# Variable selection for nonlinear Cox regression model via deep learning

arXiv: https://arxiv.org/abs/2211.09287 · HTML: https://mlsanity.com/paper/2211.09287/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [A Deep Variational Approach to Clustering Survival Data](https://mlsanity.com/paper/2106.05763/) (2021)
- [Deep Learning for Patient-Specific Kidney Graft Survival Analysis](https://mlsanity.com/paper/1705.10245/) (2017)
- [Deep Feature Selection using a Teacher-Student Network](https://mlsanity.com/paper/1903.07045/) (2019)
- [Calibrating multi-dimensional complex ODE from noisy data via deep neural networks](https://mlsanity.com/paper/2106.03591/) (2021)
- [Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks](https://mlsanity.com/paper/2204.01682/) (2022)

## Built on by (most cited first, 2 of 2)

- [Semiparametric Regression for Spatial Data via Deep Learning](https://mlsanity.com/paper/2301.03747/) (2023)
- [Deep Learning for Efficient GWAS Feature Selection](https://mlsanity.com/paper/2312.15055/) (2023)

## Abstract (arXiv)

Variable selection problem for the nonlinear Cox regression model is considered. In survival analysis, one main objective is to identify the covariates that are associated with the risk of experiencing the event of interest. The Cox proportional hazard model is being used extensively in survival analysis in studying the relationship between survival times and covariates, where the model assumes that the covariate has a log-linear effect on the hazard function. However, this linearity assumption may not be satisfied in practice. In order to extract a representative subset of features, various variable selection approaches have been proposed for survival data under the linear Cox model. However, there exists little literature on variable selection for the nonlinear Cox model. To break this gap, we extend the recently developed deep learning-based variable selection model LassoNet to survival data. Simulations are provided to demonstrate the validity and effectiveness of the proposed method. Finally, we apply the proposed methodology to analyze a real data set on diffuse large B-cell lymphoma.