Variable selection with group LASSO approach: Application to Cox regression with frailty model

In analysis of survival outcomes supplemented with both clinical information and high-dimensional gene expression data, use of the traditional Cox proportional hazards model fails to meet some emerging needs in biomedical research. First, the number of covariates is generally much larger the sample size. Secondly, predicting an outcome based on individual gene expression is inadequate because multiple biological processes and functional pathways regulate phenotypic expression. Another challenge is that the Cox model assumes that populations are homogenous, implying that all individuals have the same risk of death, which is rarely true due to unmeasured risk factors among populations. In this paper we propose group LASSO with gamma-distributed frailty for variable selection in Cox regression by extending previous scholarship to account for heterogeneity among group structures related to exposure and susceptibility. The consistency property of the proposed method is established. This method is appropriate for addressing a wide variety of research questions from genetics to air pollution. Simulated and real world data analysis shows promising performance by group LASSO compared with other methods, including group SCAD and group MCP. Future research directions include expanding the use of frailty with adaptive group LASSO and sparse group LASSO methods.