Likelihood ratio


Definition: 

positive likelihood ratio (+LR)

it is how likely the test is positive in a diseased population when you compare the positive test in a non-diseased population.

+LR= positive test in a diseased population/ positive test in a non-diseased population

Negative likelihood ratio (-LR)

 it is how likely the test is in a diseased population to be negative when you compare it to a negative test in a nondiseased population.

-LR= negative test in diseased population/ negative test in nondiseased population.

How to interpret the likelihood ratio (LR)?

the higher the LR, we can rule in disease and the lower the LR, we can rule out disease.

LR 2 increases the probability of disease by 15%, LR 5 increases the probability of disease by 30%, and LR 10 increases the probability of disease by 45%

On the contrary, LR 0.5 decreases disease probability by 15%, LR 0.2 decreases it by 30% and it is decreased by 45 % if LR is 0.1

LR 0.1 is strong evidence to rule out disease while LR 10 is strong evidence to rule in disease.

post-test odds= pre-test odds x LR

relation between odds and probability:

Probability =odds/ 1+odds

odds= probability/1-probability

Relation between sensitivity, specificity, and likelihood ratio

+LR= Sensitivity/ 1- specificity

-LR= 1- Sensitivity/ specificity



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