10.4 Sensitivity and specificity are inversely related

A perfect diagnostic test is one that has both high sensitivity and specificity such that the test parameter perfectly distinguishes diseased from healthy patients. However, some diagnostic tests can be sensitive without being specific, or vice versa. With diagnostic tests it is often possible to shift the threshold (cut-off value) used to decide whether a test result is positive or negative to optimise either sensitivity or specificity. In most cases there will be no perfect threshold as there is an inverse relationship between sensitivity and specificity.

Setting thresholds

For example, in the diagnostic test described in the next figure, the threshold could be set at position A. This would ensure that all healthy patients are deemed negative (no false positives, so high specificity) but it does mean that a large proportion of diseased patients will test negative (high false negatives, so low sensitivity). If the threshold was set at position B, then all diseased patients would test positive (no false negatives, so high sensitivity) but many healthy patients would test positive (high false positives, so low specificity).

Adjusting the cut-off threshold for a diagnostic test either increases specificity at the expense of sensitivity or increases sensitivity at the expense of specificity.The choice of threshold will depend on the nature of the disease. If you were screening for a very serious disease such as a cancer where early detection could prevent fatality, it makes sense to set the threshold so the test has high sensitivity (few false negatives). In a mass screening test for a less serious condition such as monitoring cholesterol levels or for one where early detection is not critical, it may make sense to have a higher specificity to not overburden the healthcare system.