Evaluation of the effect of chance correlations on variable selection using Partial Least Squares-Discriminant Analysis

Variable subset selection is often mandatory in high throughput metabolomics and proteomics. However, depending on the variable to sample ratio there is a significant susceptibility of variable selection towards chance correlations. The evaluation of the predictive capabilities of PLSDA models estimated by cross-validation after feature selection provides overly optimistic results if the selection is performed on the entire set and no external validation set is available. In this work, a simulation of the statistical null hypothesis is proposed to test whether the discrimination capability of a PLSDA model after variable selection estimated by cross-validation is statistically higher than that attributed to the presence of chance correlations in the original data set. Statistical significance of PLSDA CV-figures of merit obtained after variable selection is expressed by means of p-values calculated by using a permutation test that included the variable selection step. The reliability of the approach is evaluated using two variable selection methods on experimental and simulated data sets with and without induced class differences. The proposed approach can be considered as a useful tool when no external validation set is available and provides a straightforward way to evaluate differences between variable selection methods.