Integrated powered density: Screening ultrahigh dimensional covariates with survival outcomes

Modern biomedical studies have yielded abundant survival data with high-throughput predictors. Variable screening is a crucial first step in analyzing such data, for the purpose of identifying predictive biomarkers, understanding biological mechanisms, and making accurate predictions. To nonparametrically quantify the relevance of each candidate variable to the survival outcome, we propose integrated powered density (IPOD), which compares the differences in the covariate-stratified distribution functions. The proposed new class of statistics, with a flexible weighting scheme, is general and includes the Kolmogorov statistic as a special case. Moreover, the method does not rely on rigid regression model assumptions and can be easily implemented. We show that our method possesses sure screening properties, and confirm the utility of the proposal with extensive simulation studies. We apply the method to analyze a multiple myeloma study on detecting gene signatures for cancer patients' survival.