The use of two-stage Monte Carlo simulation techniques to characterize variability and uncertainty in risk analysis

Risk managers are generally interested in the range of risks in exposed populations, (e.g., the median and the 95th percentile). A range of risks in a population can reflect individual differences in behavior and susceptibility, as well as a range of contaminant levels in the environment. However, it is also important to characterize the degree of uncertainty in these risk estimates. This paper presents a method for quantifying uncertainty and variability separately in a Monte Carlo simulation. Variability is characterized by simulating risk while holding uncertain parameters constant, and uncertainty is characterized by varying these uncertain parameters between simulations, yielding a range of estimates for each summary statistic. This range quantifies the uncertainty in the risk for each percentile of the population and for various population measures, such as the mean. For example, the estimate of the risk for the 95th percentile of the population can be presented with confidence limits that describe the uncertainty for this value. The simulation output can also be used to determine which uncertain parameters have the greatest impact on the estimates of risk The method demonstrated in this paper includes an example of a cancer risk assessment at a Superfund site.