SurvICL: The First Survival Analysis Foundation Model to Surpass the Cox Model

Survival analysis is a core tool in medical statistics, used to answer "when will an event occur for a patient"—such as disease recurrence, death, or device failure. For half a century, the Cox proportional hazards model has been the gold standard in this field. Even as Tabular Foundation Models (TFMs) have comprehensively surpassed gradient-boosted trees in classification and regression tasks, survival analysis has remained an unconquered stronghold. That is, until SurvICL.

A Counterintuitive Finding: Foundation Models Can't Beat a 50-Year-Old Cox Model

The research team first conducted a systematic test: applying current mainstream tabular foundation models directly to survival analysis tasks. The results were surprising—no TFM could reliably beat the Cox model.

The reason is not hard to understand. Survival analysis deals with censored data, where we only know that an event has not occurred after a certain time point, but not exactly when it will occur. This means standard supervised learning loss functions cannot be directly applied. Additionally, clinical cohorts often have small sample sizes, making the large-scale pretraining-fine-tuning paradigm—on which foundation models rely for their advantages—difficult to apply here.

This finding itself is noteworthy: it shows that survival analysis is not a problem that can be solved by "just adding another transformer," but rather requires redesigning pretraining strategies tailored to the task's characteristics.

Censored data is the fundamental characteristic that distinguishes survival analysis from general regression tasks. Consider clinical follow-up as an example: at the end of a study, some patients are still alive, and we only know that their survival time exceeds the follow-up duration, but not the exact time of death. Such observations are called right-censored. If these samples are simply discarded, risk will be systematically overestimated; if treated as exact event times, survival time will be underestimated. The censoring mechanism is typically assumed to be "non-informative censoring," meaning censoring time and event time are independent of each other. The classic Kaplan-Meier estimator and Cox partial likelihood are both derived under this assumption. Deep survival models often need to explicitly model the censoring distribution, or employ techniques such as inverse probability weighting and ranking losses, which significantly increases modeling complexity—and is a key reason why general tabular foundation models struggle to transfer directly.

SurvICL's Core Idea: Directly Predicting Survival Curves via In-Context Learning

SurvICL's key innovation lies in transforming survival analysis into an in-context learning problem. The model does not rely on gradient updates to adapt to new datasets; instead, at inference time, it directly predicts the complete survival curve based on a small number of input samples.

Two design decisions in the pretraining phase support this capability:

Proportional-Odds Prior: A More Flexible Synthetic Data Generator

SurvICL is pretrained entirely on synthetic data. The team proposed a novel flexible proportional-odds prior to generate these synthetic datasets. Ablation experiments showed that this prior outperforms other candidate approaches in generation quality—it provides the model with sufficiently diverse and structurally sound training signals, enabling generalization to real clinical data.

The proportional odds model is a class of methods in survival analysis that stands alongside the Cox model, suitable for ordered categorical or discrete-time event outcomes. It assumes that the odds ratio of covariates on cumulative probabilities remains constant across time thresholds—that is, effects at different time points are proportional. Compared with Cox's proportional hazards assumption, proportional odds relaxes the parametric dependence on baseline hazards and performs more robustly when event times are discretized or when there are many tied time points. The "flexible proportional-odds prior" adopted by SurvICL leverages the generative capacity of this model family, synthesizing survival datasets with diverse distributional shapes and reasonable structure by randomly sampling regression coefficients, baseline odds curves, and noise levels. This prior covers a broader range of real-world data patterns than fixed parametric priors, providing richer training signals for subsequent in-context learning.

Quantile Regression Loss: Saying Goodbye to Complex Censoring Handling

Most survival models require complex likelihood functions to handle censoring. SurvICL takes a completely different approach: it is trained using a plain quantile regression loss. This is feasible because the synthetic data generator naturally provides uncensored event times—during pretraining, the model sees "complete answers," so it does not need to handle censoring at the loss function level.

