Robust variable selection methods with Cox model-a selective practical benchmark study

With the advancement of biological and medical techniques, we can now obtain large amounts of high-dimensional omics data with censored survival information. This presents challenges in method development across various domains, particularly in variable selection. Given the inherently skewed distribution of the survival time outcome variable, robust variable selection methods offer potential solutions. Recently, there has been a focus on extending robust variable selection methods from linear regression models to survival models. However, despite these developments, robust methods are currently rarely used in practical applications, possibly due to a limited appreciation of their overall good performance. To address this gap, we conduct a selective review comparing the variable selection performance of twelve robust and non-robust penalised Cox models. Our study reveals the intricate relationship among covariates, survival outcomes, and modeling approaches, demonstrating how subtle variations can significantly impact the performance of methods considered. Based on our empirical research, we recommend the use of robust Cox models for variable selection in practice based on their superior performance in presence of outliers while maintaining good efficiency and accuracy when there are no outliers. This study provides valuable insights for method development and application, contributing to a better understanding of the relationship between correlated covariates and censored outcomes.