Slide 1: What do you think? If you have a positive result on a test that is 90% sensitive and 90% specific, how does it impact your chance of truly having the disease? A) 90% likely patient has the disease. B) 9 times the odds as before the test. C) 9 times the probability as before the test.

Slide 2: To help us answer that, let’s figure out…what is a likelihood ratio?? A likelihood ratio is a number used to assess how much impact a test result has on the patient’s likelihood of having the disease. If the test is positive, use the…positive likelihood ratio = sensitivity / (1 – specificity). If the test is negative, use the…negative likelihood ratio = (1 – sensitivity) / specificity. To calculate the post-test odds of the patient having the disease… post-test odds = LR x pre-test odds.

Slide 3: Back to the question… LR+ = 0.90/(1-0.90) = 9. The likelihood ratio is applied to the odds of a disease and so the answer… B) 9 times the odds as before the test.

Slide 4: Applying this to a patient… A positive test (with 90% sensitivity and specificity) in a patient with a 1:999 pre-test odds: Post-test odds = 9 x 1/999 = 1/111. If you’re more used to probabilities, there was a 0.1% probability of disease before the test and a 0.9% probability of disease with a positive test (not that big of a change!) The same positive test in a patient with a 1:9 pre-test odds: Post-test odds = 9 x 1/9 = 1/1. If you’re more used to probabilities, there was a 10% probability of disease before the test and a 50% probability of disease with a positive tes (a much bigger change, perhaps more informative).

Slide 5: Too much math? You can use the Fagan nomogram to visually get the odds or probability based on LR. There are also numerous mobile apps available that can help you calculate this!

## References

- Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med. 1975 Jul 31;293(5):257.PMID 1143310

**Tags:**

*epidemiology, likelihood ratio, sensitivity, specificity, statistics*