Partial Least Squares and Cox model with application to gene expression

One important aspect of data-mining of microarray data is to discover the molecular variation among cancers. In microarray studies, the number n of samples is relatively small compared to the number p of genes per sample (usually in thousands). That is a considerable challenge in the context of survival prediction. This naturally calls for the use of a dimension reduction procedure together with the prediction one. In this paper, the question of survival prediction in such a high dimensional setting is addressed. We propose a new method combining Partial Least Squares (PLS) and Ridge penalized Cox regression. We review the existing methods based on PLS and (or) penalized likelihood techniques, outline their interest in some cases and theoretically explain their sometimes poor behavior. Our procedure is compared with these other methods. The performance of the resulting procedures is illustrated on two real data sets