The ROC (Receiving Operating Characteristic) curve helps in evaluating the performance of a test in distinguishing between two groups (e.g., diseased vs. non-diseased).
Y-axis: True Positive Rate (Sensitivity)
X-axis: False Positive Rate (1-Specificity)
ROC Curve Details
Defined by specificity and sensitivity at various cutoffs.
Shape of the curve is determined by the test's ability to distinguish between those with and without disease.
Example: Changing cutoffs affects sensitivity (SN) and specificity (SP).
Raising the cutoff: SN ↓, SP ↑
Lowering the cutoff: SN ↑, SP ↓
ROC Curve Characteristics
Lower Left Corner: 0% SN, 100% SP (high cutoff, zero false positives)
Top Right Corner: 100% SN, 0% SP (low cutoff, zero false negatives)
Top Left Corner: Ideal test with 100% SN and 100% SP
Curve symmetry varies in real-world applications.
Applications of the ROC Curve
Used to screen or confirm diseases.
Screening: Focus on high sensitivity (higher points on the curve).
Confirming: Focus on high specificity (leftmost points on the curve).
Golden Rule:
Screening: Prioritize Sensitivity (SN)
Diagnosing: Prioritize Specificity (SP)
Comparing Tests
Compare ROC curves to determine which test is better.
Ideal curves are closer to the top left corner of the graph.
Area Under Curve (AUC): Greater area indicates better test performance.
Related Concepts
Accuracy: Relates to the validity of the measurement.
Formula: (TP + TN) / (TP + FP + TN + FN)
More accurate tests are closer to the top left corner.
ROC curves can help determine true/false positives/negatives with additional context such as prevalence.
Summary
ROC Curve: Built on sensitivity and 1-specificity axes.