Concordance Index

evaluations.medical.concordance_index.concordance_index(events: List[int], risks: List[float]) → float

Compute Concordance index (C-index)

The concordance index is a value between 0 and 1 where:

  • 1.0 - all risk scores for happened events higher than for unhappened,

  • 0.0 - all risk scores for unhappened events higher than for happened,

  • 0.5 - random risk scores.

The formula is:

\[C\mbox{-}Index = \frac{n\_concordant\_pairs + 0.5 * n\_risk\_ties}{n\_permissible\_pairs}\]

where:

  • n_concordant_pairs - number of permissible pairs where the score is bigger for the event with label 1 than 0

  • n_risk_ties - number of permissible pairs with equal scores

  • n_permissible_pairs - number of pairs with different events

Parameters

  • events (List[int]) – If the some event happened - 1 or not happened - 0

  • risks (List[int]) – Risks scores for each event

Returns

Concordance index

Return type

float

Examples

>>> from evaluations.medical import concordance_index
>>> events = [1, 0, 1, 1, 0]
>>> risks = [0.8, 0.43, 0.62, 0.58, 0.62]
>>> concordance_index(events, risks)
0.75