Brilliant—a simple concept (diagnostics 101!) explained in a simple format. And as an associate editor of JCM, I can attest that this concept is frequently missed by submitting authors, not to mention practicing clinicians and hospital epidemiologists.
This issue is also foundational to diagnostic stewardship, as it emphasizes the importance of limiting diagnostic testing to patients who have a reasonable pre-test likelihood of disease (pre-test likelihood being the individual-patient equivalent of population prevalence).
It also explains why we’ll never “get to zero” for healthcare-associated infections (HAIs), even if all HAIs were preventable. Take the example of hospital-onset C. difficile infection (HO-CDI). The more successful your prevention program is at reducing whatever the “true” incidence of HO-CDI is, the lower will be the population prevalence—and the lower the positive predictive value (PPV) for the very sensitive CDI tests we now use. Positive tests will still occur, no doubt, and will be counted toward the HO-CDI rate—but they’ll be increasingly likely to be clinical false positives.
Now I need to go start working on a good cartoon editorial about whether CAUTI exists….

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