## What is the Diagnostic Odds Ratio?

The **Diagnostic Odds Ratio** (DOR) is a performance metric to assess the effectiveness of a diagnostic test or — within the context of machine learning — a binary classification model. It is defined as the ratio of the odds of the prediction being positive is the true value is positive, relative to the odds of the prediction being positive when the true value is negative. In other words, it is the ratio of the LR+ and the LR-.

The DOR ranges from zero to infinity. When the test is useful, its value is greater than 1. The higher the DOR, the more indicative it is of test performance. A DOR less than 1 indicates that the model predicts in the wrong direction. A DOR of 1 means that the model is useless and gives no extra information.

Just like the (positive) negative likelihood ratio, it is independent of the prevalence.

## Calculating the diagnostic odds ratio

The Diagnostic Odds Ratio can be calculated as follows:

\text{Diagnostic odds ratio, DOR} = \frac{TP/FN}{FP/TN} = \frac{TP/FP}{FN/TN} = \frac{TP \cdot TN}{FP \cdot FN}

The DOR can also be specified in terms of other performance metrics:

\text{DOR} = \frac{\text{PPV}\times\text{NPV}}{\left(1-\text{PPV}\right)\times\left(1-\text{NPV}\right)}

From this, it is clear that the DOR is the ratio of the LR+ and the LR-:

\text{DOR} = \frac{LR+}{LR-}