Overview
This lecture explains likelihood ratios, how to calculate them, and how to use them to interpret diagnostic test results in clinical practice.
What Are Likelihood Ratios?
- Likelihood ratios (LRs) synthesize sensitivity and specificity to assess how much a test result changes the probability of disease.
- LR+ (positive likelihood ratio) indicates how much the odds of disease increase with a positive test.
- LR- (negative likelihood ratio) shows how much the odds of disease decrease with a negative test.
Calculating Likelihood Ratios
- LR+ = Sensitivity / (1 - Specificity)
- LR- = (1 - Sensitivity) / Specificity
- A good LR+ is greater than 10; a good LR- is less than 0.1.
- Likelihood ratios close to 1.0 have little impact on confirming or rejecting a diagnosis.
Practical Application Example (ACL Tear)
- Estimate pretest probability (e.g., for ACL tear, 60% based on symptoms and prevalence).
- For the Lachman test: sensitivity = 85%, specificity = 94%.
- LR+ = 14, LR- = 0.16 for Lachman test.
- Use a nomogram to graphically determine post-test probability by connecting pretest probability and LR.
- For a positive Lachman, post-test probability ≈ 95%; for a negative, ≈ 18%.
Calculating Post-Test Probability (Mathematical Method)
- Convert pretest probability to odds: Odds = Probability / (1 - Probability).
- Multiply pretest odds by LR to get post-test odds.
- Convert post-test odds to probability: Probability = Odds / (Odds + 1).
- Positive test: Pretest odds 1.5 × LR+ 14 = 21; probability = 21/22 = 95%.
- Negative test: Pretest odds 1.5 × LR- 0.16 = 0.24; probability = 0.24/1.24 = 19%.
Using Tests Effectively
- Use tests with the highest LR+ to confirm a diagnosis.
- Use tests with the lowest LR- to rule out a diagnosis.
Key Terms & Definitions
- Sensitivity — Probability a test correctly detects disease when it is present.
- Specificity — Probability a test correctly identifies no disease when it is absent.
- Likelihood Ratio (LR) — Ratio summarizing how much a test result changes disease odds.
- Pretest Probability — Estimated chance of disease before a test result is known.
- Pretest Odds — Odds calculated from the pretest probability.
- Post-test Probability — Revised chance of disease after considering the test result.
Action Items / Next Steps
- Review sensitivity, specificity, and predictive values if not already done.
- Practice calculating LR+, LR-, and post-test probability for other tests.
- Optional: Read the blog post on physiotutors.com for further study.