The Beta Poisson dose-response model is not a single-hit model

The choice of a dose-response model is decisive for the outcome of quantita tive risk assessment. Single-hit models have played a prominent role in dos e-response assessment for pathogenic microorganisms, since their introducti on. Hit theory models are based on a few simple concepts that are attractiv e for their clarity and plausibility, These models, in particular the Beta Poisson model, are used for extrapolation of experimental dose-response dat a to low doses, as are often present in drinking water or food products. Un fortunately, the Beta Poisson model, as it is used throughout the microbial risk literature, is an approximation whose validity is not widely known. T he exact functional relation is numerically complex, especially for use in optimization or uncertainty analysis. Here it is shown that although the di screpancy between the Beta Poisson formula and the exact function is not ve ry large for many data sets, the differences are greatest at low doses-the region of interest for many risk applications. Errors may become very large , however? in the results of uncertainty analysis: or when the data contain little low-dose information. One striking property of the exact single-hit model is that it has a maximum risk curve, limiting the upper confidence l evel of the dose-response relation. This is due to the fact that the risk c annot exceed the probability of exposure, a property that is not retained i n the Beta Poisson approximation. This maximum possible response curve is i mportant for uncertainty analysis, and for risk assessment of pathogens wit h unknown properties.