ABSTRACT
Risk screening is commonly conducted using multiple species ecotoxicological measures such as the HC₅, the Hazardous Concentration at which 5% of species in a specified (eco)system are assumed to be stressed.   In this paper we demonstrate that the estimate of HC₅ will not vary significantly among commonly adopted parametric distribution models of species sensitivity distributions (SSDs).  Uncertainty is highly dependent on the number of species tested (sample size) and the relevance of the measurement to the assessment endpoint (e.g. acute measures for assessing chronic endpoints).  This paper cross-compares estimates of these uncertainties using different empirical and theoretical methods to propose sample to population extrapolation factors.  Some theoretical parametric methods for estimating the confidence intervals on the HC ₅ can result in large over-conservatism; particularly if positive bias reduces uncertainty.  The 95^th percentile confidence interval on the HC₅ estimate given only three chronic test results varies from 5 to 8x10⁸, depending on the estimation method adopted.

Keywords: species sensitivity distribution, SSD, uncertainty, hazardous concentration, PNEC, extrapolation factors, assessment factors, risk assessment, life cycle assessment.

INTRODUCTION
The PNEC (Predicted No Effect Concentration) is an ecotoxicological measure for multiple species systems and can be defined as, for example, the concentration below which a specified percentage of species in an ecosystem are expected to be protected.  A protection level of 95% of species is often selected as an initial basis for PNEC derivation; also termed the HC₅ (HC – Hazardous Concentration) or PAF = 0.05 (PAF – Potentially Affected Fraction of species).  The exact HCx value adopted and the associated estimation method reflect necessary trade-offs between science and pragmatism.  We do not discuss these trade-offs in this paper.1

In common practice, the toxicological potency measure of a chemical (HCx) is described by plotting a cumulative distribution curve using available single species test data, such as No Observed Effect Concentrations (NOEC – the concentration at which no statistical differentiation was observed from the control for a given chemical and species).2  Such curves are termed species sensitivity distributions (SSDs) (Posthuma and Suter 2002, OECD 1992).  Parametric representations are often adopted.  For example, assuming a log-logistic distribution of the test data: 

    (1)

Such uni-modal distributions are described by two parameters.  The median (or mean) of the log concentration measure (C), denoted a  (equivalent to log HC₅₀), and the parameter ß ( =  ) that describes the extent of spread, or the standard deviation (SD).  Typical results are presented in Figure 1, where the concentration is normalized by the median.

The US Environmental Protection Agency (EPA) generally favours use of the median estimate of the HC₅ (Stephen et al. 1985), although no consensus exists (Suter 1998, OECD 1992).  The 95 ^th percentile confidence intervals on the median HC₅ and HC ₅₀ estimates also provide an indicator of uncertainty in the context of relative comparison applications; such as comparative risk and life cycle assessment (LCA) (Hauschild & Pennington 2002).  It is therefore timely to compare and propose techniques for the estimation of HCx and associated confidence intervals.

The criteria to select a minimum sample size to sufficiently describe an SSD and to estimate a HCx is often an arbitrary policy decision; again reflecting a trade-off between uncertainty and pragmatism.  Newman et al. (2000) suggested that the required species sample size for an estimate of HC₅ to approach the so-called point of minimal observed variation is between 10 to 55 test results; with a median of 30.  The US EPA's median HC5 estimates for use in Ambient Water Quality Criteria are based on at least eight selected Genus (geometric) Mean Values (GMVs) (Stephan 1985, OECD 1992, Fawell & Hedgecott 1996, US EPA 1999).  From a comparison of the FAV calculated using 8 and 18 Genus Mean Acute Values (GMAVs), the ratio is generally within a factor of 3 (Erickson and Stephan 1988, Emans et al. 1993) and conservative (approximately log-normal distribution, median = 1.5 and 95^th percentile = 4.4) (Host et al. 1991).  Others have suggested lower numbers, such as four test results (Slooff 1992, RIZA 1999), accepting higher levels of uncertainty.

In the common absence of sufficient data from chronic exposure tests to describe the SSD, a HCx can be estimated from acute (or mixed) data sets using extrapolation factors.  Acute data (e.g. short term, high mortality), often predicted, are more readily available than chronic (e.g. long-term, low observed morbidity effects). These short-term data require extrapolation to yield a measure that is relevant in the context of chronic exposures.  Nevertheless, for many chemicals the availability of even extrapolated acute measured data may remain too limited to sufficiently describe an SSD (Weyers et al. 2000).  Data estimation techniques (Quantitative Structure Activity Relationships – QSARs) will be necessary.

To be able to estimate multiple species measures such as the HC₅ or PNEC, extrapolation approaches are adopted in common practice (Host et al. 1991; Wagner and Lokke 1991; Aldenburg and Slob 1993; Jager et al. 1997; de Zwart 2002).  Extrapolation factors (sometimes termed assessment, uncertainty, application, or safety factors) are the most routinely used approach.  These factors help adjust for differences like exposure duration between available (e.g. acute) and desired (e.g. chronic) effects measurements (EC 1996; US EPA 1994; OECD 1992).  The magnitude of the extrapolation factors is determined on the basis of the quality, quantity, and relevance of the available ecotoxicity test data.  The HC₅, for example, is usually obtained by dividing the lowest available chronic NOEC (No Observed Effect Concentration) for a minimum of algae, crustacean and fish data by a factor of 10 (OECD 1992).  The lowest acute LC ₅₀, EC₅₀, or QSAR (Quantitative Structure Activity Relationship) estimate, for the same three species is divided by a factor of 100 (OECD 1992).  A single acute value is divided by 1000.  Confidence intervals are not given and the degree of protection, or uncertainty, is usually unknown.

The deterministic extrapolation approaches, such as factors of ten, provide no insights to decision makers of the associated uncertainty (OECD 1992).  While arguably more practical in screening applications (Fawell and Hedgecott 1996), such deterministic factors are not scientifically defendable in comparative assessments such as life cycle assessment (Hauschild & Pennington 2002).  Aldenburg and Slob (1993), Host et al. (1991), and Wagner and Lokke (1991), for example, proposed statistical methods to estimate extrapolation factors with associated confidence intervals for different sample sizes (numbers of species tested).  The confidence intervals on the estimate of measures such as the HC₅ reflect associated (parameter) uncertainty.  Differences between the statistical methods include the assumption of parametric representations versus adopting empirical insights, and whether the extrapolations account for population insights or are purely based on the quantitative test sample data.

This paper provides:
· A comparison of three types of approach for estimating the influence of sample size (number of test results) on the uncertainty of HCx.
· An illustration of the additional increase in uncertainty associated with using acute versus chronic data.
· An evaluation of the deterministic extrapolation factors commonly used in risk screening.