Kernel Cox regression models for linking gene expression profiles to censored survival data

In functional genomics, one important problem is to relate the microarray gene expression profiles to various clinical phenotypes from patients. The success has been demonstrated in molecular classification of cancer in which gene expression data serve as predictors and different types of cancer are the binary or multi-categorical outcome variable. However, there has been less research in linking gene expression profiles to other types of phenotypes, in particular, the censored survival data such as patients' overall survival or cancer relapse times. In the paper, we develop a kernel Cox regression model for relating gene expression profiles to censored phenotypes in the framework the penalization method in terms of function estimation in reproducing kernel Hilbert spaces. To circumvent the problem of censoring, we use the negative partial likelihood as a loss function in the estimation procedure. The functional combinations of the original gene expression data identified by the method are highly correlated with the patients' survival times and at the same time account for the variability in the gene expression levels. We apply our method to data sets from diffuse large B-cell lymphoma, lung adenocarcinoma and breast carcinoma studies to verify its effectiveness. The results from these analyses indicate that the proposed method works very well in identifying subgroups of patients with different risks of death or relapse and in predicting the risk of relapse or death based on the gene expression profiles measured from the tumor samples taken from the patients.