A newly developed rapid diagnostic test for tuberculosis is being evaluated in a high-prevalence TB setting in India. The test has 90% sensitivity and 85% specificity. Regarding likelihood ratios and their clinical utility, all of the following statements are true EXCEPT:

Question

Accepted Answer

A. A negative likelihood ratio (LR−) of approximately 0.12 suggests that a negative test result is much more useful for ruling out TB than a positive result is for ruling it in. ## 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%

$$LR^+ = \frac{	ext{Sensitivity}}{1 - 	ext{Specificity}} = \frac{0.90}{1 - 0.85} = \frac{0.90}{0.15} = 6.0$$

$$LR^- = \frac{1 - 	ext{Sensitivity}}{	ext{Specificity}} = \frac{1 - 0.90}{0.85} = \frac{0.10}{0.85} \approx 0.12$$

## 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**:

$$	ext{Post-test odds} = 	ext{Pre-test odds} 	imes LR$$

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]

Answer

B. The post-test odds of TB following a positive test result can be calculated by multiplying pre-test odds by the positive likelihood ratio

Answer

C. The positive likelihood ratio (LR+) of this test is approximately 6.0, indicating that a positive result is 6 times more likely in TB patients than in non-TB patients

Answer

D. Likelihood ratios are independent of disease prevalence and can be applied across different populations with varying TB burden

A newly developed rapid diagnostic test for tuberculosis is being evaluated in a high-prevalence TB setting in India. The test has 90% sensitivity and 85% specificity. Regarding likelihood ratios and their clinical utility, all of the following statements are true EXCEPT:

Explanation

Concept Overview

Calculation of Likelihood Ratios

Analysis of Each Statement

Statement 1: LR+ = 6.0 — CORRECT

Statement 2: LR− is more useful for ruling out than LR+ is for ruling in — INCORRECT

Statement 3: LR are independent of prevalence — CORRECT

Statement 4: Post-test odds = Pre-test odds × LR+ — CORRECT

Summary Table: Likelihood Ratio Interpretation

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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