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This article reviews five published "second‐order" risk comparisons from the past four decades that implied precise understanding, and hence clear relationships or orderings, of the underlying risks. "Second order" here refers to efforts that extract information from original sources with the goal of relating diverse findings. All five of these publications have frequently been cited in the peer‐reviewed literature and/or in risk regulatory debate in the United States. Each is associated with at least one contemporaneous critique that the findings were excessively precise. None of these critiques suggested that an alternative relationship or ordering of the risks evaluated was more appropriate. Instead, each critique concluded that alternative, contradictory relationships were at least as plausible given data and/or analytical limitations. In one case, the critique led to the withdrawal of the original publication. The original findings have been propagated or used uncritically in subsequent literature, including political support for cost‐effectiveness analysis. In other cases, the critiques have been used to discredit quantitative risk analysis in general, especially in the cases of nuclear power and cost‐benefit analysis. Both of these outcomes are undesirable. Future risk comparisons should avoid excessive precision, include explicit discussion of uncertainty, and differentiate between plausible estimates and expected values.

Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- Defining Risk -- Structure of the Book -- Risk Analysis and Public Policy -- Problem 1-1. Getting Started -- Problem 1-2. Data Needs -- Problem 1-3. Using Data -- Problem I-A. Additional Cases -- Problem I-B. Additional Curves -- Problem l-C. Does the Dose Make the Poison? -- Problem I-D. One in a Million Risks -- Problem I-E. Surfing and Smoking -- Problem I-F. Risks of Nuclear Power -- References -- 2 Basic Models and Risk Problems -- Introduction -- Basic Modeling -- Problem 2-1. Volatile Organic Emissions from Household Materials: Wallpaper Glue -- Problem 2-2. Indoor Radon Exposure -- Problem 2-A. Problem 2-2 Revisited -- Problem 2-B. Equilibrium Concentration -- Problem 2-3. Simple PBPK Model-Continuous Dose -- Problem 2-C. Alternative Depictions -- Problem 2-4. PBPK-Finite Dose of Barium -- Problem 2-D. How Much Resolution Is Too Much? -- Problem 2-E. How Much Information Is Needed? -- Problem 2-F. Sensitivity Analysis -- Cause and Effect Relationships -- Problem 2-5. Radon and Cancer -- Mechanistic Models and Curve Fitting -- Problem 2-6. Conceiving "Mechanistic" Models -- Problem 2-7. Using the Wrong Mode~ Getting the Model Wrong -- Problem 2-8. Empirically Derived Dose Response -- Problem 2-9. Earthquakes versus Traffic Risks -- Conclusion -- References -- 3 Review of Statistics for Risk Analysis -- Introduction: Statistics and the Philosophy of Risk Assessment -- Problem 3-1. Average Radon Exposure -- Problem 3-A. Radon Exposures in Different Regions -- Problem 3-2. Working with Data -- Problem 3-3. Mean and Median: Why Wony? -- Problem 3-4. Sample Data Revisited -- Problem 3-5. Hypothesis Testing and Confidence Intervals -- Problem 3-6. Making Decisions -- Distributions -- Problem 3-7. Moving Away from Ignorance

We compare the regulatory implications of applying the traditional (linearized) and exact two‐stage dose‐response models to animal carcinogenic data. We analyze dose‐response data from six studies, representing five different substances, and we determine the "goodness‐ of‐fit" of each model as well as the 95% confidence lower limit ofthe dose corresponding to a target excess risk of 10‐5 (the target risk doseTRD). For the two concave datasets, we find that the exact model gives a substantially better fit to the data than the traditional model, and that the exact model gives aTRD that is an order of magnitude lower than that given by the traditional model. In the other cases, the exact model gives a fit equivalent to or better than the traditional model. We also show that although the exact two‐stage model may exhibit dose‐response concavity at moderate dose levels, it is always linear or sublinear, and never supralinear, in the low‐dose limit. Because regulatory concern is almost always confined to the low‐dose region extrapolation, supralinear behavior seems not to be of regulatory concern in the exact two‐stage model. Finally, we find that when performing this low‐dose extrapolation in cases of dose‐response concavity, extrapolating the model fit leads to a more conservative TRD than taking a linear extrapolation from 10% excess risk. We conclude with a set of recommendations.

Comparative risk projects can provide broad policy guidance but they rarely have adequate scientific foundations to support precise risk rankings. Many extant projects report rankings anyway, with limited attention to uncertainty. Stochastic uncertainty, structural uncertainty, and ignorance are types of incertitude that afflict risk comparisons. The recently completed New Jersey Comparative Risk Project was innovative in trying to acknowledge and accommodate some historically ignored uncertainties in a substantive manner. This article examines the methods used and lessons learned from the New Jersey project. Monte Carlo techniques were used to characterize stochastic uncertainty, and sensitivity analysis helped to manage structural uncertainty. A deliberative process and a sorting technique helped manage ignorance. Key findings are that stochastic rankings can be calculated but they reveal such an alarming degree of imprecision that the rankings are no longer useful, whereas sorting techniques are helpful in spite of uncertainty. A deliberative process is helpful to counter analytical overreaching.