`hazardous.metrics`.aj_calibration_at_t#

hazardous.metrics.aj_calibration_at_t(y_calibration, times, pred_calibration, event_of_interest=None)#

Pointwise AJ calibration error at each time point.

For each event \(k\), computes the difference between the mean predicted CIF and the marginal Aalen-Johansen CIF at every time in times:

\[AJ_k(t) = |\bar{F}_k(t) - \hat{F}^{AJ}_k(t)|\]

where \(\bar{F}_k(t) = \frac{1}{n} \sum_{i=1}^n \hat{F}_k(t \mid \mathbf{x}_i)\) is the mean predicted cumulative incidence for event \(k\) across the calibration set, and \(\hat{F}^{AJ}_k(t)\) is the marginal Aalen-Johansen CIF for event \(k\) fitted on the same set. The survival probability (event 0) is compared against the Kaplan-Meier estimate via km_calibration().

Parameters:

y_calibrationarray-like of shape (n_samples, 2): Survival outcomes of the calibration set, with columns "event" (0 for censoring, positive integers for each cause of event) and "duration" (observed time).
timesarray-like of shape (n_times,): Time points at which the CIFs were predicted. Need not be sorted; the last axis of pred_calibration must share the same ordering.
pred_calibrationarray-like of shape (n_samples, n_events+1, n_times): Predicted incidence probabilities at times for the calibration set. The second axis is indexed by event identifier in sorted order: index 0 holds the survival probability, indices 1, 2, … hold cause-specific CIFs.
event_of_interestint or None, default=None: If provided, return only the difference array for that event. If None, return a dict with one array per event.

Returns:

differencesdict of {int: ndarray of shape (n_times,)}: Pointwise difference \(AJ_k(t)\) for each event identifier, in ascending time order. Only the entry for event_of_interest is returned when that parameter is set.

hazardous.metrics.aj_calibration_at_t#

`hazardous.metrics`.aj_calibration_at_t#