Assessing Patient Survival Using Microarray Gene Expression Data Via Partial Least Squares Proportional Hazard Regression

摘要

High dimensional data sets from microarray experiments where the number of variables (genes) p far exceed the number of samples N render most traditional statistical tools of little direct use. However, some of these statistical tools when used in conjunction with an appropriate dimension reduction method can be effective. In this paper we introduce the use the proportional hazard (PH) regression (Cox 1972) in conjunction with dimension reduction by partial least squares (PLS), since the number of covariates p exceeds the number of samples N. This setting is typical of gene expression data from DNA microarrays. Specifically, for a given vector of response values which are times to event (death or censored times) and p gene expressions (covariates) we address the issue of how to assess (estimate) the survival experience (curve) when N p. The approach taken to cope with the high dimensionality is to reduce the dimension via some dimension reduction (component extraction) method in the first stage and then estimate the survival distribution using a PH regression model in the second stage. The primary methods of component extraction considered is PLS. PLS achieves dimension reduction by constructing components to maximize the covariance between he response (survival times) and the linear combination of the covariates (gene expressions) sequentially. This is analogous to principal components analysis (PCA) but the optimization criterion in PCA is variance rather than covariance in PLS. We demonstrate the use of the methodology to a diffuse large B-cell lymphoma (DLBCL) complementary DNA (cDNA) data set.