Toxicological risk analysis is at a crossroads. The traditional approach using worst case analysis is widely regarded as fundamentally flawed since it yields conclusions that are often strongly biased and presumed hyperconservative. Probabilistic analysis using Monte Carlo simulation can yield overly optimistic conclusions when used without information about the correlation structure among variables. What is needed is a conservative methodology that makes no assumptions unwarranted by empirical evidence. To be conservative means both that the estimated risk is not systematically lower than the actual impact, but also that the uncertainty around the estimate is not narrower than justified by the available data. An appropriate methodology is dependency bounds analysis which computes bounds on the distributions for arithmetic operations on random variables when only their marginal distributions are known. Used in a risk analysis, it yields conservative results because it does not depend on knowledge about the correlation structure among all of the variables used in the analysis.
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