U01.21.014 Likelihood Ratio Positive (LR⁺)

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

Formula:

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

Explanation:

  • \text{Sensitivity} = Probability that a test correctly identifies those with the disease (TP rate)
  • \text{Specificity} = Probability that a test correctly identifies those without the disease (TN rate)
  • LR^+ combines both values to show how much a positive test result increases the likelihood of disease.

Interpretation:

  • LR^+ > 10 → Strong evidence to rule in disease
  • LR^+ = 1 → No diagnostic value

Example:

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

LR^+ = \frac{0.90}{1 - 0.80} = \frac{0.90}{0.20} = 4.5

✅ Answer: LR^+ = 4.5
→ A positive test result makes the disease 4.5 times more likely.

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