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In this paper,we study the sure independence screening of ultrahigh-dimensional censored data with varying coefficient single-index model.This general model framework covers a large number of commonly used survival models.The property that the proposed method is not derived for a specific model is appealing in ultrahigh dimensional regressions,as it is difficult to specify a correct model for ultrahigh dimensional predictors.Once the assuming data generating process does not meet the actual one,the screening method based on the model will be problematic.We establish the sure screening property and consistency in ranking property of the proposed method.Simulations are conducted to study the finite sample performances,and the results demonstrate that the proposed method is competitive compared with the existing methods.We also illustrate the results via the analysis of data from The National Alzheimers Coordinating Center (NACC).