Choosing the Right Decision Threshold in High-Stakes Diagnostics
Diagnostic tests and systems of many kinds are used in a host of practical settings to assist in making a positive or negative decision about the occurrence of a particular event or the existence of a particular condition. Will an impending storm strike? Is this aircraft unfit to fly? Is that plane intending to attack this ship? Is this nuclear power plant malfunctioning? Is this assembly-line item flawed? Does this patient have the acquired immunodeficiency syndrome (AIDS) virus? Is this person lying? Is this football player using drugs? Will this school (or job) applicant succeed? Will a document so indexed contain the information sought? Does this tax return justify an audit? Is there oil in the ground here? Will the stock market advance today? Will this prisoner vindicate a parole? Are their explosives in this luggage?
These examples are a reminder that diagnostic test results do not usually constitute compelling evidence for or against the condition or event of interest, or evidence of a sort that leads directly to either a positive or negative decision. Rather, with tests that justify the term diagnosis, the evidence is a matter of degree. Test results lie along a continuum or are spread across several categories. Diagnosis is probabilistic and diagnostic decisions are made with more or less confidence. Hence, making a positive or negative decision in a systematic way requires selecting a threshold along the scale of evidence, such that values above____________________