Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent

By Noah R. Simon, Jerome H. Friedman, Trevor J. Hastie, Robert Tibshirani. 2011

2,279 citations recorded by the source corpus.

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 algorithm and competing methods.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Explanations of model predictions with live and breakDown packages (2018, methodology): “This option allows for performance of variable selection based on LASSO implemented in glmnet ((Friedman et al., 2010), (Simon et al., 2011)).”
A High Frequency Trade Execution Model for Supervised Learning (2017, positive): “Table 6 compares the performance of the RNN with the elastic net method, implemented in the R package glmnet (Friedman et al., 2010; Simon et al., 2011), for predicting the next price movement.”
Supersparse Linear Integer Models for Interpretable Classification (2013, methodology): “0 Decision Rules C50R c50, [38] CART Decision Trees CART rpart, [65] Logistic Regression LR N/A (built-in) LARS Lasso (Binomial Family) Lasso glmnet, [24, 62] LARS Ridge (Binomial Family) Ridge glmnet,[24, 62] LARS Elastic Net (Binomial Family) EN glmnet,[24, 62] Random Forests RF randomForest Suppo”
Towards Integrative Machine Learning and Knowledge Extraction (2017, methodology): “Why do we use the extension “integrative”? Machine learning has many theoretical aspects and is deeply grounded in the field of artificial intelligence (AI) [4,5], however, we want to emphasize that machine learning is a very practical field with many diverse application areas (e.”
Predicting non-small cell lung cancer prognosis by fully automated microscopic pathology image features (2016, methodology): “We built elastic net-Cox proportional hazards models 46 to select the most informative quantitative image features and calculated survival indices derived from H&E stained microscopic pathology images (see Methods).”
Mining Electronic Health Records: A Survey (2017, positive): “Lasso [Tibshirani et al. 1997] and elastic-net regularized Cox models [Simon et al. 2011b] have been developed, and have been further extended by regularizing them with convex combinations of L1 and L2 penalties [Zhang and Lu 2007].”
Benefit and harm of intensive blood pressure treatment: Derivation and validation of risk models using data from the SPRINT and ACCORD trials (2017, methodology): “Elastic net regularization is a statistical approach designed to select models in the context of collinearity, which produces challenges for older stepwise selection approaches [13,16].”
The Mortality and Medical Costs of Air Pollution: Evidence from Changes in Wind Direction (2019, positive): “8 See Simon et al. (2011) for a detailed discussion of the algorithm we employ to implement the Cox proportional hazards estimator with a Lasso penalty term.”
Machine Learning for Survival Analysis: A Survey (2017, methodology): “The EN-Cox method was proposed by Noah Simon et al. [Simon et al. 2011] where the Elastic Net penalty term shown in Table III with 0 ≤ α ≤ 1 and introduced into the log-partial likelihood function in Eq.”
An extensive experimental survey of regression methods (2019, methodology): “glmnet is the LASSO and elastic-net regularization for generalized 680 linear models (GLM) implemented in the glmnet package [17].”
Long-term Causal Inference Under Persistent Confounding via Data Combination (2022, methodology): “For the cross-validated ridge regression, we choose the default option in the R package glmnet [Simon et al., 2011].”
Multiple predicting K-fold cross-validation for model selection (2018, positive): “…the most commonly embedded in R packages for selecting penalty parameter such as glmnet for implementing Friedman, Hastie, and Tibshirani (2010), Simon, Friedman, Hastie, and Tibshirani (2011), glmpath for Park and Hastie (2007), genlasso for Tibshirani and Taylor (2011), lqa for Zou (2006),…”