A Random Effects Model for Binary Mixture Toxicity Experiments

We suggest a simple isobole analysis for binary mixture toxicity experiments. The analysis is based on estimated logarithmic effect concentrations and their corresponding standard errors. The suggested model allows for synergism/antagonism and incorporates within-mixture variation as well as between-mixture variation in a random effects model. The likelihood ratio test for the hypothesis of concentration addition (CA) is examined, in particular its small sample properties. We study two datasets on the joint effect of acifluorfen versus diquat and glyphosate versus mechlorprop, respectively, on the growth of the aquatic macrophyte Lemna minor.