Modeling infection from SARS-CoV-2 wastewater concentrations: promise, limitations, and future directions.

Estimating total infection levels, including unreported and asymptomatic infections, is important for understanding community disease transmission. Wastewater can provide a pooled community sample to estimate total infections that is independent of case reporting biases toward individuals with moderate to severe symptoms and by test-seeking behavior and access. We derive three mechanistic models for estimating community infection levels from wastewater measurements based on a description of the processes that generate SARS-CoV-2 RNA signals in wastewater and accounting for the fecal strength of wastewater through endogenous microbial markers, daily flow, and per-capita wastewater generation estimates. The models are illustrated through two case studies of wastewater data collected during 2020-2021 in Virginia Beach, VA, and Santa Clara County, CA. Median simulated infection levels generally were higher than reported cases, but at times, were lower, suggesting a discrepancy between the reported cases and wastewater data, or inaccurate modeling results. Daily simulated infection estimates showed large ranges, in part due to dependence on highly variable clinical viral fecal shedding data. Overall, the wastewater-based mechanistic models are useful for normalization of wastewater measurements and for understanding wastewater-based surveillance data for public health decision-making but are currently limited by lack of robust SARS-CoV-2 fecal shedding data.

Assessing environmentally significant effects: a better strength-of-evidence than a single P value?

Interpreting a P value from a traditional nil hypothesis test as a strength-of-evidence for the existence of an environmentally important difference between two populations of continuous variables (e.g. a chemical concentration) has become commonplace. Yet, there is substantial literature, in many disciplines, that faults this practice. In particular, the hypothesis tested is virtually guaranteed to be false, with the result that P depends far too heavily on the number of samples collected (the 'sample size'). The end result is a swinging burden-of-proof (permissive at low sample size but precautionary at large sample size). We propose that these tests be reinterpreted as direction detectors (as has been proposed by others, starting from 1960) and that the test's procedure be performed simultaneously with two types of equivalence tests (one testing that the difference that does exist is contained within an interval of indifference, the other testing that it is beyond that interval-also known as bioequivalence testing). This gives rise to a strength-of-evidence procedure that lends itself to a simple confidence interval interpretation. It is accompanied by a strength-of-evidence matrix that has many desirable features: not only a strong/moderate/dubious/weak categorisation of the results, but also recommendations about the desirability of collecting further data to strengthen findings.

Explaining differential sources of zoonotic pathogens in intensively-farmed catchments using kinematic waves.

Surveys in streams draining intensively farmed catchments can, during flood events, indicate differential time-concentration patterns between a bacterial health-risk indicator (E. coli) and a major zoonotic pathogen that it seeks to indicate-Campylobacter. The indicator's peak concentration at a monitoring station can arrive ahead of the flood peak (the pollutograph leads the hydrograph), whereas the peak pathogen concentration arrives with the flood peak (the pollutograph and hydrograph peaks coincide). In other cases the E. coli pollutograph can lag the hydrograph. These observations have generated the hypothesis that such behaviour reflects three different possible (predominant) sources of pathogens in the floodwater: (i) by sediment entrainment, (ii) via local land runoff, or (iii) from upstream releases (e.g., from dams, inflows, or upstream floods). A general theory for contaminants in idealized stream floods has been developed, considering all three sources, based on kinematic wave theory. It can explain the observed differential time-concentration patterns. The calculation procedures and associated results are intended to inform public policy, by identifying predominant pathogen sources and therefore helping to focus attention on the important delivery mechanisms. This will better inform quantitative health risk assessments for downstream water users (recreational uses, water supplies, food production and processing industries).

Has Water Quality Improved or Been Maintained? A Quantitative Assessment Procedure.

Many policies require reporting on water quality trends. This is usually addressed by testing a hypothesis positing that there was zero slope in some parameter of the sampled population over a given period. Failure to achieve "statistical significance" is often falsely interpreted as evidence that there was no trend of concern-the -value of these tests can become ever smaller as the sample size increases and so also can the detectable trend. To avoid this problem, a new trend direction assessment (TDA) procedure is proposed, based on a formulation in psychological literature that considers error risks when inferring the direction of differences between two population means. The TDA procedure abandons testing altogether and instead calculates probabilities that water quality variables have been increasing or decreasing. Nominated probability breakpoints then give rise to a graduated scale in which phrases such as "extremely likely" or "unlikely" can be used to summarize results, avoiding casting many into a "not statistically significant" box. This trend assessment procedure requires no more information than a traditional test, for which the significance level is reinterpreted as a misclassification error rate (inferring an increase when in fact there was a decrease, or vice versa). Example applications of this procedure to small and large datasets are given. This procedure also possesses a possible framework that addresses the more complex question of whether water quality has been "maintained," in which a trend magnitude of environmental significance must be defined. The TDA procedure may be applied to any environment, not just water quality.

Large-scale freshwater microbiological study: rationale, results and risks.

