Single value risks from individual risks
In this option, a percentage point can be specified for the chosen risk metric (margin of exposure (
Adjustment factors and uncertainty specification
Many sources of uncertainty that may affect input data, model assumptions and assessment methodology do not enter the assessment. In EFSA (2020a) and EFSA (2020b), thirty-four sources of uncertainty were identified and the impact of each source on the
To summarize, in the nominal run, the median of the uncertainty distribution is taken as adjustment factor. In each uncertainty run, the adjustment factor value is sampled from the uncertainty distribution. The adjustment factors for exposure and hazard are multiplied yielding the overall adjustment factor.
- Options for specifying uncertainty distributions are:
Gamma(a, b) with offset c, with shape and rate parameters a and b > 0.
Beta(a, b) scaled to the interval [
, d], with shape parameters a and b > 0.Lognormal(
, ) with offset . Parameters and specify the mean and standard deviation of the underlying normal.Log Student t(
, , ) with offset d. Parameters and specify the mean and standard deviation of the underlying normal, the degrees of freedom, > 0.
In the figures below, the consensus distributions of the experts for the combined impact of the quantified uncertainties affecting exposure are shown. When the larger part of the distribution is above 1, it is more likely that resolving the uncertainties will increase the median estimate. The vertical red line marks f = 1, where resolving the uncertainties would not change the calculated estimate.
Figure 109 Scaled gamma (a=3.26, b=3.56, offset=0.9), table 6, EFSA (2020a).
Figure 110 Scaled beta (a=2.37, b=4.26, lowerbound=0.5, upperbound=6), table 7, EFSA (2020a).
Figure 111 Scaled lognormal (
Figure 112 Scaled logstudents t (
Background-only adjustment factor
When exposures are calculated by combining focal food/substance concentrations with background concentrations, it may be appropriate to have a separate adjustment for the foreground and background. A pragmatic solution agreed with EFSA is to estimate the contribution of the foreground in the tail above the selected percentile. Suppose this contribution is
The calculation proceeds as follows:
Note that when the focal substance measurements are converted to active substances using substance conversions or deterministic substance conversions, then
In Figure 113, an example is shown where the margin of exposure is adjusted for the exposure and hazard distribution based on expert elicitation. The median adjustment factors for exposure and hazard are respectively, 1.77 and 3.01. The overall adjustment factor is 5.33.
Figure 113 Margin of exposure (model) and adjusted margin of exposure (model + expert) with uncertainty bounds.