Bounding Poorly Characterized Risks: A Lung Cancer Example

For diseases with more than one risk factor, the sum of probabilistic estimates of the number of cases caused by each individual factor may exceed the total number of cases observed, especially when uncertainties about exposure and dose response for some risk factors are high. In this study, we outline a method of bounding the fraction of lung cancer fatalities not due to specific well-studied causes. Such information serves as a "reality check" for estimates of the impacts of the minor risk factors, and, as such, complements the traditional risk analysis. With lung cancer as our example, we allocate portions of the observed lung cancer mortality to known causes (such as smoking, residential radon, and asbestos fibers) and describe the uncertainty surrounding those estimates. The interactions among the risk factors are also quantified, to the extent possible. We then infer an upper bound on the residual mortality due to "other" causes, using a consistency constraint on the total number of deaths, the maximum uncertainty principle, and the mathematics originally developed of imprecise probabilities.