A fifteen-month fortnightly survey of microbial health risk indicators and pathogens has been carried out at 25 freshwater recreational and water supply sites distributed throughout New Zealand, for: E. coli, Clostridium perfringens spores, F-RNA bacteriophage, somatic coliphage, human enteroviruses, human adenoviruses, Cryptosporidium oocysts, Giardia cysts, Salmonella and Campylobacter. Sites were selected to represent five geographical areas covering New Zealand and five categories of predominant environmental impact: birds, dairy farming, forestry/undeveloped, municipal, and sheep/pastoral farming. Six of the sites were also source waters for treated drinking-water supplies. Of the indicators, E. coli was detected in 99 % of all samples, with somatic coliphage being detected most of the time (89 %). Of the pathogens tested, Campylobacter and human adenoviruses were inferred to be the most likely to cause human waterborne illness to recreational freshwater users. Using data from all sites, an estimated 5 % of notified campylobacteriosis cases in New Zealand could be attributable to water contact recreation. The critical value for E. coli as an indicator of increased Campylobacter infection is in the range of 200-500 E. coli per 100 ml. This result has been used to derive new national water quality guidelines for recreational fresh water in New Zealand.

Statistical Considerations in Environmental Microbial Forensics.

In environmental microbial forensics, as in other pursuits, statistical calculations are sometimes inappropriately applied, giving rise to the appearance of support for a particular conclusion or failing to support an innately obvious conclusion. This is a reflection of issues related to dealing with sample sizes, the methodologies involved, and the difficulty of communicating uncertainties. In this brief review, we attempt to illustrate ways to minimize such problems. In doing so, we consider one of the most common applications of environmental microbial forensics-the use of genotyping in food and water and disease investigations. We explore three important questions. (i) Do hypothesis tests' P values serve as adequate metrics of evidence? (ii) How can we quantify the value of the evidence? (iii) Can we turn a value-of-evidence metric into attribution probabilities? Our general conclusions are as follows. (i) P values have the unfortunate property of regularly detecting trivial effects when sample sizes are large. (ii) Likelihood ratios, rather than any kind of probability, are the better strength-of-evidence metric, addressing the question "what do these data say?" (iii) Attribution probabilities, addressing the question "what should I believe?," can be calculated using Bayesian methods, relying in part on likelihood ratios but also invoking prior beliefs which therefore can be quite subjective. In legal settings a Bayesian analysis may be required, but the choice and sensitivity of prior assumptions should be made clear.

Confidence of compliance: parametric versus nonparametric approaches.

Previous classical and Bayesian formulations of compliance assessment rules based on a nonparametric approach are compared with formulations based on the assumption that compliance assessment data have been randomly drawn from a normal population with unknown mean and variance. Graphs of parametric (Bayesian) "Confidence of Compliance" curves are presented. With one exception it is concluded that compliance rules based on a nonparametric approach are the more robust, as their formulation does not depend on any assumption as to the nature of the parent distribution and because rules devised under either approach are generally similar. The exception occurs for rules based on minimizing the consumer's risk (i.e., environment's risk) when a large number of samples are to hand and goodness-of-fit tests give strong grounds for the assumption of a normal parent. In that case the parametric compliance rule--either Bayesian or classical--becomes rather less strict.

Uncertainty in most probable number calculations for microbiological assays.

Microbiological assays commonly use incubations of multiple tubes in a dilution series, and microorganism concentration is read as a most probable number (MPN) in standard tables for the observed pattern of positive tubes. Published MPN tables differ, sometimes substantially, because of use of approximate MPN calculation procedures, different rounding conventions in the results, and different methods of calculating confidence or credible intervals. We conclude that the first 2 issues can now be resolved by using recently developed exact MPN calculation methods and by reporting rounding conventions in standard tables. The third issue is not amenable to complete resolution, especially if credible interval (as opposed to confidence interval) limits are desired--as we think they most often are. In that case, Bayesian statistics are called for and the analyst must provide a distribution of concentration that was presumed to be true before the assay was performed. This is mathematically combined with the assay data, resulting in a posterior concentration distribution. These distributions may then be used to quantify the uncertainty in the MPN estimate, and the best approach is to use the highest posterior density regions of these distributions. If based on diffuse prior information (positing that, prior to an assay being performed, all positive concentrations are equally likely), then established procedures might be used to calculate the limits and publish them in standard tables. In the event that this prior assumption is held to be not satisfactory, we show results for an empirical Bayes procedure, with a Poisson prior distribution, giving credible interval widths much narrower than in the other cases examined.

Adenovirus-associated health risks for recreational activities in a multi-use coastal watershed based on site-specific quantitative microbial risk assessment.

