixture of the three isolates (where IOWA, TAMU, or UCP are equally likely), and for an oocyst selected at random from the larger population of strains. These estimated risks of infection were 0.018 and 0.028, respectively.

Fractional Poisson—A Simple Dose‐Response Model for Human Norovirus

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The models deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures.

Estimating Potential Increased Bladder Cancer Risk Due to Increased Bromide Concentrations in Sources of Disinfected Drinking Waters

Public water systems are increasingly facing higher bromide levels in their source waters from anthropogenic contamination through coal-fired power plants, conventional oil and gas extraction, textile mills, and hydraulic fracturing. Climate change is likely to exacerbate this in coming years. We estimate bladder cancer risk from potential increased bromide levels in source waters of disinfecting public drinking water systems in the United States. Bladder cancer is the health end point used by the United States Environmental Protection Agency (EPA) in its benefits analysis for regulating disinfection byproducts in drinking water. We use estimated increases in the mass of the four regulated trihalomethanes (THM4) concentrations (due to increased bromide incorporation) as the surrogate disinfection byproduct (DBP) occurrence metric for informing potential bladder cancer risk. We estimate potential increased excess lifetime bladder cancer risk as a function of increased source water bromide levels. Results based on data from 201 drinking water treatment plants indicate that a bromide increase of 50 μg/L could result in a potential increase of between 10(-3) and 10(-4) excess lifetime bladder cancer risk in populations served by roughly 90% of these plants.

Cryptosporidium Infection Risk: Results of New Dose-Response Modeling.

Cryptosporidium human dose-response data from seven species/isolates are used to investigate six models of varying complexity that estimate infection probability as a function of dose. Previous models attempt to explicitly account for virulence differences among C. parvum isolates, using three or six species/isolates. Four (two new) models assume species/isolate differences are insignificant and three of these (all but exponential) allow for variable human susceptibility. These three human-focused models (fractional Poisson, exponential with immunity and beta-Poisson) are relatively simple yet fit the data significantly better than the more complex isolate-focused models. Among these three, the one-parameter fractional Poisson model is the simplest but assumes that all Cryptosporidium oocysts used in the studies were capable of initiating infection. The exponential with immunity model does not require such an assumption and includes the fractional Poisson as a special case. The fractional Poisson model is an upper bound of the exponential with immunity model and applies when all oocysts are capable of initiating infection. The beta Poisson model does not allow an immune human subpopulation; thus infection probability approaches 100% as dose becomes huge. All three of these models predict significantly (>10x) greater risk at the low doses that consumers might receive if exposed through drinking water or other environmental exposure (e.g., 72% vs. 4% infection probability for a one oocyst dose) than previously predicted. This new insight into Cryptosporidium risk suggests additional inactivation and removal via treatment may be needed to meet any specified risk target, such as a suggested 10-4 annual risk of Cryptosporidium infection.

Total coliform and E. coli in public water systems using undisinfected ground water in the United States

Public water systems (PWSs) in the United States generate total coliform (TC) and Escherichia coli (EC) monitoring data, as required by the Total Coliform Rule (TCR). We analyzed data generated in 2011 by approximately 38,000 small (serving fewer than 4101 individuals) undisinfected public water systems (PWSs). We used statistical modeling to characterize a distribution of TC detection probabilities for each of nine groupings of PWSs based on system type (community, non-transient non-community, and transient non-community) and population served (less than 101, 101-1000 and 1001-4100 people). We found that among PWS types sampled in 2011, on average, undisinfected transient PWSs test positive for TC 4.3% of the time as compared with 3% for undisinfected non-transient PWSs and 2.5% for undisinfected community PWSs. Within each type of PWS, the smaller systems have higher median TC detection than the larger systems. All TC-positive samples were assayed for EC. Among TC-positive samples from small undisinfected PWSs, EC is detected in about 5% of samples, regardless of PWS type or size. We evaluated the upper tail of the TC detection probability distributions and found that significant percentages of some system types have high TC detection probabilities. For example, assuming the systems providing data are nationally-representative, then 5.0% of the ∼50,000 small undisinfected transient PWSs in the U.S. have TC detection probabilities of 20% or more. Communities with such high TC detection probabilities may have elevated risk of acute gastrointestinal (AGI) illness - perhaps as great or greater than the attributable risk to drinking water (6-22%) calculated for 14 Wisconsin community PWSs with much lower TC detection probabilities (about 2.3%, Borchardt et al., 2012).

