Towards quantitative uncertainty assessment for cancer risks: central estimates and probability distributions of risk in dose-response modeling.

Regulatory agencies and the scientific community have been engaged in a long-term effort to strengthen health risk assessment procedures. Recently the momentum of this effort has accelerated to increasing biological information for a variety of toxic compounds and emphasis on the policy goal of broader characterization of scientific uncertainty (in contrast to providing only a single risk estimate). For example, the OMB Regulatory Analysis Guidelines [OMB, 2003. Office of Management and Budget. Circular A-4. Available from: http://www.whitehouse.gov/omb/circulars/a004/a-4.html/] suggest that a formal quantitative uncertainty analysis be performed for economic assessments in support of major regulatory analyses, a process that can utilize both expected values and probability distributions for risk estimates. Some efforts have been made in the past to provide probability distributions of risk estimates. In this article, we examine a procedure for constructing probability distributions and expected values of risk estimates using a Bayesian framework. This approach has the advantage of mathematical soundness and computational feasibility, given the Markov chain Monte Carlo software tools that are available today. Importantly, the Bayesian framework can serve as a unifying platform for uncertainty analysis in cancer risk assessment. This paper provides some initial applications of Bayesian methods in quantitative analysis of uncertainty in cancer risk assessment, including implementation with cancer dose-response data sets for two chemicals. The Bayesian expected risk calculations provide an approach to generating a central estimate of risk that does not have the instability problems that have often limited utility of MLE risk estimates.