The fused Kolmogorov–Smirnov screening for ultra-high dimensional semi-competing risks data

Abstract

Semi-competing risks data, including probably correlated non-terminal event and terminal event times, are frequently encountered in medical research. Work on semi-competing risks data has mainly focused on the situations without or only with low-dimensional covariates. However, high and ultra-high dimensional data have been very common in modern scientific research. In this article, we propose a model-free feature screening procedure for ultra-high dimensional semi-competing risks data to discover features contributing separately or jointly to non-terminal and terminal event times via Kolmogorov–Smirnov statistics. This new approach could be used for contexts with discrete, categorical and continuous covariates, which is achieved through the technique of slice-and-fuse. It enjoys several desirable advantages inherited in the Kolmogorov–Smirnov statistics. Under rather mild conditions, we show that the newly suggested method possesses sure screening property. Monte-Carlo simulation studies are conducted to investigate the finite sample properties of our proposed procedure and make comparisons with existing methods, while a real data example is also offered for illustration.