Outliers detection in the statistical accuracy test of a pK a prediction

Abstract

The regression diagnostics algorithm REGDIA in S-Plus is introduced to examine the accuracy of pKa predicted with four programs: PALLAS, MARVIN, PERRIN and SYBYL. On basis of a statistical analysis of residuals, outlier diagnostics are proposed. Residual analysis of the ADSTAT program is based on examining goodness-of-fit via graphical diagnostics of 15 exploratory data analysis plots, such as bar plots, box-and-whisker plots, dot plots, midsum plots, symmetry plots, kurtosis plots, differential quantile plots, quantile-box plots, frequency polygons, histograms, quantile plots, quantile-quantile plots, rankit plots, scatter plots, and autocorrelation plots. Outliers in pKa relate to molecules which are poorly characterized by the considered pKa program. Of the seven most efficient diagnostic plots (the Williams graph, Graph of predicted residuals, Pregibon graph, Gray L–R graph, Index graph of Atkinson measure, Index graph of diagonal elements of the hat matrix and Rankit Q–Q graph of jackknife residuals) the Williams graph was selected to give the most reliable detection of outliers. The six statistical characteristics, \({F_{\rm exp},R^{2},R_{\rm P}^{2},{\it MEP},{\it AIC}}\), and s in pKa units, successfully examine the specimen of 25 acids and bases of a Perrin’s data set classifying four pKa prediction algorithms. The highest values \({F_{\rm exp},R^{2},R_{\rm P}^{2}}\) and the lowest value of MEP and s and the most negative AIC have been found for PERRIN algorithm of pKa prediction so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test of the REGDIA program can also be extended to test other predicted values, as log P, log D, aqueous solubility or some physicochemical properties.