Single value risks from individual risks

In this option, a percentage point can be specified for the chosen risk metric (margin of exposure or hazard index). The corresponding percentile is calculated form the distribution of individual risks. The default percentiles are a margin of exposure at 0.1% or a hazard index at 99.9%, but another value can be chosen. Indicate whether the risk metric is calculated using the inverse distribution or not. This option is provided because percentile calculation in small data sets is asymmetric in both tails. When this option is set, the percentile is calculated as the inverse of the complementary percentage of the inverse distribution. E.g., the p0.1 of the MOE distribution is calculated as 1/(p99.9 of 1/MOE distribution); the p99.9 of the HI distribution is calculated as 1/(p0.1 of 1/HI distribution).

Adjustment factors

Many sources of uncertainty that may affect input data, model assumptions and assessment methodology do not enter the assessment. In EFSA 2020 [EFSA, 2020b], [EFSA, 2020a], thirty-four sources of uncertainty were identified and the impact of each source on the MOE was quantified. Some uncertainties tend to overestimate the MOE, others tend to underestimate it. Following the guidance of the EFSA Scientific Committee, specific MOE and/or HI percentiles are adjusted using adjustment factors, e.g. from expert elicitation. They may be available as fixed values or as parametric uncertainty distributions. In the nominal run, the percentile is adjusted with the median of the uncertainty distribution. In each uncertainty run, adjustment factors are sampled from the uncertainty distribution. In the MCRA interface, for both exposure and hazard distribution separately, a fixed value or a parametric uncertainty distribution is specified.

Options for specifying uncertainty distributions are:

  • Lognormal(mu, s) with offset c. Parameters mu and s specify the mean and standard deviation of the underlying normal.

  • Log Student t(mu, s, v) with offset d. Parameters mu and s specify the mean and standard deviation of the underlying normal, v the degrees of freedom, v > 0

  • Beta(a, b) scaled to the interval [c, d], with shape parameters a and b > 0.

  • Gamma(a, b) with offset c, with shape and rate parameters a and b > 0.

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Figure 56 Scaled lognormal (mu=0.705, s=0.566, offset=1), table 8, EFSA 2020 [EFSA, 2020b].

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Figure 57 Scaled logstudents t (mu=-0.593, s=0.367, v=3, offset=0.5), table 9, EFSA 2020 [EFSA, 2020b].

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Figure 58 Scaled beta (a=2.37, b=4.26, lowerbound=0.5, upperbound=6), table 7, EFSA 2020 [EFSA, 2020a].

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Figure 59 Scaled gamma (a=3.26, b=3.56, offset=0.9), table 6, EFSA 2020 [EFSA, 2020a].

Background-only adjustment factor

When exposures are calculated by combining focal food/substance concentrations with background concentrations, it may be appropriate to have 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 \(c\). Note that \(c\) will vary in uncertainty runs. Then, the adjustment factor should be multiplied by \((1-c)\), i.e. no adjustment for the focal part.

Calculation proceeds as follows:

  1. \(p_{MOE,adjusted} = p_{MOE} \cdot (1-c) \cdot \mathit{AdjustmentFactor}_{exposure} \cdot \mathit{AdjustmentFactor}_{hazard}\)

  2. \(p_{HI,adjusted} = p_{HI} / \left [(1-c) \cdot \mathit{AdjustmentFactor}_{exposure} \cdot \mathit{AdjustmentFactor}_{hazard} \right]\)

Note that when the focal substance measurements are converted to active substances using substance conversions or deterministic substance conversions, then \(c\) is the sum of the contributions of the focal food in and all active substances to which the substance translates.

In Figure 60, 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.

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Figure 60 Margin of exposure (model) and adjusted margin of exposure (model + expert) with uncertainty bounds.