survivalpredict.metrics.integrated_brier_score_ipcw

survivalpredict.metrics.integrated_brier_score_ipcw(predictions, times, events, events_for_ipcw=None, times_for_ipcw=None, max_time=None)

Integrated Brier score weighted with the inverse probability of censoring.

Integral of Brier scores with inverse probability of censoring, to allow for a singular metric of performance. Lower the better.

Integral Brier scores for cases where censoring includes drop-up or loss of follow-up, a common occurrence in medical research. Each point in time within the survival curve is treated as an ‘outcome’ in the scores. The squared difference between an estimated probability is weighted using an inverse-event estimation. Weights are generated with the multiplicative inverse of an event-switched Kaplan-Meier estimator , where the Boolean values of events are inverted. For each interval of time of interest, if an observation is censored or expeiences event, those scores are weighted with the inverted Kaplan-Meier value for the last known time of that observation. If an individual is believed to be ‘alive’ at the point in time of interest, said scores are weighted with that time of interest’s inverted Kaplan-Meier weights.

Parameters:

  • predictions (np.ndarray) – Predicted survival curves.

  • times (np.ndarray) – True points in time that were last observed.

  • events (np.ndarray) – True indicators if event was experienced.

  • events_for_ipcw (Optional[np.ndarray], default=None) – Events to build inverse probability of censoring weights on, it is acceptable to put in training events here. If None, will use Events.

  • times_for_ipcw (Optional[np.ndarray], default=None) – Times to build inverse probability of censoring weights on, it is acceptable to put in training times here. If None, will use Times.

  • max_time (Optional[int], default=None) – Maximum time to evaluate survival curves. If None, will evaluate all times seen.

Returns:

Integral of Brier scores.

Return type:

np.ndarray

References

[1] E. Graf, C. Schmoor, W. Sauerbrei, and M. Schumacher, “Assessment and comparison of prognostic classification schemes for survival data,” Statistics in Medicine, vol. 18, no. 17-18, pp. 2529–2545, 1999.