# Optimal Cox Regression Subsampling Procedure with Rare Events

arXiv: https://arxiv.org/abs/2012.02122 · HTML: https://mlsanity.com/paper/2012.02122/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2020.

## Built on by (most cited first, 3 of 3)

- [Deep Neural Network Based Accelerated Failure Time Models using Rank Loss](https://mlsanity.com/paper/2206.05974/) (2022)
- [Flexible Deep Neural Networks for Partially Linear Survival Data: Estimation and Survival Inference](https://mlsanity.com/paper/2512.10570/) (2025)
- [Scale-invariant Optimal Sampling for Rare-events Data with Sparse Models](https://mlsanity.com/paper/2608.22597/) (2026)

## Abstract (arXiv)

Massive sized survival datasets are becoming increasingly prevalent with the development of the healthcare industry. Such datasets pose computational challenges unprecedented in traditional survival analysis use-cases. A popular way for coping with massive datasets is downsampling them to a more manageable size, such that the computational resources can be afforded by the researcher. Cox proportional hazards regression has remained one of the most popular statistical models for the analysis of survival data to-date. This work addresses the settings of right censored and possibly left truncated data with rare events, such that the observed failure times constitute only a small portion of the overall sample. We propose Cox regression subsampling-based estimators that approximate their full-data partial-likelihood-based counterparts, by assigning optimal sampling probabilities to censored observations, and including all observed failures in the analysis. Asymptotic properties of the proposed estimators are established under suitable regularity conditions, and simulation studies are carried out to evaluate the finite sample performance of the estimators. We further apply our procedure on UK-biobank colorectal cancer genetic and environmental risk factors.