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Prevalence‐free utility‐respecting summary indices of diagnostic power do not exist
Author(s) -
Hilden Jørgen
Publication year - 2000
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(20000229)19:4<431::aid-sim348>3.0.co;2-r
Subject(s) - ranking (information retrieval) , rank (graph theory) , context (archaeology) , index (typography) , test (biology) , econometrics , point (geometry) , diagnostic test , computer science , mathematical economics , statistics , mathematics , medicine , artificial intelligence , paleontology , emergency medicine , geometry , combinatorics , world wide web , biology
One would like to have a ranking method for diagnostic tests that justifiably makes no assumptions about the local ‘disease mix’, that is, about the pre‐test probabilities of the diagnostic alternatives. Assuming the simplest possible clinical context we therefore examine the following question: can a summary index of diagnostic test performance be devised which is loyal to the expected utility paradigm and, at the same time, is incidence‐free (prevalence‐free)? In other words, regardless of pre‐test probabilities, the index should rank rival tests in a way which agrees with how they might be ranked by expected utility calculations. From a practical point of view, the answer is negative; it is proved that such indices do exist, but they necessarily impose a very restrictive mathematical form on the utility framework and, what is worse, invariably go against what is medically appropriate by violating a boundedness requirement. Copyright © 2000 John Wiley & Sons, Ltd.