We used site-specific quantitative microbial risk assessment (QMRA) to assess the probability of adenovirus illness for three groups of swimmers: adults with primary contact, children with primary contact, and secondary contact regardless of age. Human enteroviruses and adenoviruses were monitored by qPCR in a multi-use watershed and Adenovirus type 40/41 was detected in 11% of 73 samples, ranging from 147 to 4117 genomes per liter. Enterovirus was detected only once (32 genomes per liter). Seven of eight virus detections occurred when E. coli concentrations were below the single sample maximum water quality criterion for contact recreation, and five of eight virus detections occurred when fecal coliforms were below the corresponding criterion. We employed dose-harmonization to convert viral genome measurements to TCID50 values needed for dose-response curves. The three scenarios considered different amounts of water ingestion and Monte Carlo simulation was used to account for the variability associated with the doses. The mean illness risk in children based on adenovirus measurements obtained over 11 months was estimated to be 3.5%, which is below the 3.6% risk considered tolerable by the current United States EPA recreational criteria for gastrointestinal illnesses (GI). The mean risks of GI illness for adults and secondary contact were 1.9% and 1.0%, respectively. These risks changed appreciably when different distributions were fitted to the data as determined by Monte Carlo simulations. In general, risk was at a maximum for the log-logistic distribution and lowest for the hockey stick distribution in all three selected scenarios. Also, under default assumptions, the risk was lowered considerably when assuming that only a small proportion of Adenovirus 40/41 (3%) was as infectious as Adenovirus type 4, compared to the assumption that all genomes were Adenovirus 4. In conclusion, site-specific QMRA on water-borne adenoviruses in this watershed provided a similar level of protection against public health risks as would be obtained by enumeration of fecal indicator bacteria under the new U.S. EPA guidelines.

Discharge-based QMRA for estimation of public health risks from exposure to stormwater-borne pathogens in recreational waters in the United States.

This study is the first to report a quantitative microbial risk assessment (QMRA) on pathogens detected in stormwater discharges-of-concern, rather than relying on pathogen measurements in receiving waters. The pathogen concentrations include seven "Reference Pathogens" identified by the U.S. EPA: Cryptosporidium, Giardia, Salmonella, Norovirus, Rotavirus, Enterovirus, and Adenovirus. Data were collected from 12 sites representative of seven discharge types (including residential, commercial/industrial runoff, agricultural runoff, combined sewer overflows, and forested land), mainly during wet weather conditions during which times human health risks can be substantially elevated. The risks calculated herein therefore generally apply to short-term conditions (during and just after rainfall events) and so the results can be used by water managers to potentially inform the public, even for waters that comply with current criteria (based as they are on a 30-day mean risk). Using an example waterbody and mixed source, pathogen concentrations were used in QMRA models to generate risk profiles for primary and secondary water contact (or inhalation) by adults and children. A number of critical assumptions and considerations around the QMRA analysis are highlighted, particularly the harmonization of the pathogen concentrations measured in discharges during this project with those measured (using different methods) during the published dose-response clinical trials. Norovirus was the most dominant predicted health risk, though further research on its dose-response for illness (cf. infection) is needed. Even if the example mixed-source concentrations of pathogens had been reduced 30 times (by inactivation and mixing), the predicted swimming-associated illness rates - largely driven by Norovirus infections - can still be appreciable. Rotavirus generally induced the second-highest incidence of risk among the tested pathogens while risks for the other Reference Pathogens (Giardia, Cryptosporidium, Adenovirus, Enterovirus and Salmonella) were considerably lower. Secondary contact or inhalation resulted in considerable reductions in risk compared to primary contact. Measurements of Norovirus and careful incorporation of its concentrations into risk models (harmonization) should be a critical consideration for future QMRA efforts. The discharge-based QMRA approach presented herein is particularly relevant to cases where pathogens cannot be reliably detected in receiving waters with detection limits relevant to human health effects.

Modification, calibration and verification of the IWA River Water Quality Model to simulate a pilot-scale high rate algal pond.

We implemented the IWA River Water Quality Model No. 1 (Reichert et al., 2001. River Water Quality Model No. 1, IWA Scientific & Technical Report No. 12) to simulate water-quality characteristics in two pilot-scale High Rate Algal Ponds. Simulation results were compared with two years' of data from the ponds. The first year's data from one pond were used for model calibration; the remaining data were used for validation. As originally formulated and parameterized, the model consistently yielded summer-time algal biomass concentrations which were too low - with consequent failures in its reproduction of dissolved oxygen, pH and nutrient dynamics. We experimented with various structural/parametric changes to improve the model's performance. The most effective strategy was to greatly increase the respiratory losses suffered by the heterotrophic osmotrophs (thereby giving the algae access to a larger fraction of the incoming dissolved organic carbon and nitrogen). This suggests that CO(2)-bubbling alone cannot entirely preclude resource-limitation of algal production. We doubt that our parameterization of heterotrophic osmotrophs is correct and infer that the algae derive a large fraction of their nutrition by direct osmotrophic uptake of dissolved organic matter. This inference is supported by the literature concerning the physiology of the dominant algal species in our ponds.