SSDs Revisited: Part I—A Framework for Sample Size Guidance on Species Sensitivity Distribution Analysis

Abstract

We propose a framework on sample size for species sensitivity distribution (SSD) analyses, with perspectives on Bayesian, frequentist, and even nonparametric approaches to estimation. The intent of a statistical sample size analysis is to ensure that the implementation of a statistical model will satisfy a minimum performance standard when relevant conditions are met. It requires that a statistical model be fully specified and that the means of measuring its performance as a function of sample size be detailed. Defining the model conditions under which sample size is calculated is often the most difficult, and important, aspect of sample size analysis because if the model is not representative, then the sample size analysis will provide incorrect guidance. Definitive guidance on sample size requires general agreement on representative models and their performance from stakeholders in important domains such as chemical safety assessments involving government regulators and industry; the present study provides an initial framework that could be used to this end in the future. In addition, our analysis provides immediate value for understanding how well current SSD analyses perform under a few basic models, sample sizes, and quantitative performance criteria. The results confirm that many analyses are adequately sized to estimate hazardous concentration percentile values (typically the 5th percentile for chemical hazard assessments). However, on the low end of sizes seen in common practice, hazardous concentration estimates can be more than 1 order of magnitude greater than the model‐defined value. Environ Toxicol Chem 2019;38:1514–1525. © 2019 SETAC

SSDs revisited: part II—practical considerations in the development and use of application factors applied to species sensitivity distributions

“…The USEPA uses an interspecies toxicity correlation estimation program to indirectly assess threatened and endangered species based on the hypothesis that taxonomically related species (e.g., congenerics) possess similar sensitivities to chemicals (Willming et al 2016). It is abundantly clear from the analyses and approaches described in the present study and in Part I, the companion study (Carr and Belanger 2019) that the need for a consensus and robust guidance on SSD development, application, and interpretation remains significant for chemical safety assessment globally (as per Belanger et al 2017). We add to the existing toolkits for assessing SSD quality, which was identified as a need by the European Centre for Ecotoxicology and Toxicology of Chemicals (2104).…”

“…In the case of SSDs based on chronic data commonly applied to wastewater contaminants and high production volume chemicals with wide‐dispersive use, the application factor need not consider acute‐to‐chronic extrapolation as long as the input data are derived from a true chronic perspective (long‐term exposure, sensitive endpoints of ecological and regulatory significance, statistically robust). Carr and Belanger () have demonstrated that sample size is a relevant factor and that when input data are sufficient in number, the HC5 output is robust, especially at n > 13. Intraspecies variability can be controlled through sound documentation and application of testing principles, as identified by Harris et al ().…”

Quantification of pesticide residues in the topsoil of Belgian fruit orchards: terrestrial environmental risk assessment

“…12 An SSD is a probabilistic extrapolation (distribution) of certain toxicological endpoints for a set of different species (species sensitivities, such as LC 50 values). 13 The SSD approach has been used to characterize environmental risk for aquatic ecosystems. 14,15 Several soil-dwelling beneficial organisms have been identified in fruit orchards.…”

Probabilistic Environmental Risk Assessment for Linear Alkyl Benzene Sulfonate (LAS) in Japan Reduces Assessment Uncertainty

“…SSDs were constructed using the SSD in R package developed by P&G (Cincinnati, USA) and discussed in Carr and Belanger [46] and Belanger and Carr [47]. SSDs were fit to a log-logistic model following normalization to C10 to C14 individual CLs and an average environmental exposure CL of C11.5.…”

“…The SSD HC5 for each homologue was calculated for each individual LAS homologue using methods described in Belanger and Carr [46]. In addition, LAS QSARs were used to normalize the mesocosm NOEC for each LAS homologue based on the mesocosm study using the QSAR that provided the most sensitive result.…”