Applying a Screening Cutoff Under Time Pressure
A community mental-health clinic serves 400 adults per month. Staff have 20 minutes per intake and one licensed supervisor. They plan to add a brief self-report depression screen scored 0–27, with a published cutoff of 10 (scores of 10 or higher are flagged for follow-up). In the clinic's population, roughly 15% of intakes meet criteria for a depressive disorder on structured interview. The screen has sensitivity 0.85 and specificity 0.80 at that cutoff. The supervisor can conduct only 25 full diagnostic interviews per month, and every flagged score currently triggers one. The director asks whether the cutoff should be kept, raised, or lowered, and how the 25 interview slots should be allocated.
1. Using the stated prevalence, sensitivity, and specificity, estimate how many of the 400 monthly intakes would be flagged and how many of those flags are true cases. What does this imply for the current plan?
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With 15% prevalence, about 60 of 400 intakes are true cases and 340 are not. True positives = 0.85 × 60 = 51. False negatives = 9. False positives = (1 − 0.80) × 340 = 68. Total flagged = 51 + 68 = 119. So only 51/119 ≈ 43% of flags are true cases; 68 people without a depressive disorder would consume follow-up. The clinic has 25 interview slots against 119 flags, so the current rule cannot be honored. Because prevalence is modest, even a decent specificity yields many false positives - positive predictive value depends on base rate, not just test accuracy. The plan needs either a higher threshold, a two-stage strategy, or explicit prioritization rather than treating every flag as equivalent.
2. The director proposes raising the cutoff to reduce false positives. What trade-offs should guide that decision, and how should the 25 interview slots be used?
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Raising the cutoff increases specificity and positive predictive value but lowers sensitivity, so more true cases are missed - a serious cost when untreated depression carries risk. The choice should be driven by the relative harm of a missed case versus an unnecessary interview, and by capacity. With 25 slots for 400 intakes, a sensible design is stepped: use the screen to triage, then prioritize flagged patients by severity indicators (e.g., item-level responses on self-harm or hopelessness, functional impairment, clinician concern) rather than raw total score alone. Patients not interviewed should still receive a brief check and clear pathways to return. The clinic should also document that the screen is not diagnostic, monitor outcomes, and revisit the cutoff if the case mix changes. Lowering the cutoff would worsen the false-positive burden without adding capacity.
3. A staff member argues the screen is invalid because 'most positive results were wrong.' Evaluate this reasoning.
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The claim confuses positive predictive value with test validity. A screen can have good sensitivity and specificity yet yield mostly false positives when prevalence is low; that is a base-rate phenomenon, not evidence the instrument is broken. The appropriate response is to report sensitivity, specificity, and predictive values transparently, and to explain that screening aims to avoid missing cases, accepting some over-referral. Validity evidence should come from local calibration - comparing screen results with structured interviews in a sample - not from the proportion of positives that are true. If the clinic wants higher predictive value at the point of a positive result, it can add a second-stage assessment, raise the threshold, or target screening to higher-prevalence groups, each with its own sensitivity cost.