# ROC Curves

Choosing the right threshold is always challenging. A Receiver Operator Characteristic curve, or ROC curve, can help decide which value of the threshold is best.

The sensitivity, or true positive rate of the model, is shown on the y-axis. And the false positive rate, or 1 minus the specificity, is given on the x-axis.

The ROC curve always starts at (0, 0) corresponding to a threshold of 1. This means we have 0 sensitivity and we won’t catch a good care cases. But since our false positive rate is 0 as well, that means that we correctly label all the poor care cases.

The ROC curve always ends at (1, 1) which corresponds to a threshold of 0. So, the threshold *decreases *as we move from (0, 0) to (1, 1).

Let’s take an approximate point (0.6, 0.98) on the curve. This point signifies that we correctly label 98% of the cases with a false positive rate of 60%.

#### So what threshold to pick?

We should pick that threshold for the trade off that we want to make-

- Cost of failing to detect positives
- Cost of raising false alarms

If we are more concerned about labelling the *good* care cases (high sensitivity) then pick the threshold which ** minimises** the

**false positive rate**

**but has a very high true positive rate.**

If we are more concerned with getting all the *poor* care cases right, having a high specificity or low false positive rate, pick the threshold that ** maximises** the true positive rate while keeping the false positive rate really low.

An ROC curve is also a great way to visualise and compare different classifiers for the same classification problem.