A screening test for a rare disease has a likelihood ratio positive (LR+) of 8 and a likelihood ratio negative (LR−) of 0.1. Which statement best describes the clinical utility of this test?

Explanation

## Understanding Likelihood Ratios (LR+ and LR−) **Key Point:** Likelihood ratios quantify how much a test result changes the probability of disease. They are independent of prevalence and directly inform clinical decision-making. ### Likelihood Ratio Positive (LR+) $$LR^+ = \frac{\text{Sensitivity}}{1 - \text{Specificity}} = \frac{\text{True Positive Rate}}{\text{False Positive Rate}}$$ **Interpretation:** - LR+ > 10: Strong evidence for disease (rules in) - LR+ 5–10: Moderate-to-good evidence for disease - LR+ 1–5: Weak evidence for disease - LR+ = 1: Test provides no diagnostic information ### Likelihood Ratio Negative (LR−) $$LR^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}} = \frac{\text{False Negative Rate}}{\text{True Negative Rate}}$$ **Interpretation:** - LR− < 0.1: Strong evidence against disease (rules out) - LR− 0.1–0.2: Good-to-excellent evidence against disease - LR− 0.2–0.5: Moderate evidence against disease - LR− = 1: Test provides no diagnostic information ### Analysis of This Test | Metric | Value | Interpretation | |--------|-------|----------------| | LR+ | 8 | Moderate-to-good evidence for ruling IN disease (5–10 range) | | LR− | 0.1 | Good-to-excellent evidence for ruling OUT disease (≤ 0.1) | **High-Yield:** An LR+ of 8 means a positive test increases the post-test odds of disease by a factor of 8 — this is considered moderate-to-good for ruling in disease. An LR− of 0.1 means a negative test decreases the post-test odds of disease by a factor of 10 — this is considered excellent for ruling out disease. Together, both values indicate a clinically useful test for both purposes. **Why Option A is wrong:** Option A states the test is "poor for ruling out the disease," but an LR− of 0.1 is at the threshold of excellent for ruling out (the standard cutoff is ≤ 0.1). Calling it "poor" is factually incorrect. **Why Option C is correct:** With LR+ = 8 (moderate-to-good for ruling in) and LR− = 0.1 (excellent for ruling out), the test demonstrates good clinical utility for both ruling in and ruling out disease. Per standard epidemiological thresholds (Park's Textbook of Preventive and Social Medicine; Sackett et al., Evidence-Based Medicine), both values fall in the clinically useful range. **Mnemonic:** **SnNOut / SpPIn** - **Sn**Nout: High **Sensitivity** → **Negative** test result → **rule Out** disease - **Sp**PIn: High **Specificity** → **Positive** test result → **rule In** disease **Clinical Pearl:** A test with LR+ ≥ 5 and LR− ≤ 0.2 is generally considered useful for both ruling in and ruling out disease. This test meets both criteria, making Option C the best descriptor of its clinical utility (Park's Textbook of PSM, 26th edition; Sackett DL, Evidence-Based Medicine).