The likelihood ratio is the proportion of people with a disease and a test result vs. people without the disease and the same test result. In other words,
P(+ve AND D) / P(+ve AND D-) = P(TP) / P(FP) = [TP/TP+FN] / [FP/FP+TN]
LR+= Sensitivity / 1 – Specificity.
This is the positive likelihood ratio (LR+)
In the same way, there is a negative likelihood ratio (LR-),
P(-ve AND D) / P(-ve AND D-) = P(FN) / P(TN) = TP/TP+FN
LR- = (1-Sensitivity) / Specificity
Note that both these ratios don’t depend on the prevalence of the disease but on the measurement techniques. A likelihood ratio of close to 1 means that the particular test has little influence on determining whether the patient has the suspected condition or not. Likelihood ratios > 10 and < 0.1 are considered to provide robust evidence for and against the diagnoses, respectively.
