<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def concordance_index_censored(event_indicator, event_time, estimate, tied_tol=1e-8):
 """Concordance index for right-censored data The concordance index is defined as the proportion of all comparable pairs in which the predictions and outcomes are concordant. Samples are comparable if for at least one of them an event occurred. If the estimated risk is larger for the sample with a higher time of event/censoring, the predictions of that pair are said to be concordant. If an event occurred for one sample and the other is known to be event-free at least until the time of event of the first, the second sample is assumed to *outlive* the first. When predicted risks are identical for a pair, 0.5 rather than 1 is added to the count of concordant pairs. A pair is not comparable if an event occurred for both of them at the same time or an event occurred for one of them but the time of censoring is smaller than the time of event of the first one. Parameters event_indicator : array-like, shape = (n_samples,) Boolean array denotes whether an event occurred event_time : array-like, shape = (n_samples,) Array containing the time of an event or time of censoring estimate : array-like, shape = (n_samples,) Estimated risk of experiencing an event 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] Harrell, F.E., Califf, R.M., Pryor, D.B., Lee, K.L., Rosati, R.A, "Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors", Statistics in Medicine, 15(4), 361-87, 1996. """

    event_indicator, event_time, estimate = _check_inputs(
        event_indicator, event_time, estimate)

    w = numpy.ones_like(estimate)

    return _estimate_concordance_index(event_indicator, event_time, estimate, w, tied_tol)