An invented clinic example
Suppose 1,000 people include 100 with a condition. At one threshold, a model flags 80 of those 100 and also flags 90 of the 900 without it. Staff receive 170 alerts, 80 of which are true positives.
At a lower threshold, imagine it flags 90 true cases and 180 false positives. Staff now receive 270 alerts. The lower threshold finds ten additional cases and produces 90 additional false alarms. These are hypothetical counts, not estimates for any product.
More detection is not the whole comparison
The second threshold improves sensitivity from 80% to 90%. But the share of alerts that are true positives falls from about 47% to 33%. Both changes can happen at once.
If every alert requires a short review, the extra workload has one meaning. If it triggers an invasive procedure, an urgent interruption, or a long wait for follow-up, the meaning changes. The threshold cannot be judged independently of the pathway after the alert.
Ask where the cutoff came from
A threshold might have been selected to meet a target sensitivity, maximize a statistical score, or fit available review capacity. Those are different objectives. A single accuracy number rarely reveals the choice.
The CDC's epidemiologic material explains why proportions require the right denominator. Here, “cases found” uses all true cases; “reliable alerts” uses all alerts. Confusing them makes a threshold sound more successful than the full table supports.
For a real system, the useful evidence includes those counts in the intended population, the uncertainty around them, and what happens after each type of result. A risk score is only one part of that workflow.
