Abstract
In this work, our aims are to do model selection, coefficient estimation and variable grouping imultaneously in Cox’s proportional hazards model.Tibshirani (1996) added L1 norm penalty function to objective function to obtain the sparsity of coefficient estimation, which is an efficient way to domodel election and coefficient estimation at one time. In traditional variable grouping methods, variables are grouped based on the prior knowledge, which is often be judged too subjective. In this work, we apply Tibshirani et al. (2005) to the partial likelihood of Cox model. The Fused LASSO penalty focuses on the combination of L1 norm and the difference of L1 norm: L1 penalty shrinkages coefficients to ensure the sparseness of coefficient estimates, while the difference of L1 penalty shrinkages the difference between the neighboring coefficients, which makes variables be grouped in the sense of nvolving same coefficient estimates. This data adaptive approach is more objective and we can estimate, select and group variables simultaneously. In our simulation, we consider three different cases: LASSO, generalized LASSO and Fused LASSO to compare the effects of the L1 and the difference of L1 penalty and apply to analysis Gene Signature for Adjuvant Chemotherapy in Resected Non–Small-Cell Lung cancer data.