A 55-year-old man from Delhi undergoes screening for coronary artery disease (CAD) using an exercise stress test (EST). He has no symptoms but multiple risk factors (hypertension, dyslipidemia, smoking history). The EST shows 2 mm ST depression in leads II, III, aVF. In this asymptomatic screening population, the prevalence of significant CAD is 10%. The EST has a sensitivity of 68% and specificity of 77% for significant CAD. Calculate the negative predictive value (NPV) and interpret what a negative EST would mean for this patient.

Explanation

## Calculating Negative Predictive Value (NPV) **Key Point:** NPV is the probability of being disease-FREE given a NEGATIVE test result. Like PPV, it depends on sensitivity, specificity, AND prevalence. ### Formula $$NPV = \frac{TN}{TN + FN} = \frac{\text{Specificity} \times (1 - \text{Prevalence})}{\text{Specificity} \times (1 - \text{Prevalence}) + (1 - \text{Sensitivity}) \times \text{Prevalence}}$$ ### Step-by-Step Calculation | Parameter | Value | |-----------|-------| | Sensitivity | 68% (0.68) | | Specificity | 77% (0.77) | | Prevalence | 10% (0.10) | | 1 − Prevalence | 90% (0.90) | | 1 − Sensitivity | 32% (0.32) | **Numerator (True Negatives):** $$0.77 \times 0.90 = 0.693$$ **Denominator:** $$0.693 + 0.32 \times 0.10 = 0.693 + 0.032 = 0.725$$ **NPV:** $$NPV = \frac{0.693}{0.725} = 0.956 \approx 95.6\%$$ ### Clinical Interpretation **High-Yield:** If the EST were **negative**, the probability that this patient does **NOT** have significant CAD is approximately **95%**. This is a strong reassurance. **Clinical Pearl:** NPV is often **higher than sensitivity** in low-prevalence populations because: - Most people in the population are disease-free (90% here). - A negative test in a disease-free person is common (true negative). - The denominator (TN + FN) is dominated by true negatives. ### Why This Matters for CAD Screening **Mnemonic: NPV-P** — **N**egative **P**redictive **V**alue is **P**owerful in low-prevalence populations. A negative test is very reassuring. **Clinical Application:** - In this asymptomatic screening cohort (10% prevalence), a **negative EST is highly reassuring** (95% confidence of no significant CAD). - However, the **positive EST in this patient is less reassuring** (would need PPV calculation: ~27%, requiring further testing like coronary angiography or CT angiography). - This illustrates why **screening tests in asymptomatic populations must have high specificity** to minimize false positives. ### Contrast: Sensitivity vs. NPV | Concept | Meaning | Value Here | |---------|---------|------------| | Sensitivity | P(positive test \| disease) | 68% | | NPV | P(no disease \| negative test) | 95.6% | They answer different questions. Sensitivity is about test performance; NPV is about clinical reassurance.