Estimating inhibition concentrations for different response scales using generalized linear models

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.