Elastic Net for Cox's Proportional Hazards Model with a Solution Path Algorithm.

نویسنده

  • Yichao Wu
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent.

We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of ℓ1 and ℓ2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, and employs warm starts to find a solution along a regularization path. We demonstrate the efficacy of our algorithm on real and simulated data sets, and find considerable speedup between our algori...

متن کامل

A cocktail algorithm for solving the elastic net penalized Cox's regression in high dimensions

We introduce a cocktail algorithm, a good mixture of coordinate decent, the majorization-minimization principle and the strong rule, for computing the solution paths of the elastic net penalized Cox’s proportional hazards model. The cocktail algorithm enjoys a proven convergence property. We have implemented the cocktail algorithm in an R package fastcox. Numerical examples show that cocktail i...

متن کامل

Novel Harmonic Regularization Approach for Variable Selection in Cox's Proportional Hazards Model

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data...

متن کامل

Regularization for Cox's Proportional Hazards Model with Np-dimensionality.

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Cox's proportional h...

متن کامل

Sheppard's correction for grouping in Cox's proportional hazards model

Cox's proportional hazards model is often t to grouped survival data, i.e. occurrence/exposure data over given time intervals and covariate strata. We derive a Sheppard correction for the bias in the grouped data analogue of Cox's maximum partial likelihood estimator. This is done via a large sample theory in which the covariate strata and time intervals shrink as the sample size increases.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Statistica Sinica

دوره 22  شماره 

صفحات  -

تاریخ انتشار 2012