Discriminating Variable Test and Selectivity Ratio Plot: Quantitative Tools for Interpretation and Variable (Biomarker) Selection in Complex Spectral or Chromatographic Profiles

Abstract

The discriminating variable (DIVA) test and the selectivity ratio (SR) plot are developed as quantitative tools for revealing the variables in spectral or chromatographic profiles discriminating best between two groups of samples. The SR plot is visually similar to a spectrum or a chromatogram, but with the most intense regions corresponding to the most discriminating variables. Thus, the variables with highest SR represent the variables most important for interpretation of differences between groups. Regions with variables that are positively or negatively correlated to each other are displayed as corresponding negative and positive regions in the SR plot. The nonparametric DIVA test is designed for connecting SR to discriminatory ability of a variable quantified as probability for correct classification. A mean probability for a certain SR range is calculated as the mean correct classification rate (MCCR) for all variables in the same SR interval. The MCCR is thus similar to a mean sensitivity in each SR interval. In addition to the ranking of all variables according to their discriminatory ability provided by the SR plot, the DIVA test connects a probability measure to each SR interval. Thus, the DIVA test makes it possible to objectively define thresholds corresponding to mean probability levels in the SR plot and provides a quantitative means to select discriminating variables. In order to validate the approach, samples of untreated cerebrospinal fluid (CSF) and samples spiked with a multicomponent peptide standard were analyzed by matrix-assisted laser desorption ionization (MALDI) mass spectrometry. The differences in the multivariate spectral profiles of the two groups were revealed using partial least-squares discriminant analysis (PLS-DA) followed by target projection (TP). The most discriminating mass-to-charge (m/z) regions were revealed by calculating the ratio of explained to unexplained variance for each m/z number on the target-projected component and displaying this measure in SR plots with quantitative boundaries determined from the DIVA test. The results are compared to some established methods for variable selection.