# Effective Ways to Build and Evaluate Individual Survival Distributions

arXiv: https://arxiv.org/abs/1811.11347 · HTML: https://mlsanity.com/paper/1811.11347/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2018.

## Built on by (most cited first, 30 of 64)

- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [Exploring Large Language Models for Feature Selection: A Data-centric Perspective](https://mlsanity.com/paper/2408.12025/) (2024)
- [Longitudinal Fairness with Censorship](https://mlsanity.com/paper/2203.16024/) (2022)
- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [Interpretable Vision-Language Survival Analysis with Ordinal Inductive Bias for Computational Pathology](https://mlsanity.com/paper/2409.09369/) (2024)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [Proper Scoring Rules for Survival Analysis](https://mlsanity.com/paper/2305.00621/) (2023)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [SCMIL: Sparse Context-aware Multiple Instance Learning for Predicting Cancer Survival Probability Distribution in Whole Slide Images](https://mlsanity.com/paper/2407.00664/) (2024)
- [Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures](https://mlsanity.com/paper/2112.04828/) (2021)
- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2410.16765/) (2024)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [A Large-Scale Neutral Comparison Study of Survival Models on Low-Dimensional Data](https://mlsanity.com/paper/2406.04098/) (2024)
- [Toward Conditional Distribution Calibration in Survival Prediction](https://mlsanity.com/paper/2410.20579/) (2024)
- [NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2505.11054/) (2025)
- [Flexible Group Fairness Metrics for Survival Analysis](https://mlsanity.com/paper/2206.03256/) (2022)
- [Efficient Training of Probabilistic Neural Networks for Survival Analysis](https://mlsanity.com/paper/2404.06421/) (2024)
- [Toward a Well-Calibrated Discrimination via Survival Outcome-Aware Contrastive Learning](https://mlsanity.com/paper/2410.11340/) (2024)
- [Adaptive Transformer Modelling of Density Function for Nonparametric Survival Analysis](https://mlsanity.com/paper/2409.06209/) (2024)
- [MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation](https://mlsanity.com/paper/2409.06525/) (2024)
- [Sample Efficient Learning of Image-Based Diagnostic Classifiers Using Probabilistic Labels](https://mlsanity.com/paper/2102.06164/) (2021)
- [Censored Quantile Regression Neural Networks for Distribution-Free Survival Analysis](https://mlsanity.com/paper/2205.13496/) (2022)
- [Experimental Comparison of Ensemble Methods and Time-to-Event Analysis Models Through Integrated Brier Score and Concordance Index](https://mlsanity.com/paper/2403.07460/) (2024)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [CoC: Chain-of-Cancer based on Cross-Modal Autoregressive Traction for Survival Prediction](https://mlsanity.com/paper/2506.15696/) (2025)
- [SurvBench: A Standardised Preprocessing Pipeline for Multi-Modal Electronic Health Record Survival Analysis](https://mlsanity.com/paper/2511.11935/) (2025)

## Abstract (arXiv)

An accurate model of a patient's individual survival distribution can help determine the appropriate treatment for terminal patients. Unfortunately, risk scores (e.g., from Cox Proportional Hazard models) do not provide survival probabilities, single-time probability models (e.g., the Gail model, predicting 5 year probability) only provide for a single time point, and standard Kaplan-Meier survival curves provide only population averages for a large class of patients meaning they are not specific to individual patients. This motivates an alternative class of tools that can learn a model which provides an individual survival distribution which gives survival probabilities across all times - such as extensions to the Cox model, Accelerated Failure Time, an extension to Random Survival Forests, and Multi-Task Logistic Regression. This paper first motivates such "individual survival distribution" (ISD) models, and explains how they differ from standard models. It then discusses ways to evaluate such models - namely Concordance, 1-Calibration, Brier score, and various versions of L1-loss - and then motivates and defines a novel approach "D-Calibration", which determines whether a model's probability estimates are meaningful. We also discuss how these measures differ, and use them to evaluate several ISD prediction tools, over a range of survival datasets.