Equivalence of concentration–response relationships in aquatic toxicology studies: Testing and implications for potency estimation

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.