Beyond the Domain of Direct Observation: How to Specify a Probability Distribution that Represents the “State of Knowledge” About Uncertain Inputs

Uncertainty is inherent in all exposure and risk assessments in which mathematical models are used to extrapolate information beyond the domain of direct observation. Uncertainty exists because models are imperfect mimics of reality. In addition, the data available for inputs are seldom directly relevant to the defined assessment endpoint. For example, data on dietary habits are often composed of daily or weekly recall surveys which impart little information about the daily consumption rate averaged over a year to a lifetime which are the typical time periods required to estimate the excess lifetime risk to a potentially exposed individual. The use of classical statistics to summarize the variability of direct observations is usually inappropriate for exposure and risk projections. Classical statistics should be restricted to instances when data are obtained from either a random or stratified random design, appropriately averaged according to the space and time requirements of the assessment, and when the data are directly relevant to the target individuals or populations of interest. These situations are rare in human health and ecological risk assessments for which extrapolations are made beyond the spatial extent and time periods in which data have been collected. Sometimes, analysts ‘‘assume’’ a dataset to be directly relevant in order to justify using the familiar tools of classical statistics. This procedure is what we call being ‘‘subjectively objective.’’ Its practice can result in misleading statements of uncertainty and can misdirect the need for additional information.