U01.21.015 Likelihood Ratio Negative (LR⁻)

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Learning Objective:
Understand and apply the formula for calculating the negative likelihood ratio (LR⁻), which indicates how much the odds of a disease decrease when a test is negative.

Formula:

LR^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}} = \frac{\text{False Negative Rate}}{\text{True Negative Rate}}

Explanation:

  • 1 - \text{Sensitivity} = Probability of a false negative result (test misses the disease).
  • \text{Specificity} = Probability of correctly identifying those without the disease (TN rate).
  • LR^- shows how much a negative test result reduces the likelihood of disease.

Interpretation:

  • LR^- < 0.1 → Strong evidence to rule out disease
  • LR^- = 1 → No diagnostic value

Example:

Given:
\text{Sensitivity} = 0.90
\text{Specificity} = 0.80

LR^- = \frac{1 - 0.90}{0.80} = \frac{0.10}{0.80} = 0.125

✅ Answer: LR^- = 0.125
→ A negative test result makes the disease 8 times less likely (1 ÷ 0.125 = 8).

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