Sensitivity Analysis Risk Characterization Method

106 methods ANOVA and variance-based method Mokhtari and Frey 2005; Ellouze et al. 2010 were tested and gave similar results as the one presented in this report. 8.4.1. Changing one Factor at a Time One way to study the model is to evaluate the change in the output following the change in one input. In order to study the model, some artificial scenarios will be tested to evaluate their impact on the risk per serving for a specific country and a particular subpopulation say: Canada, Elderly. The tested scenarios are: - Environmental contamination: from pasteurized-milk cheese baseline contamination level section 6.4, Table 20-Table 21 to exactly 1, 10, 100, 1,000, 10,000, 100,000 cfucheese; and from pasteurized-milk cheese baseline prevalence section 6.4, Table 18 to prevalences less than the 20 point of that distribution; - Growth characteristics: from pasteurized-milk cheese baseline section 6.1, Table 12- Table 13 to EGR 20 s equal to 0, ½ baseline, 2 × baseline; from baseline section 6.1, Table 14 to maximum population densities equal to the baseline -1 log 10 or to the baseline +1 log 10 ; - Transport and Marketing temperature: pasteurized-milk cheese baseline -1°C, pasteurized-milk cheese baseline +1°C; - Temperature at Retail: pasteurized-milk cheese baseline -1°C, pasteurized-milk cheese baseline +1°C; - Home storage temperature: pasteurized-milk cheese baseline -1°C, pasteurized-milk cheese baseline +1°C; - Home storage duration: maximum duration of storage at home of 28 days compared to 56 days. 8.4.2. Rank Correlation The second method used is an evaluation of the Spearman’s rank correlation between inputs to the model and outputs of the model Frey and Patil 2002. This method’s output is frequently displayed as a “tornado chart.” While frequently used in risk assessment, this sensitivity analysis also remains rough Borgonovo 2006. Exploring interactions that could occur in the model is 107 difficult and the method is insensitive to several important types of dependence between output and inputs: non-linearity and thresholds. Considering both the variability and uncertainty, the following impacts of parameters on the final outputs were explored: i impact of variable parameters on outputs: for a specific input-output pair, one Spearman’s rank correlation may be estimated for each of the N u simulations, leading to N u Spearman’s rank correlations. The median, the 0.025 th quantile, and the 0.975 th quantile of these N u values may then be used as an estimate and credible interval of the Spearman’s rank correlation for that pair; ii impact of uncertain parameters on outputs: in the uncertainty dimension, one can estimate the Spearman’s rank correlation between uncertain parameters N u values and some statistics evaluated in the variability dimension, such as the mean or specific quantiles of the risk outputs’ variability.

9. Results of the Model Application Examples

9.1. Results of the Pasteurized-Milk Cheese Baseline Model

The baseline model for pasteurized-milk cheese uses two major inputsassumptions that distinguish it from other examples that we report: • The milk for cheese-making is “fully” pasteurized, meaning that no raw milk source L. monocytogenes survives the pasteurization process; • No testing procedures are implemented. All the other inputs are set as described in the previous sections: • Contamination with L. monocytogenes occurs during the ripening process; the level of contamination and the frequency of contaminated cheeses are inferred from Gombas et al. 2003 section 6.4; • Growth rate, lag time and maximum population density distributions among L. monocytogenes in cheeses section 6.1; • Storage time and storage temperature distributions among cheeses during transport and marketing and during retail, and among cheese servings during home storage section 7; 108 • Serving size distributions section 7.4.1. ; and, • Dose-response functions section 5. 9.1.1. Organization Risk Outputs Exposure assessment outputs of interest describe the distribution for the number of L. monocytogenes in soft-ripened cheese servings. We report that result in two parts: • distribution of the number of L. monocytogenes in contaminated servings; and, • prevalence of contaminated servings, that is, prevalence of servings that contain 1 or more L. monocytogenes. Risk characterization outputs of interest describe how the probability of illness invasive listeriosis varies: - from consuming a contaminated serving among the contaminated servings that subpopulations consume; and, - from consuming a serving contaminated or not contaminated among the servings that subpopulations consume. Tabled Results Structure The exposure assessment and risk characterization outputs vary among the individual units cheeses, servings, individuals in well-defined populations. We make well-defined populations more precise, in the context of reporting the risk outputs, in sections below. We organize the risk outputs’ results into tables, with features set both to meet the management charge and to help in reporting risk outputs’ variability. Each table contains results for a single risk output. Table columns separate results for populations country × subpopulation and table rows report summary statistics from the distribution variability of that risk output. Mean, median and variance do not adequately describe the shape of distributions as skewed as these risk outputs’ distributions are; so, tables’ summary statistics report several percentiles, including ones in the lower and upper tails, as well. Results in section 9.1.2. ignore parameter uncertainty; setting parameters to their most likely values describes only variability, as appropriate to context.