This is equivalent to shifting the challenge of censoring handling to the data generation stage rather than the model training stage.

Quantile regression was first proposed by Koenker and Bassett. Its goal is not to fit the conditional mean, but to estimate specific quantiles of the conditional distribution, such as the median or the 90th percentile. Its loss function is called the pinball loss, which applies asymmetric penalties to overestimation and underestimation of quantiles. In survival analysis, directly performing quantile regression on event times naturally characterizes multiple time points of the survival curve without assuming a specific distribution family. Because SurvICL's pretraining data comes from a synthetic generator and contains no censoring, it can directly use the plain quantile regression loss, avoiding the complexity of Cox partial likelihood or parametric censoring likelihood. This design moves censoring modeling from the loss level to the data generation level, keeping the training objective simple while still outputting complete survival curves.

A Survival Analysis Benchmark with 103 Datasets

To rigorously evaluate SurvICL, the team built the largest survival analysis benchmark to date, covering 103 datasets.

In terms of evaluation strategy, they deliberately set aside 63 datasets that were completely excluded from any design decisions—including prior selection, loss function design, and hyperparameter determination. These 63 datasets constitute a truly "held-out" test set to examine the model's generalization ability.

On these 63 datasets, SurvICL was compared with 20 baseline models, covering tree models, deep models, and foundation models, with no hyperparameter tuning. The results:

• SurvICL won 82.9% of pairwise comparisons on the integrated Brier score
• The second-ranked Cox model had a win rate of 71.3%
• SurvICL is the first model to outrank Cox on small datasets

The last point is especially critical. Small datasets have long been a weakness for deep learning methods in survival analysis, and SurvICL's breakthrough on this front demonstrates that the in-context learning paradigm is indeed well-suited for low-resource clinical scenarios.

The integrated Brier score (IBS) is a commonly used metric for evaluating the calibration and discrimination of survival model predictions. The Brier score measures the mean squared error between predicted survival probabilities and true outcomes, with lower values being better. The integrated Brier score integrates the Brier score over a time interval, reflecting the model's average prediction error over the entire follow-up period, penalizing both point-in-time deviations and overall curve shape deviations. Unlike the concordance index (C-index), which focuses only on ranking, IBS is sensitive to probability calibration, making it more suitable for evaluating models like SurvICL that directly output survival curves. Pairwise comparison means counting, between each pair of models, which one achieves lower IBS on more datasets. The win rate reflects the robustness of relative advantage rather than the magnitude of absolute error.

Why This Matters

SurvICL's value goes beyond performance numbers. It reveals a path: when the data characteristics of a target task do not match standard supervised learning, starting from the pretraining data generation mechanism may be more effective than modifying model architecture or loss functions.

For clinical researchers, a model that requires no hyperparameter tuning and can stably outperform Cox on small cohorts means a lower barrier to deployment. For machine learning researchers, SurvICL demonstrates that the feasibility boundaries of foundation models in structured, censored, small-sample scenarios are being pushed wider.

Cox model has reigned for fifty years, and now it finally has a true challenger.

One-line Summary

Through synthetic data in-context learning, SurvICL becomes the first model to surpass the 50-year gold-standard Cox model on small datasets.

Paragraph Summary

Survival analysis has long been dominated by the Cox proportional hazards model. Even though tabular foundation models have comprehensively surpassed gradient-boosted trees in classification and regression, they still cannot reliably beat Cox, with the core difficulties being censored data and small-sample clinical cohorts. SurvICL transforms survival analysis into an in-context learning problem, directly predicting complete survival curves from a small number of samples at inference time. Its pretraining uses a flexible proportional-odds prior to generate synthetic data and employs a plain quantile regression loss, shifting censoring handling to the data generation stage. The team built the largest survival analysis benchmark to date, covering 103 datasets, 63 of which are fully held out. SurvICL achieves a win rate of 82.9% in pairwise comparisons on the integrated Brier score, becoming the first model to outrank Cox on small datasets.