The sensitivity (S) and specificity (E) of a test can be calculated from the positive and negative likelihood ratios (LR).
positive likelihood ratio =
= (sensitivity) / (1 - (specificity))
negative likelihood ratio =
= (1 - (sensitivity)) / (specificity)
If these are rearranged:
specificity =
= ((positive LR) – 1) / ((positive LR) – (negative LR))
sensitivity =
= (positive LR) * (1 – (negative LR)) / ((positive LR) – (negative LR))