sksurv.metrics.concordance_index_censored#

sksurv.metrics.concordance_index_censored(event_indicator, event_time, estimate, tied_tol=1e-08)[source]#

Measures the agreement between a predicted risk score and the actual time-to-event.

The concordance index is a measure of rank correlation between predicted risk scores and observed time points. It is defined as the proportion of all comparable pairs in which the predictions and outcomes are concordant. A pair of samples is concordant if the sample with a higher risk score has a shorter time-to-event. A higher concordance index indicates better model performance.

A pair of samples is considered comparable if the sample with a shorter survival time experienced an event. This means we can confidently say that the individual with the shorter time had a worse outcome. If both samples are censored, or if they experienced an event at the same time, they are not comparable.

When predicted risks are identical for a pair, 0.5 rather than 1 is added to the count of concordant pairs.

See the User Guide and [1] for further description.

Parameters:

  • event_indicator (array-like, shape = (n_samples,)) – A boolean array where True indicates an event and False indicates censoring.

  • event_time (array-like, shape = (n_samples,)) – Array containing the time of an event or time of censoring.

  • estimate (array-like, shape = (n_samples,)) – The predicted risk score for each sample (e.g., from estimator.predict(X)). A higher value indicates a higher risk of experiencing an event.

  • tied_tol (float, optional, default: 1e-8) – The tolerance value for considering ties in risk scores. If the absolute difference between two risk scores is smaller than or equal to tied_tol, they are considered tied.

Returns:

  • cindex (float) – The concordance index.

  • concordant (int) – The number of concordant pairs.

  • discordant (int) – The number of discordant pairs.

  • tied_risk (int) – The number of pairs with tied risk scores.

  • tied_time (int) – The number of comparable pairs with tied survival times.

Notes

This metric expects risk scores, which are typically returned by estimator.predict(X). It does not accept survival probabilities.

See also

concordance_index_ipcw

A less biased estimator of the concordance index.

References