How to compare separation selectivity of high-performance liquid chromatographic columns properly?

Comparison and selection of chromatographic columns is an important part of development as well as validation of analytical methods. Presently there is abundant number of methods for selection of the most similar and orthogonal columns, based on the application of limited number of test compounds as well as quantitative structure retention relationship models (QSRR), from among Snyder's hydrophobic-subtraction model (HSM) have been most extensively used. Chromatographic data of 67 compounds were evaluated using principal component analysis (PCA), hierarchical cluster analysis (HCA), non-parametric ranking methods as sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM), both applied as a consensus driven comparison, and complemented by the comparison with one variable at a time (COVAT) approach. The aim was to compare the ability of the HSM approach and the approach based on primary retention data of test solutes (logk values) to differentiate among ten highly similar C18 columns. The ranking (clustering) pattern of chromatographic columns based on primary retention data and HSM parameters gave different results in all instances. Patterns based on retention coefficients were in accordance with expectations based on columns' physicochemical parameters, while HSM parameters provided a different clustering. Similarity indices calculated from the following dissimilarity measures: SRD, GPCM Fisher's conditional exact probability weighted (CEPW) scores; Euclidian, Manhattan, Chebyshev, and cosine distances; Pearson's, Spearman's, and Kendall's, correlation coefficients have been ranked by the consensus based SRD. Analysis of variance confirmed that the HSM model produced statistically significant increases of SRD values for the majority of similarity indices, i.e. HS transformation of original retention data yields significant loss of information, and finally results in lower performance of HSM methodology. The best similarity measures were obtained using primary retention data, and derived from Kendal's and Spearman's correlation coefficients, as well as GPCM and SRD score values. Selectivity function, Fs, originally proposed by Snyder, demonstrated moderate performance.