PATHOGEN INTRUSION IN DISTRIBUTION SYSTEMS: MODEL TO ASSESS THE POTENTIAL HEALTH RISKS

A model for estimating the probability of infection from intrusion events associated with low/negative pressure occurrences in distribution system is presented. The modeling approach, based on the principle of quantitative microbial risk assessment, predicts infection rates as a function of several parameters: the orifice equation (for calculation of intrusion flow rate), the external contaminant concentration, the starting time, the duration of low/negative pressures, the location and extent of intrusion area, the hydraulic and operational conditions in the distribution system, consumption events at fixed-times and dose-response information for specific microorganisms. The approach combines the use of a probabilistic model to determine the possible range of contaminant mass rates that could be encountered and the use of a hydraulic model to determine population exposure to contaminated water once an intrusion event has taken place. Using a model distribution system (EPANET Example Network 2), the effects of intrusion event characteristics (starting time, duration, location, contaminant mass rate) on the probability for an healthy adult of being infected by Cryptosporidium from sewage contamination of the distribution system were investigated. Based on the current model assumptions, results show that the risk of infection may vary over several orders of magnitude depending upon where the water is consumed and the intrusion event characteristics.

On the Use of Total Aerobic Spore Bacteria to Make Treatment Decisions due to Cryptosporidium Risk at Public Water System Wells

Spore reduction can be used as a surrogate measure of Cryptosporidium natural filtration efficiency. Estimates of log10 (log) reduction were derived from spore measurements in paired surface and well water samples in Casper Wyoming and Kearney Nebraska. We found that these data were suitable for testing the hypothesis (H0) that the average reduction at each site was 2 log or less, using a one-sided Students t-test. After establishing data quality objectives for the test (expressed as tolerable Type I and Type II error rates), we evaluated the tests performance as a function of the (a) true log reduction, (b) number of paired samples assayed and (c) variance of observed log reductions. We found that 36 paired spore samples are sufficient to achieve the objectives over a wide range of variance, including the variances observed in the two data sets. We also explored the feasibility of using smaller numbers of paired spore samples to supplement bioparticle counts for screening purposes in alluvial aquifers, to differentiate wells with large volume surface water induced recharge from wells with negligible surface water induced recharge. With key assumptions, we propose a normal statistical test of the same hypothesis (H0), but with different performance objectives. As few as six paired spore samples appear adequate as a screening metric to supplement bioparticle counts to differentiate wells in alluvial aquifers with large volume surface water induced recharge. For the case when all available information (including failure to reject H0 based on the limited paired spore data) leads to the conclusion that wells have large surface water induced recharge, we recommend further evaluation using additional paired biweekly spore samples.

Response to: Comment on “Cryptosporidium Infection Risk: Results of New Dose-Response Modeling”--Discussion of Underlying Assumption and Their Implications

To the editor––We thank the authors for their comment on our recently published article. They raise valid concerns regarding the models used for Cryptosporidium dose–response analysis. We recognize the tension between analyzing the data in a way that allows the data to speak freely and analyzing the data based on mechanistic constructs about the infection process. We believe that both perspectives are important. Regarding concern 1 (“unacknowledged assumption that all Cryptosporidium isolates share a single dose–response relationship and are therefore equally infectious”), we disagree with the word “unacknowledged,” as we state that our four simple models assume insignificant differences among isolates, and that our two hierarchical models include isolate-specific parameters. The data, when shown together (as in our article), show that the great differences in dosing levels––rather than isolate differences in potency––led to multilevel models that did their best to separately fit each study’s data, but failed in terms of total likelihood. Our article shows that the simple models are superior, but perhaps more questions are raised than answered. We believe that only low-dose data can answer the important questions and provide a basis for defensible low-dose risk analysis. We appreciate comments regarding apparent inconsistencies between model assumptions, clinical experience, and other evidence (concerns 2 and 3). It