How to read a paper: Papers that report diagnostic or screening tests

A correspondent has pointed out an error of terminology in this paper by Trisha Greenhalgh (30 August, pp 540-3). The value described as the negative likelihood ratio and expressed in the formula (1-sensitivity)/specificity is, in reality, not the negative likelihood ratio but a value which is described by the question, “How much more likely is a negative result to be found in a person with, as opposed to without, the condition?” The negative likelihood ratio is described by the question, “How much more likely is a negative result to be found in a person without, as opposed to with, the condition?” and is expressed by the formula specificity/ (1-sensitivity). In the example given, a negative urine test for glucose does indeed reduce the window cleaner's baseline chances of diabetes to 0.78 of the pretest likelihood, but the negative likelihood ratio of the test is the reciprocal of this value—that is, 1.28.