Survival impact index and ultrahigh‐dimensional model‐free screening with survival outcomes

Summary Motivated by ultrahigh‐dimensional biomarkers screening studies, we propose a model‐free screening approach tailored to censored lifetime outcomes. Our proposal is built upon the introduction of a new measure, survival impact index (SII). By its design, SII sensibly captures the overall influence of a covariate on the outcome distribution, and can be estimated with familiar nonparametric procedures that do not require smoothing and are readily adaptable to handle lifetime outcomes under various censoring and truncation mechanisms. We provide large sample distributional results that facilitate the inference on SII in classical multivariate settings. More importantly, we investigate SII as an effective screener for ultrahigh‐dimensional data, not relying on rigid regression model assumptions for real applications. We establish the sure screening property of the proposed SII‐based screener. Extensive numerical studies are carried out to assess the performance of our method compared with other existing screening methods. A lung cancer microarray data is analyzed to demonstrate the practical utility of our proposals.