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 variabilité et de l'incertitude sur l’évaluation de l'exposition Marie Cornu, Régis Pouillot, Afssa 1

Exposure assessment "Exposure assessment should provide an estimate with associated uncertainty of the (variability in) occurrence and level of the pathogen in a specified portion of a certain food at the time of consumption in a specified population." European Commission, 2003 2

Why should we consider variability and uncertainty? Fictive examples : • Variability • « The mean number of Lm per meal is 1… » says the expert while most individuals eat no Lm and others eat 10 6 cfu/meal !!! • Uncertainty • « 1% of individuals eat 10 2 Lm per meal … » says the expert while the 1% estimate is not known with precision and may vary from 0.0005% to 10% depending on the assumptions!!! • Risk management may differ whether or not variability and uncertainty are considered • this is not a statistician whim 3

Variability 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 • Examples: differences in serving sizes between infants/children/teenagers/adults, male versus female… • Variability within a (sub-) population • Examples: variability of serving sizes from one person to another, from one serving (cocktail) to another (main meal)… 4

Uncertainty Uncertainty represents our lack of knowledge and includes : • scenario uncertainty Uncertainty due to necessary selection of processes to model • model uncertainty Uncertainty due to necessary simplification of modelled processes • parameter uncertainty Analytical uncertainty (measurement errors) Sampling uncertainty (too small samples) 5

Contamination at t 0 (?) parameters Growth model Consumption Contamination at the time of consumption Monte Carlo Exposure 6

Consumption: consumption rates and serving sizes 7

Consumption variability Empirical cumulative distributions of smoked seafood serving sizes (USA population) 8

Consumption uncertainty • Uncertainty linked to data source • National individual dietary survey (e.g. INCA) • Reporting errors • Purchase database (e.g. Secodip) • Aggregated data / home • Uncertainty due to survey duration • Uncertaintly due to sample size • Usually relatively high sample sizes, depends of products: • Smoked salmon : 162 days of consumption / 21 000 recorded 9

Contamination: Prevalence and level of contamination 10

t 0 ? ÿ t 0 = consumption (e.g. Lindqvist & Westöö, 2000) • Prevalence • Level of contamination at the time of contamination • No growth model ÿ t 0 = end of processing or retail (e.g. FDA, 2003) • Prevalence • Level of contamination at the initial stage (end of processing or retail) • Growth model: storage conditions + growth parameters ÿ t 0 = primary production (e.g. Bemrah et al ., 1998) • Classical "farm-to-fork model" (including all sources of contamination) 11

Prevalence • Variability : • Between sub-categories: • Between-farm or between-factory (Miconnet et al ., submitted) • Between-season variability • Between-year variability (general decrease) • Variability within a sub-category: • Confused with uncertainty • Uncertainty: • Analytical uncertainty • Sensitivity and specificity, reproductibility • Sampling uncertainty (low sample sizes) • Bayesian approach: Beta priors • Frequentist approach: confidence distribution 12

2 cold-smoked salmon production sites 13 Miconnet et al ., submitted

Level of contamination (at t 0 ) • Variability : • Between sub-categories • Usually neglected • Variability within a sub-category • Use of histograms, distributions… • Uncertainty: • Analytical uncertainty • Censored data (< threshold), repeatability, reproducibility • Sampling uncertainty • Very low sample sizes 14

Growth modelling 15

Growth Models • Primary model Use in inference: Fitted to growth curves Use in simulation: Predicts the evolution of the population along time Parameters: N 0 , λ (or lag or or q 0 ), µ (or µ max or d.t .), N max (or MPD ) Models: modified Gompertz, lag exponential, logistic with delay, Baranyi, … • Secondary model Use in inference: Fitted to observed growth rates (or lag times) Use in simulation: Predicts the effect of environment (temperature, pH, a w …) Parameters: regression meaningless coefficients, or cardinal values Models: polynomial models, cardinal models, gamma models… van Gerwen & Zwietering, 1998. 16

Growth variability? • Environmental variability: • Variability of time-temperature conditions ÿ Distributions of ( t , θ ) or of scores (Rosset et al ., submitted) • Between-product variability ÿ Distribution of µ opt or b 2 (FDA, 2003) or of (pH, aw…) • Within-product variability ÿ Often neglected (confused with uncertainty) • L. monocytogenes variability: • Between-strain variability ÿ Variability of the growth rate at one temperature (Bergis et al., 2004), and/or cardinal values ( T min …) (Pouillot et al ., 2003) • Within-strain variability ÿ Often neglected (confused with uncertainty) 17

Growth uncertainty • Parameter uncertainty • Sampling uncertainty • Regression errors • Analytical uncertainty • Model uncertainty (or variability ?) ß Primary growth model error ß Secondary growth model error on µ ß Secondary growth model error on λ 18

Simulations 19

How to model separately V & U: input parameters • Hyperparameters / Embedded distributions Variability distribution : X ~ Gaussian (Mean, Standard deviation) Uncertainty distribution on its parameters : Mean ~ BetaPert (Min, MP, Max) • Probability trees X ~ BetaPert (min, most probable, max) with a "confidence level" p X ~ Gaussian (mean, standard deviation) with a "confidence level" 1- p • Non-parametric Bootstrap 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}… • Parametric Bootstrap Similar to non parametric Bootstrap, with a variability parametric distribution 20

How to model separately V & U: modelling • Point estimate of given percentiles • Insufficient and statistically incorrect • Monte-Carlo • Comparison of the model result including “Variability” vs “Variability and Uncertainty” • Second order simulation • need to separate variability from uncertainty which may be difficult / arbitrary • Bayesian method • The Bayesian framework allows to infer on parameter variability and uncertainty (using hyperparameters) and to evaluate exposure in a single step • but still difficult for complex models 21

Contamination at t 0 (?) parameters Growth model Consumption Contamination at the time of consumption Monte Carlo Exposure 22

2-dimensional Monte Carlo Uncertain fixed parameters Uncertain fixed parameters Uncertain fixed parameters Simulation Simulation Simulation MC #2 MC #1 MC #1000 … 23

Conclusion • Exposure assessment, only a part of a whole risk assessment • Integration of variability and uncertainty distributions in a global model • Selecting / neglecting variability and uncertainty sources • In most published risk assessments, some (or even most) variability and uncertainty sources are (explicitly or not) neglected • Selection of modelled variability and uncertainty distributions, often leaded by feasibility, and not by sounded sanitary/scientific reasons ! • Simplifying hypotheses have to be (at least) clearly stated and (as far as possible) questionned 24

References 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 inference. Application to L. monocytogenes . Int. J. Food Microbiol . 81:87-104. 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 assessments. J Food Prot 61, 1541-9. 25