Variable selection for censored data with greedy algorithm based adaptive quantile regression models

The application of quantile regression offers a versatile and appealing approach for analyzing censored data, particularly within the accelerated failure time (AFT) model, where the focus lies on the significance of conditional quantile functions in regression analysis. The extension is achieved through the integration of well-established greedy algorithms-sure independence screening (SIS), tilting, and PC-simple-resulting in the development of Quant-SIS, Quant-Tilting, and Quant-PC techniques, respectively. These techniques prove to be adaptable, efficient, and consistent variable selection algorithms for high-dimensional datasets due to the inherent properties of sure independence, tilting correlation, and partial faithfulness. We compare the performance of the proposed methods with two competitive approaches from the existing literature. Through a comprehensive series of simulation studies encompassing diverse scenarios including varying collinearity levels among covariates, levels of censoring, and quantiles-we demonstrate their efficacy. Additionally, we apply the proposed methods to real-world microarray data from Diffuse Large B-cell Lymphoma (DLBCL) patients. This application showcases the ability of our techniques to accurately identify genes associated with the survival time of DLBCL patients. The results indicate a substantial enhancement in performance, as the modified quantile regression techniques for censored data significantly outperform existing methods across a wide spectrum of cases.