# Factor-Augmented Regularized Model for Hazard Regression

arXiv: https://arxiv.org/abs/2210.01067 · HTML: https://mlsanity.com/paper/2210.01067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Estimating Number of Factors by Adjusted Eigenvalues Thresholding](https://mlsanity.com/paper/1909.10710/) (2019)
- [Robust high dimensional factor models with applications to statistical machine learning](https://mlsanity.com/paper/1808.03889/) (2018)
- [High-dimensional Ordinary Least-squares Projection for Screening Variables](https://mlsanity.com/paper/1506.01782/) (2015)
- [Factor-Adjusted Regularized Model Selection](https://mlsanity.com/paper/1612.08490/) (2016)
- [Large Covariance Estimation through Elliptical Factor Models](https://mlsanity.com/paper/1507.08377/) (2015)
- [Robust Covariance Estimation for Approximate Factor Models](https://mlsanity.com/paper/1602.00719/) (2016)

## Built on by (most cited first, 1 of 1)

- [Communication-Efficient Distributed Estimation and Inference for Cox's Model](https://mlsanity.com/paper/2302.12111/) (2023)

## Abstract (arXiv)

A prevalent feature of high-dimensional data is the dependence among covariates, and model selection is known to be challenging when covariates are highly correlated. To perform model selection for the high-dimensional Cox proportional hazards model in presence of correlated covariates with factor structure, we propose a new model, Factor-Augmented Regularized Model for Hazard Regression (FarmHazard), which builds upon latent factors that drive covariate dependence and extends Cox's model. This new model generates procedures that operate in two steps by learning factors and idiosyncratic components from high-dimensional covariate vectors and then using them as new predictors. Cox's model is a widely used semi-parametric model for survival analysis, where censored data and time-dependent covariates bring additional technical challenges. We prove model selection consistency and estimation consistency under mild conditions. We also develop a factor-augmented variable screening procedure to deal with strong correlations in ultra-high dimensional problems. Extensive simulations and real data experiments demonstrate that our procedures enjoy good performance and achieve better results on model selection, out-of-sample C-index and screening than alternative methods.