sksurv.nonparametric.cumulative_incidence_competing_risks#

sksurv.nonparametric.cumulative_incidence_competing_risks(event, time_exit, time_min=None, conf_level=0.95, conf_type=None, var_type='Aalen')[source]#

Non-parametric estimator of Cumulative Incidence function in the case of competing risks.

See the User Guide and [1] for further details.

Parameters:

  • event (array-like, shape = (n_samples,)) – Contains event indicators.

  • time_exit (array-like, shape = (n_samples,)) – Contains event/censoring times. ‘0’ indicates right-censoring. Positive integers (between 1 and n_risks, n_risks being the total number of different risks) indicate the possible different risks. It assumes there are events for all possible risks.

  • time_min (float, optional, default: None) – Compute estimator conditional on survival at least up to the specified time.

  • conf_level (float, optional, default: 0.95) – The level for a two-sided confidence interval on the cumulative incidence curves.

  • conf_type (None or {'log-log'}, optional, default: None.) – The type of confidence intervals to estimate. If None, no confidence intervals are estimated. If “log-log”, estimate confidence intervals using the log hazard or \(log(-log(S(t)))\).

  • var_type (None or one of {'Aalen', 'Dinse', 'Dinse_Approx'}, optional, default: 'Aalen') – The method for estimating the variance of the estimator. See [2], [3] and [4] for each of the methods. Only used if conf_type is not None.

Returns:

  • time (array, shape = (n_times,)) – Unique times.

  • cum_incidence (array, shape = (n_risks + 1, n_times)) – Cumulative incidence at each unique time point. The first dimension indicates total risk (cum_incidence[0]), the dimension i=1,…,n_risks the incidence for each competing risk.

  • conf_int (array, shape = (n_risks + 1, 2, n_times)) – Pointwise confidence interval (second axis) of the Kaplan-Meier estimator at each unique time point (last axis) for all possible risks (first axis), including overall risk (conf_int[0]). Only provided if conf_type is not None.

Examples

Creating cumulative incidence curves:

>>> from sksurv.datasets import load_bmt
>>> dis, bmt_df = load_bmt()
>>> event = bmt_df["status"]
>>> time = bmt_df["ftime"]
>>> n_risks = event.max()
>>> x, y, conf_int = cumulative_incidence_competing_risks(event, time, conf_type="log-log")
>>> plt.step(x, y[0], where="post", label="Total risk")
>>> plt.fill_between(x, conf_int[0, 0], conf_int[0, 1], alpha=0.25, step="post")
>>> for i in range(1, n_risks + 1):
>>>    plt.step(x, y[i], where="post", label=f"{i}-risk")
>>>    plt.fill_between(x, conf_int[i, 0], conf_int[i, 1], alpha=0.25, step="post")
>>> plt.ylim(0, 1)
>>> plt.legend()
>>> plt.show()

References

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