A Bootstrap Prediction Confidence Band for QMRA Beta-Poisson Dose-Response Models

microbial risks associated with food, water, and wastewater use in agriculture (e.g., [1, 3, 5]). The core part of the QMRA framework is the dose-response analysis which models the mathematical characterization of the relationship between the dose administered and the probability of adverse effect (typically, the probability of infection) in the exposed population [1, 2, 6]. Among different microbial dose-response models proposed in the literature, the beta-Poisson models remain the most popular plausible models in practice [1, 2, 7].The beta-Poisson dose-response model and its special case, the exponential doseresponse model have been well studied and widely employed to characterize infectivity of various viral, bacterial, and protozoan pathogens since the 1980s [1, 2, 7, 8]. Because a beta-Poisson model has two parameters, a confidence band about the doseresponse curve cannot be calculated directly from the confidence intervals of the parameter estimates. It is well accepted in QMRA practice to employ a parametric bootstrap algorithm [9] to construct a confidence band for the dose-response curve[1, 2, 8, 10].The upper limit of the estimated confidence band is used as the worst case scenario in risk assessment.