Fallback, simpler method to compute concordance.

    Assumes the data has been verified by lifelines.utils.concordance_index first.

def _naive_concordance_summary_statistics(event_times, predicted_event_times, event_observed):
    """
    Fallback, simpler method to compute concordance.

    Assumes the data has been verified by lifelines.utils.concordance_index first.
    """
    num_pairs = 0.0
    num_correct = 0.0
    num_tied = 0.0

    for a, time_a in enumerate(event_times):
        pred_a = predicted_event_times[a]
        event_a = event_observed[a]
        # Don't want to double count
        for b in range(a + 1, len(event_times)):
            time_b = event_times[b]
            pred_b = predicted_event_times[b]
            event_b = event_observed[b]

            if _valid_comparison(time_a, time_b, event_a, event_b):
                num_pairs += 1.0
                crct, ties = _concordance_value(time_a, time_b, pred_a, pred_b, event_a, event_b)
                num_correct += crct
                num_tied += ties

    return (num_correct, num_tied, num_pairs)