Risk Analysis, Vol. 16, No. 4. I996 Quantifying Water Pathogen Risk in an Epidemiological Framework Joseph N. Ei~enberg,'.~ Edmund Y. W. Seto,' Adam W. Olivieri? and Robert C. Spear' Received September 20. 1995; revised Februaty 27, I996 Traditionally, microbial risk assessors have used point estimates to evaluate the probability that an individual will become infected. We developed a quantitative approach that shifts the risk char- acterization perspective from point estimate to distributional estimate, and from individual to pop- ulation. To this end, we first designed and implemented a dynamic model that tracks traditional epidemiological variables such as the number of susceptible, infected, diseased, and immune, and environmental variables such as pathogen density. Second, we used a simulation methodology that explicitly acknowledges the uncertainty and variability associated with the data. Specifically, the approach consists of assigning probability distributions to each parameter, sampling from these distributions for Monte Carlo simulations, and using a binary classification to assess the output of each simulation. A case study is presented that explores the uncertainties in assessing the risk of giardiasis when swimming in a recreational impoundment using reclaimed water. Using literature- based information to assign parameters ranges, our analysis demonstrated that the parameter de- scribing the shedding of pathogens by infected swimmers was the factor that contributed most to the uncertainty in risk. The importance of other parameters was dependent on reducing the a priori range of this shedding parameter. By constraining the shedding parameter to its lower subrange, treatment efficiency was the parameter most important in predicting whether a simulation resulted in prevalences above or below non outbreak levels. Whereas parameters associated with human exposure were important when the shedding parameter was constrained to a higher subrange. This Monte Carlo simulation technique identified conditions in which outbreaks and/or nonoutbreaks are likely and identified the parameters that most contributed to the uncertainty associated with a risk prediction. KEY WORDS: Microbial risk characterization; epidemiological model; Monte Carlo simulations; uncertainty and variability. 1. INTRODUCTION exposures to environmental chemicals and pathogens are often quite low, and empirical studies can no longer pro- duce sufficiently sensitive information to be the sole means of assessing these risks."' Therefore, methodolo- gies for this assessment have increasingly relied on in- direct measures of risk by using analytical models for the estimation of the intensity of human exposure and the probability of human response from this exposure. Attempts to provide a quantitative framework for the assessment of human health risks associated with the ingestion of waterborne pathogens have generally fo- To assess risks from biological, chemical, and physical agents in the environment, public health agen- ties have traditionally relied on epidemiology to provide a direct empirical assessment on risk. However, current I 140 Warren Hall, School of Public Health, University of California, Berkeley, California 94720. Eisenberg, Olivieri and Associates, 1400 Jackson St., Oakland, Cal- ifornia 94612. ' To whom all correspondence should be addressed. 549 ~~~~-~~~~~Y~~~x~o-o~~Y$oY 5O/1 o 1996 Society for R~sk AnalysisEisenberg, Seto, Olivieri, and Spear cused on static models that calculated the probability of individual infection or disease as a result of a single exposure event.(2-5) These models, all of the same generic form, are based on dose-response data which are used to fit a standard distribution function such as an expo- nential or beta function. This model structure does not provide ways to incorporate epidemiological data such as incubation period, immune status, duration of disease, and the rate of symptomatic development, or exposure data such as processes affecting the pathogen concentra- tion. These are all factors important in the disease pro- cess and necessary to be able to track variables such as the number of susceptible, infected, diseased, and im- mune within a population group. To take advantage of the available infectious dis- ease and dose-response data, we took a population per- spective in the development of a mathematical model that characterizes the human disease risk of waterborne pathogen exposure. Based on the host/microbe interac- tion, this approach makes explicit the mechanistic as- pects of the infectious disease process and provides a structure from which data are gathered. The existing dose-response model(23' was imbedded into an epide- miological framework, relying on a large base of literature describing the use of dynamic population mod- els in the study of epidemics.t6) These dynamic popula- tion models emphasize the importance of how the susceptible, infected, diseased, or immune status of in- dividuals within a defined population group vary over time. In addition to these four epidemiologically-based variables, our model incorporates a state variable to ac- count for the dynamics of pathogen concentration at the site of exposure. To provide a quantitative description of an infec- tious disease process requires a model that consists of a large number of parameters and state variables. A meth- odological problem with obtaining information from such a complex model is that the high levels of uncer- tainty and variability inherent in environmental proc- esses preclude the use of traditional parameter estimation techniques. In general, biological systems have a high degree of variability due to both genetic and other dif- ferences between individuals and environmental factors that are not explicitly modeled. In addition, data col- lected from biological systems contains uncertainty that primarily arises from the high cost of experimentation. The impact of high levels of uncertainty and variability is reflected in the type of data seen in the literature. For example, in an assessment of giardiasis, Veazie et report an average disease duration of 14.8 days with a range of 1-120. Shaw et a/.@) report that in half of the cases the disease lasted 7 days and a fourth more than
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