Ranking and similarity for quantitative structure–retention relationship models in predicting Lee retention indices of polycyclic aromatic hydrocarbons

Quantitative structure–(chromatographic) retention relationship (QSRR) models for prediction of Lee retention indices for polycyclic aromatic hydrocarbons (PAHs) were gathered from the literature and the predictive performances of models were compared. Numerous Lee retention indices (46) were served as a reliable basis for ranking by a recently developed novel method of ordering based on the sum of ranking differences (SRD) [TrAC, Trends Anal. Chem. 29 (2010) 101–109], by which the best model can be selected easily. Two kinds of references for ranking were accepted, average (consensus) and the experimental retention indices. Leave-many-out cross validation of the SRD procedure provides an easy way to group similar models. Significant differences among models can be revealed by using Wilcoxon's matched pair test.Principal component analysis (PCA) and cluster analysis (CA) arranged the models in three groups, i.e. similarities among models are manifested. The classical exploratory techniques and cross-validation (CV) justified the findings based on SRD ranking, i.e. the seven fold CV can be applied for pattern recognition. Generalized pair correlation method (GCPM) provided very similar grouping pattern to the procedures based of sum of ranking differences. The two methods (SRD and GPCM) exert astonishingly similar grouping (pattern recognition) though their background philosophy and way of calculation are totally different.

Cross-validation of sum of ranking differences (SRDs emphasizes the pattern in the data (Box and Whisker plot of SRD values (Y axis) for different models (M1–M24) and experimental values Iexp). The average was used as benchmark.Figure optionsDownload as PowerPoint slideHighlights
► Sum of ranking differences (SRD) ranks and groups seemingly equivalent models.
► Generalized pair correlation method (GPCM) also works as pattern recognition method.
► Best and worst models can be selected unambiguously.
► SRD and GPCM are ordering techniques and similarity measures.
► Principal Component and Cluster Analysis reveal very similar groupings.
► Validation by comparison of correlation measures and randomization test.