Mlonte Carlo Techniques for Quantitative Uncertainty Analysis in Public Health Risk Assessments

Most public health risk assessments assume and combine a series of average, conservative, and worst-case values to derive a conservative point estimate of risk. This procedure has major limitations. This paper demonstrates a new methodology for extended uncertainty analyses in public health risk assessments using Monte Carlo techniques. The extended method begins as do some conventional methods--with the preparation of a spreadsheet to estimate exposure and risk. This method, however, continues by modeling key inputs as random variables described by probability density functions (PDFs). Overall, the technique provides a quantitative way to estimate the probability distributions for exposure and health risks within the validity of the model used. As an example, this paper presents a simplified case study for children playing in soils contaminated with benzene and benzo(a)pyrene (BaP).     

A Trivariate Distribution for the Height,Weight, and Fat of Adult Men*

Using exploratory data analysis, probability plots, scatterplots, and computer animations to rotate and visualize the data, we fit a trivariate Normal distribution to data for the height, the natural logarithm of body weight, and the body fat for 646 men between the ages of 50 and 80 years as reported by the medical staff of the U.S. Veterans Administration's “Normative Aging Study” in Boston, MA. Although these data do not include any children, women, or young men, the measurements represent the best data that we could find through a 4-year search. We believe that these data are well measured and reliable for men in the specified age range and that these data reveal an interesting statistical pattern for use in probabilistic PBPK models.     

Principles for Conduct of Pest Risk Analyses: Report of an Expert Workshop

The North American Free Trade Agreement (NAFTA) and the General Agreement on Tariffs and Trade (GATT) have focused attention on risk assessment of potential insect, weed, and animal pests and diseases of livestock. These risks have traditionally been addressed through quarantine protocols ranging from limits on the geographical areas from which a product may originate, postharvest disinfestation procedures like fumigation, and inspections at points of export and import, to outright bans. To ensure that plant and animal protection measures are not used as nontariff trade barriers, GATT and NAFTA require pest risk analysis (PRA) to support quarantine decisions. The increased emphasis on PRA has spurred multiple efforts at the national and international level to design frameworks for the conduct of these analyses. As approaches to pest risk analysis proliferate, and the importance of the analyses grows, concerns have arisen about the scientific and technical conduct of pest risk analysis. In January of 1997, the Harvard Center for Risk Analysis (HCRA) held an invitation-only workshop in Washington, D.C. to bring experts in risk analysis and pest characterization together to develop general principles for pest risk analysis. Workshop participants examined current frameworks for PRA, discussed strengths and weaknesses of the approaches, and formulated principles, based on years of experience with risk analysis in other setting and knowledge of the issues specific to analysis of pests. The principles developed highlight the both the similarities of pest risk analysis to other forms of risk analysis, and its unique attributes.     

Principles of Good Practice for the Use of Monte Carlo Techniques in Human Health and Ecological Risk Assessments

We propose 14 principles of good practice to assist people in performing and reviewing probabilistic or Monte Carlo risk assessments, especially in the context of the federal and state statutes concerning chemicals in the environment. Monte Carlo risk assessments for hazardous waste sites that follow these principles will be easier to understand, will explicitly distinguish assumptions from data, and will consider and quantify effects that could otherwise lead to misinterpretation of the results. The proposed principles are neither mutually exclusive nor collectively exhaustive. We think and hope that these principles will evolve as new ideas arise and come into practice.     

Distributions of Total Job Tenure for Men and Women in Selected Industries and Occupations in the United States, February 1996

This article develops and fits probability distributions for the variability in projected (total) job tenure for adult men and women in 31 industries and 22 occupations based on data reported by the U.S. Department of Labor's Bureau of Labor Statistics. It extends previously published results and updates those results from January 1987 to February 1996. The model provides probability distributions for the variability in projected (total) job tenures within the time range of the data, and it extrapolates the distributions beyond the time range of the data, i.e., beyond 25 years.     

Fitting Second-Order Finite Mixture Models to Data with Many Censored Values Using Maximum Likelihood Estimation

Finite mixture models, that is, weighted averages of parametric distributions, provide a powerful way to extend parametric families of distributions to fit data sets not adequately fit by a single parametric distribution. First-order finite mixture models have been widely used in the physical, chemical, biological, and social sciences for over 100 years. Using maximum likelihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmental Protection Agency for the concentration of Radon 222 in drinking water supplied from ground water, even when 28% of the data fall at or below the minimum reporting level. Extending the use of maximum likelihood, we also illustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set.