Feature screening based on distance correlation for ultrahigh-dimensional censored data with covariate measurement error

Feature screening is an important method to reduce the dimension and capture informative variables in ultrahigh-dimensional data analysis. Its key idea is to select informative variables using correlations between the response and the covariates. Many methods have been developed for feature screening. These methods, however, are challenged by complex features pertinent to the data collection as well as the nature of the data themselves. Typically, incomplete response caused by right-censoring and covariate measurement error are often accompanying with survival analysis. Even though many methods have been proposed for censored data, little work has been available when both incomplete response and measurement error occur simultaneously. In addition, the conventional feature screening methods may fail to detect the truly important covariates that are marginally independent of the response variable due to correlations among covariates. In this paper, we explore this important problem and propose the model-free feature screening method in the presence of the censored response and error-prone covariates. In addition, we also develop the iteration method to improve the accuracy of selecting all important covariates. Numerical studies are reported to assess the performance of the proposed method. Finally, we implement the proposed method to a real dataset.