Deviance residuals based PLS regression for censored data in high dimensional setting

The PLS Cox regression has been proposed in the framework of PLS generalized linear regression as an alternative to the Cox model when dealing with highly correlated covariates. However, in high dimensional settings the algorithm becomes computer-intensive and a more efficient algorithm must be used. In this article we propose an alternative both faster and easier to carry out by the direct use of standard procedures which are available in most statistical softwares. Recently, Segal suggested a solution to the Cox–Lasso algorithm when dealing with high dimensional data. Following Segal, we propose a Deviance Residuals based PLS regression (PLSDR) as an alternative to the PLS–Cox model in high dimensional settings. The PLSDR algorithm only needs to carry out null deviance residuals using a simple intercept Cox model and use these as outcome in a standard PLS regression. This algorithm which can be extended to kernels to deal with non-linearity can also be viewed as a variable selection method in a threshold penalized formulation. An application carried out on gene expression from patients with diffuse large B-cell lymphoma shows the practical interest of using deviance residuals as outcomes in PLS regression when dealing with very many descriptors and censored data.