Methods to Approximate Joint Uncertainty and Variability in Risk

As interest in quantitative analysis of joint uncertainty and interindividual variability (JUV) in risk grows, so does the need for related computational shortcuts. To quantify JUV in risk, Monte Carlo methods typically require nested sampling of JUV in distributed inputs, which is cumbersome and time‐consuming. Two approximation methods proposed here allow simpler and more rapid analysis. The first consists of new upper‐bound JUV estimators that involve only uncertainty or variability, not both, and so never require nested sampling to calculate. The second is a discrete‐probability‐calculus procedure that uses only the mean and one upper‐tail mean for each input in order to estimate mean and upper‐bound risk, which procedure is simpler and more intuitive than similar ones in use. Application of these methods is illustrated in an assessment of cancer risk from residential exposures to chloroform in Kanawah Valley, West Virginia. Because each of the multiple exposure pathways considered in this assessment had separate modeled sources of uncertainty and variability, the assessment illustrates a realistic case where a standard Monte Carlo approach to JUV analysis requires nested sampling. In the illustration, the first proposed method quantified JUV in cancer risk much more efficiently than corresponding nested Monte Carlo calculations. The second proposed method also nearly duplicated JUV‐related and other estimates of risk obtained using Monte Carlo methods. Both methods were thus found adequate to obtain basic risk estimates accounting for JUV in a realistically complex risk assessment. These methods make routine JUV analysis more convenient and practical.