A novel method based on similarity and triangulation for predicting the toxicities of various binary mixtures

There is currently no generally accepted model to predict the hormesis of mixtures. In order to accurately predict the hormesis of a mixture, we developed a method based on similarity and triangulation, which we named SimTri in this paper. SimTri takes the mixture as scatter points in space, which is constructed by the concentration axes of various components in the mixture system. To test the predictive capability of SimTri, the toxicities of three different types of binary mixtures (no hormetic compound, one hormetic compound, and two hormetic compounds) on Vibrio qinghaiensis sp.-Q67 were determined at 0.25 h and 12 h. For each mixture system, the toxicities of five mixture rays, which were designed by direct equipartition ray design, were used for the internal validation (leave-one-out cross-validation, LOOCV). The toxicities of two mixture rays, which were designed by fixed-ratio ray design on the basis of the NOEC and EC₇₀ ratios, were used for the external validation. The results of LOOCV and external validation indicated that the accuracy of SimTri was greater than 90%, which means that SimTri can accurately predict the toxicity of three different types of binary mixtures and may provide a new way to predict the toxicity of mixtures.