Enter the number of concordant pairs and discordant pairs, and the total number of possible pairs into the calculator to determine the Concordance Index.

## Concordance Index Formula

The following formula is used to calculate the Concordance Index (C-index).

C-index = Σ (O_i - E_i) / N

Variables:

- C-index is the Concordance Index
- O_i is the number of concordant pairs
- E_i is the number of discordant pairs
- N is the total number of possible pairs

To calculate the Concordance Index, subtract the number of discordant pairs from the number of concordant pairs. Then, divide the result by the total number of possible pairs. The resulting value is the Concordance Index, which measures the predictive accuracy of a model. A C-index of 0.5 suggests that the model is no better than random chance, while a C-index of 1.0 indicates perfect predictive accuracy.

## What is a Concordance Index?

A Concordance Index, also known as C-index, is a statistical measure used in predictive modeling to evaluate the accuracy of predictions in relation to actual outcomes. It is commonly used in survival analysis and measures the relative ranking of predicted and observed event times. The C-index ranges from 0.5 to 1.0, where 0.5 indicates a model no better than random chance and 1.0 indicates a perfect model. It is equivalent to the area under the receiver operating characteristic (ROC) curve when dealing with binary outcomes.

## How to Calculate Concordance Index?

The following steps outline how to calculate the Concordance Index.

- First, determine the number of concordant pairs (O_i).
- Next, determine the number of discordant pairs (E_i).
- Next, calculate the difference between the number of concordant pairs and discordant pairs (O_i – E_i).
- Next, sum up the differences calculated in the previous step (Σ (O_i – E_i)).
- Finally, divide the sum of differences by the total number of possible pairs (N) to calculate the Concordance Index (C-index = Σ (O_i – E_i) / N).

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Number of concordant pairs (O_i) = 25

Number of discordant pairs (E_i) = 10

Total number of possible pairs (N) = 50