Sensitivity and Specificity Calculator
Calculate diagnostic test accuracy metrics including PPV, NPV, and likelihood ratios
Diagnostic Test Analysis
2×2 Confusion Matrix
| Disease Present | Disease Absent | Total | |
|---|---|---|---|
| Test Positive | True Positive (TP) ✅✅ | False Positive (FP) ❌✅ | 0 |
| Test Negative | False Negative (FN) ✅❌ | True Negative (TN) ❌❌ | 0 |
| Total | 0 | 0 | 0 |
Matrix explanation:
- True Positive (TP): Disease present, test positive - Correct positive result
- False Positive (FP): Disease absent, test positive - Incorrect positive result
- False Negative (FN): Disease present, test negative - Incorrect negative result
- True Negative (TN): Disease absent, test negative - Correct negative result
Percentage of population with the disease (needed for Bayesian PPV/NPV calculation)
Example: COVID-19 Rapid Test
Scenario: Rapid Antigen Test Evaluation
Sample: 1000 individuals tested
True Positives: 85 (correctly identified positive cases)
False Positives: 20 (healthy individuals testing positive)
False Negatives: 15 (infected individuals testing negative)
True Negatives: 880 (healthy individuals testing negative)
Calculated Results
Sensitivity: 85/(85+15) = 85.0% - Good at detecting infection
Specificity: 880/(880+20) = 97.8% - Excellent at confirming non-infection
PPV: 85/(85+20) = 81.0% - 81% of positive results are correct
NPV: 880/(880+15) = 98.3% - 98.3% of negative results are correct
Accuracy: (85+880)/1000 = 96.5% - Overall test accuracy
Key Metrics Guide
Sensitivity (TPR)
Ability to correctly identify positive cases
High sensitivity = Few false negatives
Specificity (TNR)
Ability to correctly identify negative cases
High specificity = Few false positives
PPV & NPV
Predictive values depend on disease prevalence
Higher prevalence = Higher PPV
Clinical Application Tips
Screening tests should have high sensitivity to minimize missed cases
Confirmatory tests should have high specificity to minimize false alarms
Consider prevalence when interpreting PPV and NPV
Likelihood ratios help assess diagnostic value
Balance sensitivity and specificity based on clinical consequences
Understanding Diagnostic Test Statistics
Core Concepts
Diagnostic test evaluation uses a 2×2 confusion matrix to calculate key performance metrics. These statistics help clinicians understand how well a test performs in detecting or ruling out disease.
Sensitivity vs Specificity Trade-off
There's often a trade-off between sensitivity and specificity. Adjusting test thresholds to increase one typically decreases the other. The optimal balance depends on the clinical consequences of false positives versus false negatives.
Remember: A test with 95% sensitivity will miss 5% of actual cases (false negatives), while a test with 95% specificity will incorrectly label 5% of healthy individuals as positive (false positives).
Key Formulas
Basic Metrics:
Sensitivity = TP / (TP + FN)
Specificity = TN / (TN + FP)
Accuracy = (TP + TN) / (TP + TN + FP + FN)
Predictive Values:
PPV = TP / (TP + FP)
NPV = TN / (TN + FN)
Likelihood Ratios:
LR+ = Sensitivity / (1 - Specificity)
LR- = (1 - Sensitivity) / Specificity
Prevalence Effect
PPV and NPV are highly dependent on disease prevalence. In low-prevalence populations, even highly specific tests may have poor PPV due to many false positives.
Screening vs Diagnosis
Screening tests prioritize sensitivity to catch all cases, while confirmatory tests prioritize specificity to avoid false diagnoses.
ROC Analysis
ROC curves plot sensitivity vs (1-specificity) to evaluate test performance across different thresholds and compare multiple tests.