A Robust Approach to Risk Assessment Based on Species Sensitivity Distributions

The guidelines for setting environmental quality standards are increasingly based on probabilistic risk assessment due to a growing general awareness of the need for probabilistic procedures. One of the commonly used tools in probabilistic risk assessment is the species sensitivity distribution (SSD), which represents the proportion of species affected belonging to a biological assemblage as a function of exposure to a specific toxicant. Our focus is on the inverse use of the SSD curve with the aim of estimating the concentration, HCp, of a toxic compound that is hazardous to p% of the biological community under study. Toward this end, we propose the use of robust statistical methods in order to take into account the presence of outliers or apparent skew in the data, which may occur without any ecological basis. A robust approach exploits the full neighborhood of a parametric model, enabling the analyst to account for the typical real-world deviations from ideal models. We examine two classic HCp estimation approaches and consider robust versions of these estimators. In addition, we also use data transformations in conjunction with robust estimation methods in case of heteroscedasticity. Different scenarios using real data sets as well as simulated data are presented in order to illustrate and compare the proposed approaches. These scenarios illustrate that the use of robust estimation methods enhances HCp estimation.

Benchmark dose profiles for joint-action continuous data in quantitative risk assessment

Benchmark analysis is a widely used tool in biomedical and environmental risk assessment. Therein, estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a prespecified benchmark response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This paper demonstrates how the benchmark modeling paradigm can be expanded from the single-agent setting to joint-action, two-agent studies. Focus is on continuous response outcomes. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile-a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR-is defined for use in quantitative risk characterization and assessment.

Benchmark dose profiles for joint-action quantal data in quantitative risk assessment

Benchmark analysis is a widely used tool in public health risk analysis. Therein, estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a prespecified Benchmark Response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This article demonstrates how the benchmark modeling paradigm can be expanded from the single-dose setting to joint-action, two-agent studies. Focus is on response outcomes expressed as proportions. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile (BMP) - a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR - is defined for use in quantitative risk characterization and assessment. The resulting, joint, low-dose guidelines can improve public health planning and risk regulation when dealing with low-level exposures to combinations of hazardous agents.

Maximum likelihood estimation with binary-data regression models: small-sample and large-sample features

Many inferential procedures for generalized linear models rely on the asymptotic normality of the maximum likelihood estimator (MLE). Fahrmeir & Kaufmann (1985, Ann. Stat., 13, 1) present mild conditions under which the MLEs in GLiMs are asymptotically normal. Unfortunately, limited study has appeared for the special case of binomial response models beyond the familiar logit and probit links, and for more general links such as the complementary log-log link, and the less well-known complementary log link. We verify the asymptotic normality conditions of the MLEs for these models under the assumption of a fixed number of experimental groups and present a simple set of conditions for any twice differentiable monotone link function. We also study the quality of the approximation for constructing asymptotic Wald confidence regions. Our results show that for small sample sizes with certain link functions the approximation can be problematic, especially for cases where the parameters are close to the boundary of the parameter space.

A sensitivity analysis of the social vulnerability index

The Social Vulnerability Index (SoVI), created by Cutter et al. (2003), examined the spatial patterns of social vulnerability to natural hazards at the county level in the United States in order to describe and understand the social burdens of risk. The purpose of this article is to examine the sensitivity of quantitative features underlying the SoVI approach to changes in its construction, the scale at which it is applied, the set of variables used, and to various geographic contexts. First, the SoVI was calculated for multiple aggregation levels in the State of South Carolina and with a subset of the original variables to determine the impact of scalar and variable changes on index construction. Second, to test the sensitivity of the algorithm to changes in construction, and to determine if that sensitivity was constant in various geographic contexts, census data were collected at a submetropolitan level for three study sites: Charleston, SC; Los Angeles, CA; and New Orleans, LA. Fifty-four unique variations of the SoVI were calculated for each study area and evaluated using factorial analysis. These results were then compared across study areas to evaluate the impact of changing geographic context. While decreases in the scale of aggregation were found to result in decreases in the variance explained by principal components analysis (PCA), and in increases in the variance of the resulting index values, the subjective interpretations yielded from the SoVI remained fairly stable. The algorithm's sensitivity to certain changes in index construction differed somewhat among the study areas. Understanding the impacts of changes in index construction and scale are crucial in increasing user confidence in metrics designed to represent the extremely complex phenomenon of social vulnerability.