How much overtesting is needed to safely exclude a diagnosis? A different perspective on triage testing using bayes' theorem

Ruling out disease often requires expensive or potentially harmful confirmation testing. For such testing, a less invasive triage test is often used. Intuitively, few negative confirmatory tests suggest success of this approach. However, if negative confirmation tests become too rare, too many disease cases could have been missed. It is therefore important to know how many negative tests are needed to safely exclude a diagnosis. We quantified this relationship using Bayes’ theorem, and applied this to the example of pulmonary embolism (PE), for which triage is done with a Clinical Decision Rule (CDR) and D-dimer testing, and CT-angiography (CTA) is the confirmation test. For a maximum proportion of missed PEs of 1% in triage-negative patients, we calculate a 67% 'mandatory minimum' proportion of negative CTA scans. To achieve this, the proportion of patients with PE undergoing triage testing should be appropriately low, in this case no higher than 24%. Pre-test probability, triage test characteristics, the proportion of negative confirmation tests, and the number of missed diagnoses are mathematically entangled. The proportion of negative confirmation tests—not too high, but definitely not too low either—could be a quality benchmark for diagnostic processes.