WilcoxCV: an R package for fast variable selection in cross-validation

In the last few years, numerous methods have been proposed for microarray-based class prediction. Although many of them have been designed especially for the case n << p ( much more variables than observations), preliminary variable selection is almost always necessary when the number of genes reaches several tens of thousands, as usual in recent data sets. In the two-class setting, the Wilcoxon rank sum test statistic is, with the t-statistic, one of the standard approaches for variable selection. It is well known that the variable selection step must be seen as a part of classifier construction and, as such, be performed based on training data only. When classifier accuracy is evaluated via cross-validation or Monte Carlo cross-validation, it means that we have to perform p Wilcoxon or t-tests for each iteration, which becomes a daunting task for increasing p. As a consequence, many authors often perform variable selection only once using all the available data, which can induce a dramatic underestimation of error rate and thus lead to misleadingly reporting predictive power. We propose a very fast implementation of variable selection based on the Wilcoxon test for use in cross-validation and Monte Carlo cross-validation ( also known as random splitting into learning and test sets). This implementation is based on a simple mathematical formula using only the ranks calculated from the original data set.