Dimension reduction of microarray gene expression data: the accelerated failure time model.

The construction of the components of Partial Least Squares (PLS) is based on the maximization of the covariance/correlation between linear combinations of the predictors and the response. However, the usual Pearson correlation is influenced by outliers in the response or in the predictors. To cope with outliers, we replace the Pearson correlation with the Spearman rank correlation in the optimization criteria of PLS. The rank-based method of PLS is insensitive to outlying values in both the predictors and response, and incorporates the censoring information by using an approach of Nguyen and Rocke (2004) and two approaches of reweighting and mean imputation of Datta et al. (2007). The performance of the rank-based approaches of PLS, denoted by Rank-based Modified Partial Least Squares (RMPLS), Rank-based Reweighted Partial Least Squares (RRWPLS), and Rank-based Mean-Imputation Partial Least Squares (RMIPLS), is investigated in a simulation study and on four real datasets, under an Accelerated Failure Time (AFT) model, against their un-ranked counterparts, and several other dimension reduction techniques. The results indicate that RMPLS is a better dimension reduction method than other variants of PLS as well as other considered methods in terms of the minimized cross-validation error of fit and the mean squared error of fit in the presence of outliers in the response, and is comparable to other variants of PLS in the absence of outliers. Supplementary Materials are available at http://www.worldscinet.com/jbcb/