Risks calculation

A (cumulative) risk assessment aims to characterise the health impact due to exposure to one or multiple substances causing common adverse health effects. The health impact is characterized by a distribution of individual risks, expressed by a risk metric (i.e., a margins of exposure (MOE) or a hazard index (HI)) comparing exposures and hazard characterizations at the chosen level (external or internal). Hazard characterisations are included as single values or in a probabilistic way.

The aim is to specify the probability that a random individual from a defined (sub)population will have an exposure high enough to cause a particular health effect of a predefined magnitude, the critical effect size. The exposure level that results in exactly that critical effect in a particular person is that person’s individual critical hazard dose (ICED). Individuals in a population typically show variation, both in their individual exposure and in their hazard characterization. Both the variation in exposure and the variation in hazard characterization are quantified in the form of probability distributions. Assuming independence between both distributions, they are combined by Monte Carlo methods. The proportion of the MOE distribution below the (safety/uncertainty) threshold (or the proportion of the HI distribution above 1) is the probability of critical exposure (POCE) in the particular (sub)population. Uncertainties involved in the overall risk assessment (i.e., both regarding exposure and hazard characterisation) are quantified using Monte Carlo and bootstrap methods. This results in an uncertainty distribution for any statistic of interest.

In Figure 91, margin of exposures for a number of substances are shown. As shown, the distinction between variability (grey bars, 90% probability) and uncertainty (whiskers) is retained. This is discussed in van der Voet and Slob (2007) and van der Voet et al. (2009).

Figure 91 Individual margin of exposure (MOE) plot for multiple substances.

In Figure 92, hazards versus exposures are plotted for the same substances.

Figure 92 Hazard vs. exposure plot for multiple substances. 95% bivariate confidence areas for target hazard dose distribution and exposure distribution. Inner ellipses express variability, outer ellipses uncertainty.

Inverse distribution

Risk can be calculated as a distribution of either margin of exposure (MOE) or hazard index (HI), if at least one of the inputs exposure and hazard characterisation is a distribution. The risk distribution is characterised by percentiles. To accommodate for matching results of MOE and HI in the case of percentiles, there is an option to calculate percentiles via the complementary percentile of the inverse distribution in order to handle numerical differences when calculating percentiles for a left or right tail. For example, the p1 percentile of the MOE distribution can optionally be calculated as 1 divided by p99 of the corresponding 1/MOE (i.e., HI) distribution.

Risk by food

The option calculate risks by modelled foods is available when the target dose level is external. Dietary exposures preserving all the information of exposures of modelled foods are used to calculate risks statistics for modelled foods and to calculate the percentages at risk of modelled foods in the background and foreground based on the specified threshold in the safety plot.