# Efficient Learning of Survival Analysis Models Under Outcome-Dependent Truncation and Censoring

arXiv: https://arxiv.org/abs/2610.12538 · HTML: https://mlsanity.com/paper/2610.12538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 8 Oct 2026.

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

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Computationally and Statistically Efficient Truncated Regression](https://mlsanity.com/paper/2010.12000/) (2020)
- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussians](https://mlsanity.com/paper/2410.01656/) (2024)
- [Near-Optimal Dynamic Matching via Coarsening with Application to Heart Transplantation](https://mlsanity.com/paper/2602.04989/) (2026)
- [Position: Machine Learning for Heart Transplant Allocation Policy Optimization Should Account for Incentives](https://mlsanity.com/paper/2602.04990/) (2026)
- [Learning Potentials for Dynamic Matching and Application to Heart Transplantation](https://mlsanity.com/paper/2602.08878/) (2026)
- [Linear Regression with Unknown Truncation Beyond Gaussian Features](https://mlsanity.com/paper/2602.12534/) (2026)
- [Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis](https://mlsanity.com/paper/2606.02671/) (2026)
- [Cox Regression Model Under Dependent Truncation](https://mlsanity.com/paper/1803.09830/) (2018)
- [Preference Elicitation for Policy Optimization and Application to Aligning Heart Transplantation with Human Values](https://mlsanity.com/paper/2608.28620/) (2026)

## Abstract (arXiv)

Modern machine learning models are typically trained on data assumed to be representative of the predictive tasks the model will face in the future, but practical datasets violate this assumption. We focus on outcome-dependent truncation in which an observation appears in the training data depending on its label. Our work connects two largely distinct literatures: efficient learning under truncation and survival analysis. Existing methods for truncated survival analysis do not characterize the optimization landscape and instead rely on iterative procedures such as expectation maximization. We address this gap and prove that Cox regression can be efficiently learned under truncated and right-censored data using first-order optimization when the baseline hazard is known (despite nonconvexity). In contrast, when the baseline hazard is learned jointly, we construct identifiable and correctly specified models whose negative log-likelihood contains strict suboptimal local minima. On experiments with four survival datasets, we show that accounting for truncation reduces the prediction bias induced by naive Cox regression and extends to neural networks. We also show orders of magnitude speedups compared to standard expectation maximization.