Taking into account variability and uncertainty in exposure - - PowerPoint PPT Presentation
Taking into account variability and uncertainty in exposure assessment Prise en compte de la variabilit et de l'incertitude sur lvaluation de l'exposition Marie Cornu, Rgis Pouillot, Afssa 1 Exposure assessment "Exposure
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European Commission, 2003
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Fictive examples :
while most individuals eat no Lm and others eat 106 cfu/meal !!!
while the 1% estimate is not known with precision and may vary from 0.0005% to 10% depending on the assumptions!!!
are considered
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Variability represents a true heterogeneity of the population that is a consequence of the physical system and irreducible (but better characterized) by further measurements. Variability between sub-populations
infants/children/teenagers/adults, male versus female…
from one serving (cocktail) to another (main meal)…
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Uncertainty due to necessary selection of processes to model
Uncertainty due to necessary simplification of modelled processes
Analytical uncertainty (measurement errors) Sampling uncertainty (too small samples)
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at the time of consumption
parameters
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Empirical cumulative distributions of smoked seafood serving sizes (USA population)
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ÿ t0 = consumption (e.g. Lindqvist & Westöö, 2000)
ÿ t0 = end of processing or retail (e.g. FDA, 2003)
ÿ t0 = primary production (e.g. Bemrah et al., 1998)
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Miconnet et al., submitted
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Use in inference: Fitted to growth curves Use in simulation: Predicts the evolution of the population along time Parameters: N0, λ (or lag or or q0), µ (or µmax or d.t.), Nmax (or MPD) Models: modified Gompertz, lag exponential, logistic with delay, Baranyi, … Use in inference: Fitted to observed growth rates (or lag times) Use in simulation: Predicts the effect of environment (temperature, pH, aw…) Parameters: regression meaningless coefficients, or cardinal values Models: polynomial models, cardinal models, gamma models…
van Gerwen & Zwietering, 1998.
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ÿDistributions of (t,θ) or of scores (Rosset et al., submitted)
ÿDistribution of µopt or b2 (FDA, 2003) or of (pH, aw…)
ÿOften neglected (confused with uncertainty)
ÿVariability of the growth rate at one temperature (Bergis et al., 2004), and/or cardinal values (Tmin…) (Pouillot et al., 2003)
ÿOften neglected (confused with uncertainty)
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ß Primary growth model error ß Secondary growth model error on µ ß Secondary growth model error on λ
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Variability distribution : X ~ Gaussian (Mean, Standard deviation) Uncertainty distribution on its parameters : Mean ~ BetaPert (Min, MP, Max)
X ~ BetaPert (min, most probable, max) with a "confidence level" p X ~ Gaussian (mean, standard deviation) with a "confidence level" 1-p
Variability empirical distribution: X ∈ {1, 3, 5, …, 7} Uncertainty distribution of variability distributions: X ∈ {1, 3, 5, …, 7} or {1, 3, 3, …, 7} or {3, 3, 3, …, 7} or {1, 5, 5, …, 7}…
Similar to non parametric Bootstrap, with a variability parametric distribution
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Uncertainty”
arbitrary
uncertainty (using hyperparameters) and to evaluate exposure in a single step
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at the time of consumption
parameters
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Uncertain fixed parameters
Simulation MC #1
Uncertain fixed parameters
Simulation MC #2
Uncertain fixed parameters
Simulation MC #1000
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and uncertainty sources are (explicitly or not) neglected
leaded by feasibility, and not by sounded sanitary/scientific reasons !
as possible) questionned
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Bemrah et al., 1998. Quantitative risk assessment of human listeriosis from consumption of soft cheese made from raw milk. Prev. Vet. Med. 37:129-145 Bergis et al., 2004. Variability of growth of L. monocytogenes in artificially contamainted cold- smoked salmon. Poster in this conference. European commission, 2003. Risk assessment of food borne bacterial pathogens:Quantitative methodology relevant for human exposure assessment. http://europa.eu.int/comm/food/fs/sc/ssc/out308_en.pdf FDA/USDA (2003). Quantitative assessment of relative risk to public health from foodborne L. monocytogenes among selected categories of ready-to-eat foods. http://www.foodsafety.gov/~dms/Lmr2-toc.html Lindqvist & Westöö, 2000. Quantitative risk assessment for L. monocytogenes in smoked or gravad salmon and rainbow trout in Sweden. Int J Food Microbiol 58, 181-96. Miconnet et al., accepted. Uncertainty distribution associated with estimating a proportion in microbial risk assessment Risk Analysis Pouillot et al., 2003. Estimation of uncertainty and variability in bacterial growth using Bayesian
Rosset et al., accepted. Time-temperature profiles of chilled ready-to-eat foods in school catering and probabilistic analysis of L. monocytogenes growth. Int. J. Food Microbiol van Gerwen & Zwietering, 1998. Growth and inactivation models to be used in quantitative risk