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 margin of exposure (MOE), more general as used in the MCRA output H/E; or a hazard index (HI), as used in MCRA E/H, comparing exposures and hazard characterizations at the chosen level (external or internal). Hazard characterisations are included as single values or in a probabilistic way.
Figure 104 Risk (exposure/hazard) total distribution (triazoles).
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 \(H/E\) ratio distribution below the (safety/uncertainty) threshold (or the proportion of the \(E/H\) ratio distribution above e.g. 0.01 (in general 1) is the probability of critical effect (POCE), here 13%, 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.
Figure 105 Uncertainty of percentiles.The boxplots for uncertainty show the p25 and p75 as edges of the box, and p2.5 and p97.5 as edges of the whiskers. The reference (nominal) value is indicated with the dashed black line, the median with the solid black line within the box. Outliers are displayed as dots outside the wiskers. Risk is specified as the ratio exposure/hazard (triazoles).
In Figure 106, the risk ratios exposure/hazard 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 106 Risk ratio (exposure/hazard) plot for multiple substances (triazoles). The threshold (0.01) is indicated with the left vertical line, the vertical black line on the right indicates threshold value = 1.
In Figure 107, hazards versus exposures are plotted for the same substances.
Figure 107 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 (ratio H/E) and hazard index (ratio E/H):
exposures are cumulated over substances using RPFs and the risk distribution is estimated based on the hazard characterisation of the reference substance and the cumulative exposure. All RPFs should be supplied. See also cumulative RPF weighted risk distribution.
risk is calculated per substance as a ratio of each hazard characterization and the exposure. Then, the risk is estimated as the cumulated sum of ratios over all substances. All hazard characterisations should be supplied. In formula:
For the risk ratio \(E/H\):
where summation is over the number of substances per individual(day).
For the risk ratio \(H/E\):
where summation is over the number of substances per individual(day).
Figure 108 Cumulative risk exposure/hazard ratios (median) in the population (metals).
The blue line indicates the median value of the cumulative risks in the population. Note that the cumulative sum of the medians of the risk ratios of the contributing substances, here metals (red areas) does not necessarily add up to the cumulative risk (blue line). Simulations with multivariate lognormal distributions without correlation suggest that for moderate percentiles like the median the cumulative risk is higher than the risk calculated as sum of ratios.
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.