An ROC curve (receiver operating characteristic curve) is a graph that shows the performance of a binary classification model by plotting the true positive rate against the false positive rate at various threshold settings. Analysts commonly use it in conjunction with logistic regression, machine learning classifiers, and diagnostic test evaluation. The curve illustrates the trade-off between sensitivity (true positive rate) and specificity (1 – false positive rate). A model with a curve closer to the top-left corner generally performs better.
To determine the false positive rate, the ROC curve examines how often the model incorrectly classifies a negative case as positive. This is assessed at different thresholds—cutoff values used to decide whether a prediction is labeled as positive or negative. At each possible decision threshold, it calculates the percentage of actual negatives that were mistakenly labeled as positives. By comparing this with the true positive rate across different thresholds, the ROC curve helps identify where the model performs best without too many false alarms.
For example, in a medical test that assigns a risk score from 0 to 1, setting the threshold at 0.5 might mean anyone with a score above 0.5 is classified as “positive.” By shifting the threshold up or down, you change how sensitive or specific the test is. The ROC curve compares the true and false positive rates across these different thresholds to help identify the best threshold value for deciding whether a test result should be considered positive or negative. A high area under the curve (AUC) indicates that the test has strong overall accuracy.
ROC Curve by Davide Chicco and Giuseppe Jurman, “The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification”, BioData Mining 16, 4 (2023). https://doi.org/10.1186/s13040-023-00322-4, CC BY 4.0, Link