Risks calculation

‘A method is proposed for integrated probabilistic risk assessment where exposure assessment and hazard characterization are both included 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 (\(\mathit{CES}\)). The exposure level that results in exactly that \(\mathit{CES}\) in a particular person is that person’s individual critical effect dose (\(\mathit{ICED}\)). Individuals in a population typically show variation, both in their individual exposure (\(\mathit{IEXP}\)) and in their \(\mathit{ICED}\). Both the variation in \(\mathit{IEXP}\) and the variation in \(\mathit{ICED}\) are quantified in the form of probability distributions. Assuming independence between both distributions, they are combined (by Monte Carlo) into a distribution of the individual margin of exposure (\(\mathit{IMoE}\)). The proportion of the \(\mathit{IMoE}\) distribution below unity is the probability of critical exposure (\(\mathit{PoCE}\)) in the particular (sub)population. Uncertainties involved in the overall risk assessment (i.e., both regarding exposure and effect assessment) are quantified using Monte Carlo and bootstrap methods. This results in an uncertainty distribution for any statistic of interest, such as the probability of critical exposure (\(\mathit{PoCE}\)). The method is illustrated based on data for the case of dietary exposure to the organophosphate acephate. We present plots that concisely summarize the probabilistic results, retaining the distinction between variability and uncertainty. We show how the relative contributions from the various sources of uncertainty involved may be quantified.’ (abstract from [45]).

Figure 52 Individual Margin of Exposure (IMoE) plot for multiple chemicals.

A statistical model is presented extending the integrated probabilistic risk assessment (IPRA) model of van der Voet and Slob (2007) The aim is to characterise the health impact due to one or more chemicals present in food causing one or more health effects. For chemicals with hardly any measurable safety problems we propose health impact characterisation by margins of exposure. In this probabilistic model not one margin of exposure is calculated, but rather a distribution of individual margins of exposure (\(\mathit{IMoE}\)) which allows quantifying the health impact for small parts of the population. A simple bar chart is proposed to represent the \(\mathit{IMoE}\) distribution and a lower bound (\(\mathit{IMoEL}\)) quantifies uncertainties in this distribution. It is described how \(\mathit{IMoE}\) distributions can be combined for dose-additive compounds and for different health effects. Health impact assessment critically depends on a subjective valuation of the health impact of a given health effect, and possibilities to implement this health impact valuation step are discussed. Examples show the possibilities of health impact characterisation and of integrating \(\mathit{IMoE}\) distributions. The paper also includes new proposals for modelling variable and uncertain factors describing food processing effects and intraspecies variation in sensitivity.’ (abstract from: van der Voet et al, 2009 [46]).

Figure 53 Example of MCRA Hazard vs. Exposure plot for multiple chemicals. 95% bivariate confidence areas for target hazard dose distribution \(\mathit{ICED}\) and exposure distribution \(\mathit{IEXP}\). Inner ellipses express variability, outer ellipses uncertainty.