Quantitative structure-activity relationships. VI. Non-linear dependence of biological activity on hydrophobic character: calculation procedures for bilinear model.

The bilinear model, log 1/C = a log P--b log (betaP + 1) + c, is a new model for the qunatitative description of non-linear relationships between hydrophobic character and biological activity. In contrast to the parabolic Hansch model the bilinear model considers the particular effect that a linear relationship exists between lipophilicity and biological activity up to a point where this linear relationship breaks down to a non-linear relationship. Two different calculation procedures for the bilinear mode, a stepwise iteration method and the Taylor series iteration method, are explained and demonstrated with examples. The bilinear model and the parabolic Hansch model are compared by means of the statistical parameters r, s and F, by a partial F test and by an analysis of the residuals obtained with both models.