## Concept Overview **Key Point:** Likelihood ratios (LR+ and LR−) are test characteristics that are independent of prevalence. However, their **clinical utility** in ruling in or ruling out disease depends on the magnitude of the ratio and the clinical context — not on which ratio is "more useful" in absolute terms. ## Calculation of Likelihood Ratios Given: Sensitivity = 90%, Specificity = 85% $$LR^+ = \frac{\text{Sensitivity}}{1 - \text{Specificity}} = \frac{0.90}{1 - 0.85} = \frac{0.90}{0.15} = 6.0$$ $$LR^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}} = \frac{1 - 0.90}{0.85} = \frac{0.10}{0.85} \approx 0.12$$ ## Analysis of Each Statement ### Statement 1: LR+ = 6.0 — **CORRECT** The calculation is accurate. An LR+ of 6.0 means a positive test is 6 times more likely in TB patients than in non-TB patients. **Clinical Pearl:** An LR+ of 6 is considered **moderately strong** (LR+ > 10 is strong; 5–10 is moderate; 2–5 is weak). ### Statement 2: LR− is more useful for ruling out than LR+ is for ruling in — **INCORRECT** This statement makes an **unjustified comparison** and misinterprets the clinical utility of likelihood ratios. **High-Yield:** The usefulness of a likelihood ratio depends on: 1. **Its magnitude** — how far from 1.0 it is 2. **The clinical context** — what threshold of certainty is needed 3. **The pre-test probability** — how likely the disease is before testing In this case: - LR+ = 6.0 (moderately strong for ruling in) - LR− = 0.12 (moderately strong for ruling out) Neither is inherently "more useful." A LR− of 0.12 means a negative test is only 12% as likely in TB patients as in non-TB patients — this is useful for ruling out, but the statement's claim that it is "much more useful" for ruling out than LR+ is for ruling in is **not supported** by the magnitudes alone. **Mnemonic:** **SpPin** and **SnNout** — **Sp**ecificity rules **P**ositive **in**; **Sn**ensitivity rules **N**egative **out**. Both are equally valid clinical tools; neither is universally "more useful." ### Statement 3: LR are independent of prevalence — **CORRECT** Likelihood ratios are derived from sensitivity and specificity, which are intrinsic test properties independent of prevalence. Therefore, LR+ and LR− can be applied across populations with different TB burdens. **Key Point:** This is a major advantage of likelihood ratios over PPV/NPV — they are portable across settings. ### Statement 4: Post-test odds = Pre-test odds × LR+ — **CORRECT** This is the **odds form of Bayes' theorem**: $$\text{Post-test odds} = \text{Pre-test odds} \times LR$$ This is the most practical way to update probability after a test result. ## Summary Table: Likelihood Ratio Interpretation | LR+ Value | Interpretation | Clinical Utility | |-----------|----------------|------------------| | > 10 | Strong | Strongly rules in disease | | 5–10 | Moderate | Moderately rules in | | 2–5 | Weak | Weak evidence for disease | | 1 | No information | Test is useless | | 0.5–0.2 | Weak | Weak evidence against disease | | 0.2–0.1 | Moderate | Moderately rules out | | < 0.1 | Strong | Strongly rules out disease | In this question: LR+ = 6.0 (moderate for ruling in) and LR− = 0.12 (moderate for ruling out) are roughly equivalent in strength. [cite:Park 26e Ch 10]
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