# T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP

arXiv: https://arxiv.org/abs/2103.04556 · HTML: https://mlsanity.com/paper/2103.04556/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 8 Mar 2021.

## Builds on (most cited first, 14 of 14)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [A Scalable Discrete-Time Survival Model for Neural Networks](https://mlsanity.com/paper/1805.00917/) (2018)
- [Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals](https://mlsanity.com/paper/2007.12975/) (2020)
- [Censored Quantile Regression Forest](https://mlsanity.com/paper/2001.03458/) (2020)
- [LEO-Py: Estimating likelihoods for correlated, censored, and uncertain data with given marginal distributions](https://mlsanity.com/paper/1910.02958/) (2019)

## Built on by (most cited first, 8 of 8)

- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift](https://mlsanity.com/paper/2506.23453/) (2025)
- [Smoothing-Based Conformal Prediction for Balancing Efficiency and Interpretability](https://mlsanity.com/paper/2509.22529/) (2025)
- [Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better](https://mlsanity.com/paper/2601.21455/) (2026)

## Abstract (arXiv)

It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence band of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP (Katzman et al., 2018; Kvamme et al., 2019)), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm WCCI, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm T-SCI, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.