survivalpredict.metrics.integrated_brier_score_administrative

survivalpredict.metrics.integrated_brier_score_administrative(predictions, times, events, max_time=None, times_start=None)

Integrated Brier score for administrative censorship.

Integral of Brier scores for administrative censorship, to allow for a singular metric of performance. Lower the better.

Administrative brier scores is appropriate in cases where censoring is a function of time. When a individual is marked as censored due to the fact that they have not experienced event at the last observed time, and not due to a lack of follow-up or drop out. This is ideal for industry, where churned/converted/failed individuals are often known with relative certainty.

Within survival analysis, each ‘outcome’ of the Brier scores is a distinct time within the survival curve. Administrative Brier scores simply look at the squared difference between the survival curve and the known survival; censored intervals are excluded from the score.

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.

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

  • times_start (Optional[np.ndarray], default=None) – Starting point for observation. If not passed in, all times_start times are assumed to be 0.

Returns:

Integral of Brier scores.

Return type:

ndarray of shape (n_samples), dtype=np.float64

References

[1] Kvamme, Håvard & Borgan, Ørnulf. (2019). The Brier Score under Administrative Censoring: Problems and Solutions. 10.48550/arXiv.1912.08581.