Prediction of lethal/effective concentration/dose in the presence of multiple auxiliary covariates and components of variance

Predictors of the percentile lethal/effective concentration/dose are commonly used measures of efficacy and toxicity. Typically such quantal‐response predictors (e.g., the exposure required to kill 50% of some population) are estimated from simple bioassays wherein organisms are exposed to a gradient of several concentrations of a single agent. The toxicity of an agent may be influenced by auxiliary covariates, however, and more complicated experimental designs may introduce multiple variance components. Prediction methods lag examples of those cases. A conventional two‐stage approach consists of multiple bivariate predictions of, say, medial lethal concentration followed by regression of those predictions on the auxiliary covariates. We propose a more effective and parsimonious class of generalized nonlinear mixed‐effects models for prediction of lethal/effective dose/concentration from auxiliary covariates. We demonstrate examples using data from a study regarding the effects of pH and additions of variable quantities 2',5'‐dichloro‐4'‐nitrosalicylanilide (niclosamide) on the toxicity of 3‐trifluoromethyl‐4‐nitrophenol to larval sea lamprey ( Petromyzon marinus ). The new models yielded unbiased predictions and root‐mean‐squared errors (RMSEs) of prediction for the exposure required to kill 50 and 99.9% of some population that were 29 to 82% smaller, respectively, than those from the conventional two‐stage procedure. The model class is flexible and easily implemented using commonly available software.