Quantitative microbial risk assessment: uncertainty and measures of central tendency for skewed distributions |
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Authors: | K K Benke A J Hamilton |
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Institution: | (1) Department of Primary Industries, Primary Industries Research Victoria, Parkville Centre, PO Box 4166, Parkville, VIC, 3052, Australia;(2) School of Life and Environmental Sciences, Deakin University, PO Box 423, Warrnambool, VIC, 3280, Australia;(3) School of Resource Management, Faculty of Land and Food Resources, The University of Melbourne, 500 Yarra Boulevard, Richmond, VIC, 3121, Australia |
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Abstract: | In the past, arithmetic and geometric means have both been used to characterise pathogen densities in samples used for microbial
risk assessment models. The calculation of total (annual) risk is based on cumulative independent (daily) exposures and the
use of an exponential dose–response model, such as that used for exposure to Giardia or Cryptosporidium. Mathematical analysis suggests that the arithmetic mean is the appropriate measure of central tendency for microbial concentration
with respect to repeated samples of daily exposure in risk assessment. This is despite frequent characterisation of microbial
density by the geometric mean, since the microbial distributions may be Log normal or skewed in nature. Mathematical derivation
supporting the use of the arithmetic mean has been based on deterministic analysis, prior assumptions and definitions, the
use of point-estimates of probability, and has not included from the outset the influence of an actual distribution for microbial
densities. We address these issues by experiments using two real-world pathogen datasets, together with Monte Carlo simulation,
and it is revealed that the arithmetic mean also holds in the case of a daily dose with a finite distribution in microbial
density, even when the distribution is very highly-skewed, as often occurs in environmental samples. Further, for simplicity,
in many risk assessment models, the daily infection risk is assumed to be the same for each day of the year and is represented
by a single value,
which is then used in the calculation of p
Σ, which is a numerical estimate of annual risk, P
Σ, and we highlight the fact that is simply a function of the geometric mean of the daily complementary risk probabilities (although it is sometimes approximated
by the arithmetic mean of daily risk in the low dose case). Finally, the risk estimate is an imprecise probability with no
indication of error and we investigate and clarify the distinction between risk and uncertainty assessment with respect to
the predictive model used for total risk assessment. |
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Keywords: | Cryptosporidium Dose– response Pathogen Risk Simulation Uncertainty |
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