# Approximating Partial Likelihood Estimators via Optimal Subsampling

arXiv: https://arxiv.org/abs/2210.04581 · HTML: https://mlsanity.com/paper/2210.04581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2022.

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

- [Scalable Cox Regression via Grouped Risk Sets and Sharper LogSumExp Rates](https://mlsanity.com/paper/2609.40120/) (2026)

## Abstract (arXiv)

With the growing availability of large-scale biomedical data, it is often time-consuming or infeasible to directly perform traditional statistical analysis with relatively limited computing resources at hand. We propose a fast subsampling method to effectively approximate the full data maximum partial likelihood estimator in Cox's model, which largely reduces the computational burden when analyzing massive survival data. We establish consistency and asymptotic normality of a general subsample-based estimator. The optimal subsampling probabilities with explicit expressions are determined via minimizing the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator. We propose a two-step subsampling algorithm for practical implementation, which has a significant reduction in computing time compared to the full data method. The asymptotic properties of the resulting two-step subsample-based estimator is also established. Extensive numerical experiments and a real-world example are provided to assess our subsampling strategy.