ROC Curves
Overview
The ROC curve is a standard tool for evaluating how well a diagnostic test or predictive score discriminates between two states (disease present vs absent) across all possible thresholds.
It visualises the trade‑off between sensitivity and specificity, provides a summary measure of discrimination (AUC), and helps inform threshold selection in the light of clinical consequences (NICE glossary; NICE diagnostics guidance).
Definition and axes
- ROC plots sensitivity (true positive rate) on the vertical axis against 1 - specificity (false positive rate) on the horizontal axis for every possible cut‑off of a continuous or ordinal test (NICE glossary).
- Each point on the curve represents a single threshold; moving along the curve shows the balance between detecting more true positives and accepting more false positives.
Area under the curve (AUC)
- The AUC is the probability that a randomly chosen case (disease present) has a higher test value than a randomly chosen control (disease absent). It ranges from 0 to 1 (NICE diagnostics guidance).
- Practical interpretation (commonly used bands):
- ≈1.0: perfect discrimination.
- 0.90-0.99: excellent.
- 0.80-0.89: good.
- 0.70-0.79: fair/modest.
- 0.50-0.69: poor; 0.50 = no discriminative ability (diagonal “no‑skill” line).
- Reporting: always give AUC with 95% confidence intervals and, when comparing curves, appropriate p values and paired/unpaired tests as relevant (NICE diagnostics guidance).