A 42-year-old woman from Delhi presents with a 3-month history of progressive dyspnea and fatigue. Clinical examination reveals a diastolic murmur at the apex. Transthoracic echocardiography is performed to assess for mitral stenosis. The echocardiographic findings are compared against cardiac catheterization (gold standard). In the study population of 200 patients: - True positives (echo positive, catheter positive): 45 - False positives (echo positive, catheter negative): 15 - True negatives (echo negative, catheter negative): 120 - False negatives (echo negative, catheter positive): 20 What is the sensitivity of transthoracic echocardiography for detecting mitral stenosis in this cohort?

Explanation

## Calculation of Sensitivity **Key Point:** Sensitivity measures the ability of a test to correctly identify those WITH the disease. It answers: "Of all patients who truly have the disease, how many does the test catch?" ### Formula $$\text{Sensitivity} = \frac{\text{True Positives (TP)}}{\text{TP + False Negatives (FN)}}$$ ### Step-by-Step Calculation 1. **Identify TP and FN from the data:** - True Positives = 45 (echo positive AND catheter positive) - False Negatives = 20 (echo negative BUT catheter positive) 2. **Total patients with disease (by gold standard):** - TP + FN = 45 + 20 = 65 3. **Apply formula:** $$\text{Sensitivity} = \frac{45}{45 + 20} = \frac{45}{65} = 0.692 = 69.2\%$$ ### Clinical Interpretation **High-Yield:** A sensitivity of 69.2% means that if a patient truly has mitral stenosis (confirmed by catheterization), echocardiography will detect it only 69.2% of the time. Conversely, 30.8% of true cases are missed (false negatives). **Clinical Pearl:** This relatively modest sensitivity suggests that a negative echo does NOT rule out mitral stenosis in a high-risk patient—further investigation (e.g., stress echo, cardiac catheterization) may be warranted if clinical suspicion remains high. ### Sensitivity vs. Specificity Comparison | Metric | Formula | Meaning | Use Case | |--------|---------|---------|----------| | **Sensitivity** | TP / (TP + FN) | Ability to identify disease | Rule OUT disease (negative test reassures) | | **Specificity** | TN / (TN + FP) | Ability to identify non-disease | Rule IN disease (positive test confirms) | **Mnemonic:** **SeNsitivity = TP / (TP + FN)** — think "**N**egative" in the denominator to remember False **N**egatives are included. High sensitivity = few false negatives = good at ruling out disease (SnOUT: Sensitive test, Negative result rules OUT).