# Univariate Cox scores and time-dependent metrics

Source: https://onco.cc/terms/time-dependent-auc/  
OnCo record `time-dependent-auc` (Term). Data CC BY-NC 4.0, attribute "Data from OnCo (onco.cc)"; commercial use needs a licence.

## TL;DR

A univariate Cox model fits one gene at a time against survival and its z-score ranks genes by prognostic strength; the Breslow approximation is how the fit handles patients whose events fall on the same day.

## Summary

Proportional hazards models relate the time before an event to covariates, with each covariate's effect multiplying the hazard (Wikipedia). Fitting one gene at a time across twenty thousand genes gives a marginal prognostic score per gene, a common feature-selection step that must be done inside the training fold; tied event times are handled by the Breslow or Efron approximations to the partial likelihood. The model assumes hazards stay proportional over time, which many cancer covariates violate.

## Fields

- Kind: Term
- Last checked: 2026-09-24
- Also known as: univariate Cox; univariate Cox score; Cox z-score; per-gene Cox; Breslow approximation; Breslow method for ties; Cox partial likelihood; proportional hazards assumption
- Tags: cansim-terms

## Notes

- Listed in the CanSim terms map 1.0.0 (docs/onco/terms.json, generated 2026-09-24), CC BY 4.0, attribution: CanSim project, an open, public-data-first cancer foundation-model programme; CanSim page path /terms/univariate-cox-score.

## Sources

- Wikipedia: https://en.wikipedia.org/wiki/Proportional_hazards_model
- Wikipedia: https://en.wikipedia.org/wiki/Proportional_hazards_model

## Connected records

- terms: [C-index (concordance index), Harrell's and Uno's](https://onco.cc/terms/concordance-index/), [Cancer AI vocabulary (CanSim terms map)](https://onco.cc/terms/cancer-ai-vocabulary/), [Censoring and events in survival data](https://onco.cc/terms/censoring-and-events/), [Hazard ratio (HR)](https://onco.cc/terms/hazard-ratio/), [Kaplan-Meier curve, censoring and proportional hazards](https://onco.cc/terms/kaplan-meier-curve/), [Loss functions: cross-entropy and mean squared error](https://onco.cc/terms/cross-entropy-mse/)

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JSON: https://onco.cc/api/v1/entities/time-dependent-auc.json