Estimators of annual probability of infection for quantitative microbial risk assessment

Four estimators of annual infection probability were compared pertinent to Quantitative Microbial Risk Analysis (QMRA). A stochastic model, the Gold Standard, was used as the benchmark. It is a product of independent daily infection probabilities which in turn are based on daily doses. An alternative and commonly-used estimator, here referred to as the Naïve, assumes a single daily infection probability from a single value of daily dose. The typical use of this estimator in stochastic QMRA involves the generation of a distribution of annual infection probabilities, but since each of these is based on a single realisation of the dose distribution, the resultant annual infection probability distribution simply represents a set of inaccurate estimates. While the medians of both distributions were within an order of magnitude for our test scenario, the 95th percentiles, which are sometimes used in QMRA as conservative estimates of risk, differed by around one order of magnitude. The other two estimators examined, the Geometric and Arithmetic, were closely related to the Naïve and use the same equation, and both proved to be poor estimators. Lastly, this paper proposes a simple adjustment to the Gold Standard equation accommodating periodic infection probabilities when the daily infection probabilities are unknown.