Questions: Diagnostic Cutoff Scores and Classification Accuracy

Question 1

A hospital lowers the cutoff score on a depression screening test, so more people screen positive. What happens to sensitivity and specificity?

• A. Both sensitivity and specificity increase — a lower cutoff is more accurate overall
• B. Sensitivity increases and specificity decreases — more true cases are caught but more false alarms are generated
• C. Specificity increases and sensitivity decreases — the stricter threshold catches only true cases
• D. Neither changes — the AUC is fixed and cutoff placement does not affect classification accuracy

Answer: (B)

Lowering the cutoff means more people pass the threshold, which catches more true positives (higher sensitivity) but also flags more people who don't have the condition (lower specificity). This is the fundamental trade-off: sensitivity and specificity move in opposite directions as you shift the cutoff. Option D is a common misconception — the AUC is fixed (it summarizes the test's overall discriminatory ability), but sensitivity and specificity at any particular cutoff absolutely change with threshold placement.

Question 2

A researcher compares two screening tests. Test A has AUC = 0.91; Test B has AUC = 0.64. Which conclusion is most accurate?

• A. Test A has higher sensitivity than Test B at every possible cutoff
• B. Test B should never be used clinically because it performs below 0.70
• C. Test A is more discriminating overall — across all possible cutoffs it better separates true positives from true negatives
• D. Test A is always the better choice regardless of the clinical context

Answer: (C)

AUC summarizes overall discriminatory accuracy across all possible cutoffs. A higher AUC means the test better separates cases from non-cases on average. However, AUC does not tell you which test has higher sensitivity at any specific cutoff (option A is wrong — high overall AUC doesn't mean dominance at every single threshold). Option B is overly rigid — a test with AUC 0.64 may still be useful in low-resource settings or for preliminary screening. Option D ignores that clinical context (costs of false positives vs. false negatives) should drive test and cutoff selection.

Question 3

A test with high sensitivity will necessarily also have high specificity, since both indicate a well-performing test.

• T. True
• F. False

Answer: False

Sensitivity and specificity trade off structurally. Sensitivity measures how well the test identifies true positives; specificity measures how well it excludes true negatives. Lowering the cutoff raises sensitivity (fewer missed cases) but lowers specificity (more false positives). A perfect test would have both, but real tests always sacrifice one for the other at any given cutoff. A useful mnemonic: high sensitivity means few false negatives (good for ruling out); high specificity means few false positives (good for ruling in).

Question 4

Choosing where to place a diagnostic cutoff score is a values judgment — not a purely statistical optimization — because different clinical contexts call for different tolerances for false positives versus false negatives.

• T. True
• F. False

Answer: True

This is the central ethical insight of the topic. Statistics can tell you the sensitivity and specificity at every possible cutoff, but they cannot tell you which error is worse. For suicidality screening, missing a true case (false negative) is catastrophic — so you set a low threshold and accept more false alarms. For allocating scarce services, generating many false positives wastes resources and causes harm — so you set a higher threshold. The choice reflects values about harm, not just accuracy, and should be made explicitly rather than buried in a 'standard' cutoff.

Question 5

Why is choosing a diagnostic cutoff score described as a values judgment rather than a purely statistical decision? Give an example of two clinical contexts that would warrant different cutoff placements for the same test.

Model answer: Any cutoff placement involves accepting more of one error type (false positives or false negatives) at the expense of the other. That trade-off cannot be resolved statistically — it depends on the relative costs of each error in context. For example, a cutoff for suicidality screening should be set low (high sensitivity) because missing a true case can be fatal, even at the cost of many false alarms that follow-up assessment can filter. A cutoff for allocating a scarce treatment resource should be set higher (high specificity) to avoid misallocating limited resources to people who don't need the treatment.

The ROC curve maps sensitivity against false positive rate at every possible threshold, but it cannot choose among them. That choice requires a values framework: who is harmed by each error type, how badly, and how recoverable is the harm? Ethical diagnostic practice requires making these assumptions explicit and transparent, and communicating confidence intervals and misclassification rates alongside any classification decision.