survival.metrics.concordance_index_censored

survival.metrics.concordance_index_censored(event_indicator, event_time, estimate)

Concordance index for right-censored data

The concordance index is defined as the proportion of all comparable pairs in which the predictions and outcomes are concordant.

Samples are comparable if for at least one of them an event occurred. If the estimated risk is larger for the sample with a higher time of event/censoring, the predictions of that pair are said to be concordant. If an event occurred for one sample and the other is known to be event-free at least until the time of event of the first, the second sample is assumed to outlive the first. When predicted risks are identical for a pair, 0.5 rather than 1 is added to the count of concordant pairs. A pair is not comparable if an event occurred for both of them at the same time or an event occurred for one of them but the time of censoring is smaller than the time of event of the first one.

Parameters:

event_indicator : array-like, shape = [n_samples,]

Boolean array denotes whether an event occurred

event_time : array-like, shape = [n_samples,]

Array containing the time of an event or time of censoring

estimate : array-like, shape = [n_samples,]

Estimated risk of experiencing an event

Returns:

cindex : float

Concordance index

concordant : int

Number of concordant pairs

discordant : int

Number of discordant pairs

tied_risk : int

Number of pairs having tied estimated risks

tied_time : int

Number of pairs having an event at the same time

References

[R14]

Harrell, F.E., Califf, R.M., Pryor, D.B., Lee, K.L., Rosati, R.A, “Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors”, Statistics in Medicine, 15(4), 361-87, 1996.