A 52-year-old man from Delhi presents with a 3-month history of persistent cough and weight loss of 5 kg. Chest X-ray shows a right upper lobe infiltrate. Sputum smear microscopy for acid-fast bacilli (AFB) is negative on two occasions. A new rapid molecular test (GeneXpert MTB/RIF) is performed and returns positive for *Mycobacterium tuberculosis*. In a validation study of this GeneXpert test in 500 TB suspects, 180 patients had culture-confirmed TB: the test was positive in 162 of these culture-positive cases and positive in 28 of the 320 culture-negative cases. What is the sensitivity of GeneXpert MTB/RIF in this study population?

Explanation

## Sensitivity Calculation **Key Point:** Sensitivity is the proportion of truly diseased individuals who test positive. It answers: "Of all patients who actually have TB (culture-positive), how many did the test correctly identify?" ### Formula $$\text{Sensitivity} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}}$$ ### Application to This Study | Category | Count | |----------|-------| | Culture-confirmed TB (true disease) | 180 | | GeneXpert positive among TB cases (TP) | 162 | | GeneXpert negative among TB cases (FN) | 18 | | Culture-negative (no TB) | 320 | | GeneXpert positive among non-TB (FP) | 28 | $$\text{Sensitivity} = \frac{162}{162 + 18} = \frac{162}{180} = 0.90 = 90\%$$ **High-Yield:** Sensitivity is **disease-centric** — it focuses only on the 180 culture-positive patients and asks: what fraction did the test catch? The 320 culture-negative patients are irrelevant to sensitivity calculation. **Clinical Pearl:** A sensitivity of 90% for GeneXpert MTB/RIF means that if a TB patient walks into the clinic, there is a 90% chance the test will be positive. This high sensitivity makes it excellent for **ruling out TB** (high sensitivity = low false-negative rate). **Mnemonic:** **SNOUT** — **S**ensitivity rules **OUT**. High sensitivity means few false negatives; a negative test in a high-sensitivity test reliably excludes disease. ## Why This Matters in TB Diagnosis GeneXpert MTB/RIF has become the WHO-recommended initial test for TB because of its high sensitivity (>95% in most populations), rapid turnaround, and ability to detect rifampicin resistance simultaneously.