100 Other risk characterization outputs of interest are:
- the risk per contaminated serving,
p s
cs
R
,
, that is the probability of illness following the
consumption of a random contaminated serving by an individual in population p
Elderly, Immunocompromised, Pregnant or General in the country c. A contaminated serving is defined as a serving including one or more cells of L. monocytogenes;
- the prevalence of contaminated servings, P
s
, that is, the probability that a random serving of cheese contains one or more cells of L. monocytogenes.
Recall that all of these outputs are distributions that describe how the risk output varies over a reference population of interest. For simplicity, we will provide some statistics characterizing
these distributions such as the mean, the standard deviation and some quantiles.
The number of cases per year will not be provided due to the unknown number of servings in the population.
8.2. Estimator for the Risk Outputs
The risk outputs of interest cannot be extracted directly from the literature but, rather, are synthesized by using a set of mathematical models and equations that link several input
parameters to the risk outputs see Appendix, section “Model Documentation”. Stochastic, uncertain inputs then yield stochastic, uncertain outputs whose distributions can be evaluated
either analytically or by simulation.
Because the overall integration of the model to derive the final distribution of each of the risk outputs is analytically intractable, a Monte-Carlo simulation was used. Monte-Carlo simulation
is a simulation sampling method: input parameters’ values are sampled from their input distributions, thus simulating the action of sampling from the inputs’ variability distributions,
subject to our uncertainty. The modeled risk output calculated using those inputs propagates the inputs’ variability and acts as a sample from the risk output’s probability distribution, subject to
our uncertainty about the inputs.
101 This computer-intensive framework allows a random sample from the analytically intractable
distribution of the risk output to be obtained. Summary statistics that we produce from the simulated risk output Monte-Carlo sample converge to the corresponding summary statistics
from the risk output’s distribution in large enough simulations. Summary statistics about how those summary statistics change across the uncertainty about inputs, converge to an expression of
our uncertainty about the risk output’s distribution in large enough simulations.
The estimator’s specification is generally completed by referring to the Monte-Carlo simulation size below, sampling method, and randomization method. The estimators’ characteristics,
convergence properties and standard errors are examined in the Appendix section “Simulation Estimator Characteristics for the Risk Outputs”.
