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Diagnostic Tools to Determine the Quality of "Transparent" Regression-Based QSARs: The "Modelling Power" Plot

A bivariate plot is presented for comparing two or more QSAR models. It is based on two new statistics associated with a regression model, the "descriptive power" (Dp), which is estimated through the relative uncertainty of model coefficients, and the "predictive power" (Pp), which is estimated through both the fitted and cross-validated explained variance of the response variable (i.e., biological activity). An algorithm was developed for performing equivalent multiple linear regression and partial-least-squares calculations. The results were validated by comparison with widely accepted commercial software. Dp and Pp statistics are defined to vary from 0 to 100%, so the modeler has a intuitive impression of the descriptive (i.e., global importance of the selected descriptors) and predictive (i.e., possibility of performing QSAR or just SAR estimations) power. These statistics represent a point in the Dp versus Pp "modelling power" plot, which facilitates visual multiple models comparison, but also could be used to substitute classical statistics and could even be combined to obtain a unique parameter to define (or compare) the model's quality.