Md Hasinur Rahaman Khan and JEH Shaw
Variable Selection with The Modified Buckley-James Method and The Dantzig Selector for High-dimensional Survival Data
Abstract: We develop variable selection approaches for accelerated failure time models that consist of a group of algorithms that are based on a synthesis of the two widely used techniques in survival analysis and variable selection area—the Buckley–James method and the Dantzig selector. Two algorithms are based on the two proposed modified Buckley–James estimating methods that are designed for high–dimensional censored data. Other three algorithms are based on weighted Dantzig selector for which two weights obtained from the two proposed synthesis based algorithms and other weight is obtained from a proposed form. The methods are easy to understand and they do estimation and variable selection simultaneously. Furthermore, they can deal with collinearity among the covariates and also among the groups of covariates. We conducted several simulation studies and one empirical analysis with a microarray dataset. Both numerical studies demonstrated a reasonable satisfied level of variable selection performances. In addition, the microarray data analysis showed that the methods may perform similarly to other three correlation-based greedy variable selection techniques in literature—SIS, TCS, and PC-simple. This empirical study also found that the sure independence screening technique improves considerably the performance of most of the proposed methods.
Keywords: Accelerated failure time (AFT); Buckley–James estimating equation; Dantzig selector; Variable selection.