This report presents guidelines for evaluating uncertainty in mathematical equations and computer models applied to assess human health and environmental risk. Uncertainty analyses involve the propagation of uncertainty in model parameters and model structure to obtain confidence statements for the estimate of risk and identify the model components of dominant importance. Uncertainty analyses are required when there is no a priori knowledge about uncertainty in the risk estimate and when there is a chance that the failure to assess uncertainty may affect the selection of wrong options for risk reduction. Uncertainty analyses are effective when they are conducted in an iterative mode. When the uncertainty in the risk estimate is intolerable for decision-making, additional data are acquired for the dominant model components that contribute most to uncertainty. This process is repeated until the level of residual uncertainty can be tolerated.
In this report, analytical and numerical methods for error propagation are presented along with methods for identifying the most important contributors to uncertainty. Monte Carlo simulation with either Simple Random Sampling (SRS) or Latin Hypercube Sampling (LHS) is proposed as the most robust method for propagating uncertainty through either simple or complex models. A distinction is made between simulating a stochastically varying assessment endpoint (i.e., the distribution of individual risks in an exposed population) and quantifying uncertainty due to lack of knowledge about a fixed but unknown quantity (e.g., a specific individual, the maximally exposed individual, or the mean, median, or 95%-tile of the distribution of exposed individuals).
Emphasis is placed on the need for subjective judgment to quantify uncertainty when relevant data are absent or incomplete. Therefore, the results of an uncertainty analysis will differ among risk assessors because of differences in the interpretation of the current state of knowledge. Despite these differences, the subjective confidence intervals from an uncertainty analysis should produce a reasonably 'high' probability of bounding the true risk provided that risk assessors avoid overconfidence in quantifying the level of certainty associated with important model components.
When hazardous substances are released into the environment, an evaluation is necessary to determine the possible impact these substances may have on human health and other biota. To address this question, a risk assessment is performed to quantify the potential detriment and evaluate the effectiveness of proposed remediation measures. A baseline risk assessment performed according to currently recommended United States Environmental Protection Agency (EPA) methods (EPA, 1989) produces a single point estimate of risk. Such point estimates fail to address the inherent uncertainty in the estimates of risk. At best, the single values obtained from this method may be considered as upperbound (conservative) estimates of risk to a maximally exposed individual. The chance of underestimating the true risk to an exposed individual is minimized. However, the chance of overstating the risk may be large.
A less biased approach to risk assessment uses uncertainty analysis to estimate the degree of confidence that can be placed in the risk estimate. A discussion of uncertainty is critical to the full characterization of risk to more fully evaluate the implications and limitations of the risk assessment (EPA, 1992). To date, an uncertainty analysis, if performed at all, is usually restricted to a qualitative statement of confidence in the result; for instance, uncertainty in the point estimate that is less than one order of magnitude (a factor of 10) is considered 'low,' uncertainty in the point estimate greater than one order of magnitude but less than two orders of magnitude (a factor of 100) is considered 'moderate,' and uncertainty that exceeds two orders of magnitude is considered 'high' (EPA, 1989). Unfortunately, these qualitative statements of uncertainty are difficult to assess, let alone defend, particularly when the assessment involves potential
exposure to several contaminants transferred over a number of different pathways (Hoffman and Hammonds,1994).
A more defensible approach is to perform a quantitative analysis of uncertainty using either analytical or numerical techniques to propagate uncertainty in the components of the risk assessment equations into an assessment of uncertainty in the overall result. If the risk assessment process can be modified to permit several iterations, then uncertainty analysis can be a valuable tool for identifying and ranking the contaminants and exposure pathways of concern. Such rankings can be used to guide the acquisition of additional data to reduce uncertainty in risk estimates. An uncertainty analysis is additionally useful to weigh the benefits against the costs of alternative remedial actions.