Harvey's Garden

Likelihood ratio

2 min read

  • Definition
    • A measure of how much a specific test result will raise or lower the pre-test probability of a disease. It combines sensitivity and specificity into a single number.
    • Unlike sensitivity and specificity, LRs are less influenced by disease prevalence.
  • Positive Likelihood Ratio (LR+)
    • Formula: LR+ = Sensitivity / (1 - Specificity)
      • This can be read as: (True Positive Rate) / (False Positive Rate).
    • Interpretation: How much more likely is a positive test result in a person with the disease compared to a person without it.
      • LR+ > 1: Increases the likelihood of disease. The higher the number, the more useful the test for ruling in a Dx.
      • LR+ > 10: Large and often conclusive increase in likelihood of disease.
      • LR+ = 1: Test is uninformative.
    • Example: An LR+ of 25 means a positive test result is 25 times more likely to be seen in a person with the disease than in someone without it.
  • Negative Likelihood Ratio (LR-)
    • Formula: LR- = (1 - Sensitivity) / Specificity
      • This can be read as: (False Negative Rate) / (True Negative Rate).
    • Interpretation: How much less likely is a negative test result in a person with the disease compared to a person without it.
      • LR- < 1: Decreases the likelihood of disease. The lower the number (closer to 0), the more useful the test for ruling out a Dx.
      • LR- < 0.1: Large and often conclusive decrease in likelihood of disease.
      • LR- = 1: Test is uninformative.
    • Example: An LR- of 0.1 means a negative result is associated with a 10-fold decrease in the odds of having the disease.
  • Clinical Utility & Key Concepts
    • LRs are used to calculate post-test probability from pre-test probability.
    • The key formula involves odds: Post-test odds = Pre-test odds x LR.
    • Remember: Odds = P / (1-P), where P is probability.
    • In summary:
      • High LR+ → Rules IN disease (SpIN). A highly Specific test has a low false positive rate (1-Specificity), leading to a high LR+.
      • Low LR- → Rules OUT disease (SnOUT). A highly Snensitive test has a low false negative rate (1-Sensitivity), leading to a low LR-.

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