Generalized Jaccard feature screening for ultra-high dimensional survival data

To identify critical genomes that influence a cancer patient's survival time, feature screening methods play a vital role in this biomedical field. Most of the current research relies on a fixed survival function model, which limits its universality in practical applications. In this paper, we propose the Generalized Jaccard coefficient (GJAC), which extends the traditional Jaccard coefficient from comparing binary vectors' similarity to calculating the correlation between the general vectors. The larger the GJAC value, the higher the sample similarity. Using the GJAC, we introduce a novel model-free screening method to select the active set of covariates in ultra-high dimensional survival data. Through Monte Carlo simulations, GJAC-Sure Independence Screening (GJAC-SIS) shows a higher accuracy, lower errors, and an excellent applicability in different types of survival data compared with other existing model-free feature screening methods in survival data. Additionally, in the real cancer datasets (DLBCL), GJAC-SIS can screen out two additional important genomes, which are certified in the real biomedical experiment, while the other five methods can't. As a result, GJAC-SIS achieves a high screening precision, delivers a more effective screening outcome, and has a better utility and universality.