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 96, 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 96 Individual margin of exposure (\(MOE\)) plot for multiple substances.
In Figure 97, hazards versus exposures are plotted for the same substances.
Figure 97 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.
Risk metric calculation type
Currently, two types of risk metric calculation types are available. Both for the margin of exposure and hazard index:
exposures are cumulated over substancse using RPFs and the risk distribution is estimated based on the hazard characterisation of the reference substance and the cumulative exposure. See also cumulative RPF weighted risk distribution.
risk is calculated per pubstance as a ratio of each hazard characterization and the exposure. Then, the risk is estimated as the cumulated sum of ratios over all substances. In formula:
For the hazard index \(HI\):
where summation is over the number of substances per individual(day).
For the margin of exposure or more precise \(MOET\):
where summation is over the number of substances per individual(day).
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. The option is especially useful for small data sets where percentile calculation is asymmetric in both tails. When set, the percentile is calculated as the inverse of the complementary percentage of the inverse distribution. E.g., the \(p_{1}\) of the \(\operatorname{MOE}\) distribution is calculated as 1/(\(p_{99}\) of 1/\(\operatorname{MOE}\) distribution); the \(p_{99}\) of the \(\operatorname{HI}\) distribution is calculated as 1/(\(p_{1}\) of 1/\(\operatorname{HI}\) 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.