sksurv.metrics.concordance_index_ipcw

sksurv.metrics.concordance_index_ipcw(survival_train, survival_test, estimate, tau=None, tied_tol=1e-08)

Concordance index for right-censored data based on inverse probability of censoring weights.

This is an alternative to the estimator in concordance_index_censored() that does not depend on the distribution of censoring times in the test data. Therefore, the estimate is unbiased and consistent for a population concordance measure that is free of censoring.

It is based on inverse probability of censoring weights, thus requires access to survival times from the training data to estimate the censoring distribution. Note that this requires that survival times survival_test lie within the range of survival times survival_train. This can be achieved by specifying the truncation time tau. The resulting cindex tells how well the given prediction model works in predicting events that occur in the time range from 0 to tau.

The estimator uses the Kaplan-Meier estimator to estimate the censoring survivor function. Therefore, it is restricted to situations where the random censoring assumption holds and censoring is independent of the features.

See [1] for further description.

Parameters:
  • survival_train (structured array, shape = (n_train_samples,)) – Survival times for training data to estimate the censoring distribution from. A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
  • survival_test (structured array, shape = (n_samples,)) – Survival times of test data. A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
  • estimate (array-like, shape = (n_samples,)) – Estimated risk of experiencing an event of test data.
  • tau (float, optional) – Truncation time. The survival function for the underlying censoring time distribution \(D\) needs to be positive at tau, i.e., tau should be chosen such that the probability of being censored after time tau is non-zero: \(P(D > \tau) > 0\). If None, no truncation is performed.
  • tied_tol (float, optional, default: 1e-8) – The tolerance value for considering ties. If the absolute difference between risk scores is smaller or equal than tied_tol, risk scores are considered tied.
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 comparable pairs sharing the same time

References

[1]Uno, H., Cai, T., Pencina, M. J., D’Agostino, R. B., & Wei, L. J. (2011). “On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data”. Statistics in Medicine, 30(10), 1105–1117.