High-Dimensional Cox Regression Analysis in Genetic Studies with Censored Survival Outcomes

With the advancement of high-throughput technologies, nowadays high-dimensional genomic and proteomic data are easy to obtain and have become ever increasingly important in unveiling the complex etiology of many diseases. While relating a large number of factors to a survival outcome through the Cox relative risk model, various techniques have been proposed in the literature. We review some recently developed methods for such analysis. For high-dimensional variable selection in the Cox model with parametric relative risk, we consider the univariate shrinkage method (US) using the lasso penalty and the penalized partial likelihood method using the folded penalties (PPL). The penalization methods are not restricted to the finite-dimensional case. For the high-dimensional (n -> infinity, n << p) or ultrahigh-dimensional case (n -> infinity, p << n), both the sure independence screening (SIS) method and the extended Bayesian information criterion (EBIC) can be further incorporated into the penalization methods for variable selection. We also consider the penalization method for the Cox model with semiparametric relative risk, and the modified partial least squares method for the Cox model. The comparison of different methods is discussed and numerical examples are provided for the illustration. Finally, areas of further research are presented.