# Inverse-Weighted Survival Games

arXiv: https://arxiv.org/abs/2111.08175 · HTML: https://mlsanity.com/paper/2111.08175/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 64 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 16 of 16)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [A Scalable Discrete-Time Survival Model for Neural Networks](https://mlsanity.com/paper/1805.00917/) (2018)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework](https://mlsanity.com/paper/1801.05512/) (2018)
- [Differentiable Game Mechanics](https://mlsanity.com/paper/1905.04926/) (2019)
- [Countdown Regression: Sharp and Calibrated Survival Predictions](https://mlsanity.com/paper/1806.08324/) (2018)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [The Brier Score under Administrative Censoring: Problems and Solutions](https://mlsanity.com/paper/1912.08581/) (2019)
- [Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals](https://mlsanity.com/paper/2007.12975/) (2020)
- [Deep Learning for Survival Outcomes](https://mlsanity.com/paper/1904.10345/) (2019)
- [Survival analysis as a classification problem](https://mlsanity.com/paper/1909.11171/) (2019)

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

- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [Survival Mixture Density Networks](https://mlsanity.com/paper/2208.10759/) (2022)
- [Proper Scoring Rules for Survival Analysis](https://mlsanity.com/paper/2305.00621/) (2023)
- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Neural Frailty Machine: Beyond proportional hazard assumption in neural survival regressions](https://mlsanity.com/paper/2303.10358/) (2023)
- [Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2410.16765/) (2024)
- [Hazard Gradient Penalty for Survival Analysis](https://mlsanity.com/paper/2205.13717/) (2022)
- [Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2406.14085/) (2024)

## Abstract (arXiv)

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.