  Wide heterogeneity exists in cancer patients' survival, ranging from a few
months to several decades. To accurately predict clinical outcomes, it is vital
to build an accurate predictive model that relates patients' molecular profiles
with patients' survival. With complex relationships between survival and
high-dimensional molecular predictors, it is challenging to conduct
non-parametric modeling and irrelevant predictors removing simultaneously. In
this paper, we build a kernel Cox proportional hazards semi-parametric model
and propose a novel regularized garrotized kernel machine (RegGKM) method to
fit the model. We use the kernel machine method to describe the complex
relationship between survival and predictors, while automatically removing
irrelevant parametric and non-parametric predictors through a LASSO penalty. An
efficient high-dimensional algorithm is developed for the proposed method.
Comparison with other competing methods in simulation shows that the proposed
method always has better predictive accuracy. We apply this method to analyze a
multiple myeloma dataset and predict patients' death burden based on their gene
expressions. Our results can help classify patients into groups with different
death risks, facilitating treatment for better clinical outcomes.
