A 42-year-old woman from rural Maharashtra presents with a 3-month history of persistent cough and low-grade fever. Chest X-ray shows an upper lobe infiltrate. A tuberculin skin test (TST) is performed and reads 15 mm induration at 48 hours. In this population, the prevalence of active TB is 5%. The TST has a sensitivity of 85% and specificity of 90% for active TB. What is the positive predictive value (PPV) of this TST result, and what does it tell us about the likelihood of active TB in this patient?

Explanation

## Calculating Positive Predictive Value (PPV) **Key Point:** PPV is the probability of disease GIVEN a positive test result. It depends on both test accuracy (sensitivity, specificity) AND disease prevalence in the population. ### Formula $$PPV = \frac{TP}{TP + FP} = \frac{\text{Sensitivity} \times \text{Prevalence}}{\text{Sensitivity} \times \text{Prevalence} + (1 - \text{Specificity}) \times (1 - \text{Prevalence})}$$ ### Step-by-Step Calculation | Parameter | Value | |-----------|-------| | Sensitivity | 85% (0.85) | | Specificity | 90% (0.90) | | Prevalence | 5% (0.05) | | 1 − Prevalence | 95% (0.95) | **Numerator (True Positives):** $$0.85 \times 0.05 = 0.0425$$ **Denominator:** $$0.0425 + (1 - 0.90) \times 0.95 = 0.0425 + 0.10 \times 0.95 = 0.0425 + 0.095 = 0.1375$$ **PPV:** $$PPV = \frac{0.0425}{0.1375} = 0.309 \approx 31\%$$ ### Clinical Interpretation **High-Yield:** Even though the TST is positive and the test has 85% sensitivity and 90% specificity, the **probability that this patient actually has active TB is only ~31%**. This is because TB prevalence in the population is low (5%). **Clinical Pearl:** In low-prevalence populations, even a "good" test produces many false positives. This is why: - A positive TST in a low-prevalence setting requires **additional confirmatory testing** (sputum AFB smear, GeneXpert MTB/RIF, culture). - Clinical judgment and radiological findings (upper lobe infiltrate here) must be integrated with the test result. - The TST alone cannot diagnose TB; it indicates TB infection (latent or active). ### Why This Matters in Practice **Mnemonic: PPVP** — **P**ositive **P**redictive **V**alue depends on **P**revalence. Low prevalence → low PPV, even with high sensitivity/specificity. **Warning:** Students often confuse sensitivity (85%) with PPV. Sensitivity tells us "if the patient has TB, what's the chance the test is positive?" PPV tells us "if the test is positive, what's the chance the patient has TB?" These are NOT the same.