What is the likelihood ratio of a lab test?

• A. The ratio of true positives to false positives
• B. The ratio of specificity to sensitivity
• C. The ratio of probability of a given test result among diseased individuals to probability among non-diseased; LR+ = Sensitivity / (1 - Specificity)
• D. The product of likelihood and prior probability

Answer: (C)

A likelihood ratio for a lab test tells you how much more likely a given test result is in someone with the disease compared with someone without it. For a positive result, it compares P(test positive | disease) to P(test positive | no disease). Since sensitivity is P(T+ | D+) and 1 − specificity is P(T+ | D−), the positive likelihood ratio is sensitivity divided by (1 − specificity). This number shows how the odds of disease shift after a positive test and is the bridge between pretest probability and post-test probability when using Bayes’ updating. The other options don’t capture this definition: true positives to false positives isn’t a standard diagnostic measure, specificity to sensitivity isn’t the correct ratio, and the product of likelihood and prior relates to Bayes’ theorem but is not the likelihood ratio itself.