Table A.3.

Short summary of what each method contributes to uncertainty analysis, illustrated by examples for the melamine case study. Some methods provide inputs to the analysis (shown in italics), while others contribute to the output (shown in quotes). The right hand column provides a link to more detail

Method	Short summary of contribution Examples based on melamine case study. Apparent conflicts between results are due to differing assumptions made for different methods.	Section no.
Descriptive expression	Contribution to output: ‘Exposure of children could potentially exceed the TDI by more than threefold, but it is currently unknown whether such high level scenarios occur in Europe’	B.1.
Ordinal scale	Contribution to output: ‘The conclusion of the risk assessment is subject to “Medium to high” uncertainty’	B.2.
Matrices for confidence/uncertainty	Contribution to output: ‘The conclusion of the risk assessment is subject to “Low to medium” to “Medium to high” confidence’	B.3.
NUSAP	Contribution to output: ‘Of three parameters considered, consumption of Chinese chocolate contributes most to the uncertainty of the risk assessment’	B.4.
Uncertainty tables for quantitative questions	Contribution to output: ‘The worst case exposure is estimated at 269% of the TDI but could lie below 30% or up to 1,300%’	B.5.
Uncertainty tables for categorical questions	Contribution to output: ‘It is Very likely (90–100% probability) that melamine has the capability to cause adverse effects on kidney in humans’ (Hazard assessment)	B.6.
Interval analysis	Contribution to output: ‘The worst case exposure is estimated to lie between 11 and 66 times the TDI’	B.7.
Expert knowledge elicitation	Input to uncertainty analysis: A distribution for use in probabilistic calculations, representing expert judgement about the uncertainty of the maximum fraction of milk powder used in making milk chocolate	B.8. and B.9.
Confidence intervals	Input to uncertainty analysis: 95% confidence intervals representing uncertainty due to sampling variability for the geometric mean and standard deviation of body weight were (10.67, 11.12) and (1.13, 1.17) respectively	B.10.
The bootstrap	Input to uncertainty analysis: A bootstrap sample of values for mean and standard deviation of log body‐weight distribution, as an approximate representation of sampling uncertainty for use in probabilistic calculations	B.11.
Bayesian inference	Input to uncertainty analysis: Distributions quantifying uncertainty due to sampling variability about the mean and standard deviation of log body weight, for use in probabilistic calculations	B.12.
Probability bounds	Contribution to output: ‘There is at most a 10% chance that the worst case exposure exceeds 37 times the TDI’	B.13.
1D Monte Carlo (uncertainty only)	Contribution to output: ‘There is a 95% chance that the worst case exposure lies between 14 and 30 times the TDI, with the most likely values lying towards the middle of this range’	B.14.
2D Monte Carlo (uncertainty and variability)	Contribution to output: ‘There is a 95% chance that the percentage of 1–2 year old children exceeding the TDI is between 0.4% and 5.5%, with the most likely values lying towards the middle of this range’	B.14.
Deterministic calculations with conservative assumptions	Contribution to output: ‘The highest estimate of adult exposure was 120% of the TDI, while for children consuming both biscuits and chocolate could potentially exceed the TDI by more than threefold’	B.16.
Sensitivity analysis (various methods)	Contribution to output: ‘Exposure is most sensitive to variations in melamine concentration and to a lesser extent chocolate consumption’	B.17.