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In the analysis of survival outcome supplemented with both clinicalinformation and high-dimensional gene expression data, use of the traditionalCox proportional hazards model (1972) fails to meet some emerging needs inbiomedical research. First, the number of covariates is generally much largerthe sample size. Secondly, predicting an outcome based on individual geneexpression is inadequate because multiple biological processes and functionalpathways regulate the expression associated with a gene. Another challenge isthat the Cox model assumes that populations are homogenous, implying that allindividuals have the same risk of death, which is rarely true due to unmeasuredrisk factors among populations. In this paper we propose group LASSO withgamma-distributed frailty for variable selection in Cox regression by extendingprevious scholarship to account for heterogeneity among group structuresrelated to exposure and susceptibility. The consistency property of theproposed method is established. This method is appropriate for addressing awide variety of research questions from genetics to air pollution. Simulatedanalysis shows promising performance by group LASSO compared with othermethods, including group SCAD and group MCP. Future directions includeexpanding the use of frailty with adaptive group LASSO and sparse group LASS.

Variable selection via Group LASSO Approach : Application to the Cox Regression and frailty model