Learning Objective
By the end of this module, medical students will be able to interpret the key properties of diagnostic tests—sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and test efficiency—and apply them clinically to screening and confirmation scenarios.
Key Definitions
| Term | Formula | Clinical Relevance | Mnemonic |
|---|---|---|---|
| Sensitivity (True Positive Rate) | TP / (TP + FN) | The ability of a test to correctly identify those with the disease. High sensitivity → low false negatives. Ideal for screening. | SN-N-OUT → Sensitive test, Negative result rules OUT disease |
| Specificity (True Negative Rate) | TN / (TN + FP) | Ability of a test to correctly identify those without disease. High specificity → low false positives. Ideal for confirmation. | SP-P-IN → Specific test, Positive result rules IN disease |
| Positive Predictive Value (PPV) | TP / (TP + FP) | The probability that a person with a positive test actually has the disease. Varies with prevalence. | – |
| Negative Predictive Value (NPV) | TN / (TN + FN) | The probability that a person with a negative test actually does not have the disease. Varies inversely with prevalence. | – |
| Test Efficiency | (TP + TN) / (TP + TN + FP + FN) | Overall accuracy of a test | – |
Key Point: Sensitivity and specificity are intrinsic properties of a test. PPV and NPV depend on disease prevalence.
Interpreting Test Results
Screening vs Confirmation
- High sensitivity: Good for screening (low false negatives).
- High specificity: Good for confirming diagnosis (low false positives).
Prevalence Effects
- PPV increases with high pretest probability (disease is more likely).
- NPV decreases with high pretest probability.
Cutoff Values
| Cutoff | Effect on Sensitivity | Effect on Specificity |
|---|---|---|
| Lower | ↑ Sensitivity, ↓ Specificity | More false positives, fewer false negatives |
| Higher | ↓ Sensitivity, ↑ Specificity | Fewer false positives, more false negatives |
| Practical (B) | Balance between sensitivity & specificity | Compromise for clinical decision-making |
2×2 Table for Diagnostic Tests
| Disease Status | Test Positive | Test Negative | Total |
|---|---|---|---|
| Disease Present | TP | FN | TP + FN |
| Disease Absent | FP | TN | FP + TN |
| Total | TP + FP | FN + TN | TP + FP + FN + TN |
step by step, using a clear 2×2 table example so you can see exactly how sensitivity and specificity are calculated.
Step 1: Start with a 2×2 Table
| Disease Status | Test Positive | Test Negative | Total |
|---|---|---|---|
| Disease Present | TP = 80 | FN = 20 | 100 |
| Disease Absent | FP = 10 | TN = 90 | 100 |
| Total | 90 | 110 | 200 |
- TP (True Positive): Diseased patients correctly testing positive = 80
- FN (False Negative): Diseased patients incorrectly testing negative = 20
- FP (False Positive): Healthy patients incorrectly testing positive = 10
- TN (True Negative): Healthy patients correctly testing negative = 90
Step 2: Calculate Sensitivity
Formula:
Sensitivity=TPTP+FN\text{Sensitivity} = \frac{TP}{TP + FN}
Stepwise Calculation:
- Identify TP = 80
- Identify FN = 20
- Add TP + FN = 80 + 20 = 100
- Divide TP by total diseased: 80 / 100 = 0.8
Interpretation: 80% of patients with the disease test positive.
Step 3: Calculate Specificity
Formula:
Specificity=TNTN+FP\text{Specificity} = \frac{TN}{TN + FP}
Stepwise Calculation:
- Identify TN = 90
- Identify FP = 10
- Add TN + FP = 90 + 10 = 100
- Divide TN by total healthy: 90 / 100 = 0.9
Interpretation: 90% of patients without the disease test negative.
Step 4: Quick Summary Table
| Property | Formula | Calculation | Result |
|---|---|---|---|
| Sensitivity | TP / (TP + FN) | 80 / (80+20) | 80% |
| Specificity | TN / (TN + FP) | 90 / (90+10) | 90% |
Key Points
- SN-N-OUT: Sensitive → Negative → rules OUT disease
- SP-P-IN: Specific → Positive → rules IN disease
- PPV & NPV are prevalence-dependent
- Efficiency measures overall accuracy
- Screening uses high sensitivity; confirmation uses high specificity
