Legal mandates exist for the protection of aquatic life and human health from the impacts of toxins released into receiving waters. To accomplish this objective, numeric environmental quality criteria are set. Data utilized commonly in the development of such criteria include no‐observed‐effect concentrations (NOECs), lowest‐observed‐effect concentrations (LOECs) and effective concentrations (ECs). The NOEC and LOEC are design‐sensitive indices and are open to strong criticism. The EC indices are often estimated through the inversion of a fitted parametric regression model. One criticism leveled against the EC estimation routines has been that one model cannot be appropriate for the variety of different biological endpoints that are studied in aquatic toxicology. These biological endpoints include survival (dichotomous response), fecundity (counts), and biomass/growth (continuous response). In the present study, generalized linear models (GLiMs) are shown to provide a general model for data commonly encountered in aquatic toxicology. The proposed EC estimator, labeled a relative inhibition or RI estimator, is derived in this GLiM framework. This estimator represents the concentration, or more generally, the exposure level to some hazard, associated with a specified level of change in the response relative to the control response. Along with the construction of this estimator, standard errors and confidence intervals are presented. This RI estimator is then applied to dichotomous, count, and continuous responses to illustrate its use.

Abstract-The purpose of this study was to describe statistical procedures to test the equivalence of concentration-response relationships in acute toxicology studies and to illustrate the implications of nonequivalence on potency endpoints such as LC10, LC50, or LC90. A logistic regression model for binary response endpoints such as mortality that allowed for the examination of equivalence of slopes and intercepts of the responses between populations is described. Test statistics were derived from comparing nested regression models. This procedure was used to test the equivalence of concentration versus acute mortality response relationships between two nonpolar, narcotic chemicals in a single population of fish and between two populations of fish with different exposure histories to a polycyclic aromatic hydrocarbon. These case studies illustrate different outcomes in the comparison of concentration-response relationships and demonstrate the need to consider more than a single endpoint (e.g., LC50) in a risk assessment context when nonparallel concentration-responses are observed.

Two populations of fathead minnows (F1, offspring of survivors of an acute fluoranthene exposure; N1, naive hatchery fish born in outdoor ponds) were concurrently exposed to approximately 850 μg/L of copper for 132 h. During the exposure, 49% of the F1 and 85% of the N1 minnows died. A curled operculum deformity, detected in 54% of the F1 population, was significantly related to mortality. A failure time regression model, combining both the F1 and N1 populations together, was fit to examine the relationship between population type (F1 or N1), body condition (weight/length3), presence of an operculum deformity, and different allozymes on time to death (TTD). The model indicated that type of population, body condition, the presence of an operculum deformity, and three loci (GPI‐1*, IDHP‐1*, and MDH‐2*) were significantly related to TTD. The F1 minnows had a higher survival rate and longer average TTD compared to N1 minnows. In comparison to the N1 population, the F1 population possessed a higher frequency of genotypes associated with increased survivorship at the IDHP‐1* and MDH‐2* loci. Weight (and body condition) was negatively correlated with survivorship. Minnows with a severe operculum deformity, believed to be a result of parental exposure to fluoranthene, had a 100% mortality rate and exhibited a considerably reduced TTD compared to nondeformed minnows. Multilocus heterozygosity was not related to TTD for either population. This study indicates that genetic factors may exhibit stronger effects on survivorship than other factors (e.g., weight/body condition) commonly associated with fitness.

Many extrapolation issues surface in quantitative risk assessments. The extrapolation from high-dose animal studies to low-dose human exposures is of particular concern. Physiologically based pharmacokinetic (PBPK) models are often proposed as tools to mitigate the problems of extrapolation. These models provide a representation of the disposition, metabolism, and excretion of xenobiotics that are believed to possess the potential of inducing adverse human health responses. Given a model of xenobiotic disposition that is applicable for multiple species and appropriate for nonlinearity of the xenobiotic biotransformation process, better extrapolation may be possible. Unfortunately, the true structure of these models (e.g. number of compartments, type of metabolism, etc.) is seldom known, and attributes of these models (tissue volumes, partition coefficients, etc.) are often experimentally determined and often only central measures of these quantities are reported. We describe the use of PBPK models in risk assessment, the structural and parameter uncertainty in these models, and provide a simple illustration of how these characteristics can be incorporated in a statistical analysis of PBPK models. Additional complexity in the analysis of variability in the models is also outlined. This discussion is illustrated using data from methylene chloride.