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Statistica Sinica 22 (2012), 271-294

doi:http://dx.doi.org/10.5705/ss.2010.107





ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS

MODEL WITH A SOLUTION PATH ALGORITHM


Yichao Wu


North Carolina State University


Abstract: For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.



Key words and phrases: Cox's proportional hazards model, elastic net, LARS, LASSO, ordinary differential equation, solution path algorithm.
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