Allocating 600 Sealant Slots Between Two Schools
A county health department receives a one-year grant of $60,000 for a school-based sealant program. Screening plus sealants costs about $45 per child, and the program has capacity for roughly 600 children. Two elementary schools are candidates. School A: 320 second-graders, 38% with untreated caries or white-spot lesions on screening, 71% enrolled in Medicaid, and limited access to a dental home. School B: 280 second-graders, 9% with untreated caries, 22% on Medicaid, and most children already have a private dentist. The hygienist screening protocol has a sensitivity of 0.85 and a specificity of 0.90 for identifying children who need treatment. The department wants to maximize the number of true high-need children identified and treated.
1. Calculate the positive and negative predictive values for both schools and explain what the difference means for the program's yield.
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Use prevalence as the pretest probability. PPV = (Se x P) / (Se x P + (1 - Sp)(1 - P)); NPV = (Sp)(1 - P) / (Sp(1 - P) + (1 - Se)(P)).
School A (P = 0.38):
- PPV = (0.85 x 0.38) / (0.85 x 0.38 + 0.10 x 0.62) = 0.323 / (0.323 + 0.062) = 0.323 / 0.385 = 0.84
- NPV = (0.90 x 0.62) / (0.90 x 0.62 + 0.15 x 0.38) = 0.558 / (0.558 + 0.057) = 0.91
School B (P = 0.09):
- PPV = (0.85 x 0.09) / (0.85 x 0.09 + 0.10 x 0.91) = 0.0765 / (0.0765 + 0.091) = 0.0765 / 0.1675 = 0.46
- NPV = (0.90 x 0.91) / (0.90 x 0.91 + 0.15 x 0.09) = 0.819 / (0.819 + 0.0135) = 0.98
Interpretation. The test is identical; only the prevalence changes. In School A, about 84 of every 100 children flagged actually need care, so staff time converts efficiently into treatment. In School B, fewer than half of flagged children truly need treatment - over half of the follow-up effort and parent outreach is spent on false positives, even though the test "rules out" disease very well there. Sensitivity and specificity are properties of the test; predictive values are properties of the setting, which is why the same protocol should not be deployed identically in both schools.
2. Recommend how to allocate the 600 slots and justify it with the numbers. What additional data would you want?
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Allocation. Prioritize School A first - all 320 second-graders - because the PPV of 0.84 means the screening-to-treatment pathway is efficient and the need is highest. Assign the remaining 280 slots to School B, but do not apply the same blanket screening. In School B, use the screen as a rule-out (NPV 0.98) and add a second criterion - a positive screen plus Medicaid or no dental home, or a parent-reported pain or visible plaque - to raise the post-test probability before committing resources.
Rough yield math. In School A, expected true cases: 320 x 0.38 = about 122 children needing treatment; the screen captures about 0.85 x 122 = 104, with 104/0.84 achieved because a few false positives also get sealed. In School B, expected true cases: 280 x 0.09 = about 25, with roughly 21 captured - a fraction of the benefit for the same per-child cost.
Additional data needed: number of children who already have a dental home (to avoid duplicating care), sealant retention capacity, parental consent rates, language and transportation barriers, cost per case actually prevented rather than per child screened, and baseline caries severity, not just presence. Also useful: whether the district has a history of sealant program participation and whether a dental hygienist can provide interim therapeutic restorations for cavitated cases.
3. If the grant is renewed for three years, what evaluation design and outcome measures would demonstrate whether the program worked?
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Design. A single-group pre/post comparison cannot distinguish program effect from secular trends or regression to the mean. Better: a quasi-experimental design with a comparison school of similar demographics that does not receive the program, or a staggered rollout in which schools are randomized to year 1 versus year 2 - ethically defensible when resources cannot cover everyone at once. Calibrate examiners and report inter-examiner reliability (kappa) so changes in measurement are not mistaken for changes in disease.
Outcome measures:
- Process: percentage of eligible children screened and consented; sealant placement rate; retention at 6 and 12 months (a program that seals but loses sealants within a year has not produced benefit).
- Outcome: new cavitated caries increments in sealed versus unsealed first molars, examined by a blinded examiner; proportion of children with a dental home after the program; referral completion rate for children needing restorative care.
- Efficiency: cost per child served and cost per carious surface prevented.
Analysis caution. Count children, not surfaces, when computing confidence intervals - surfaces within a mouth are correlated. Report absolute differences with confidence intervals, not only p-values, and report results for all enrolled children (intention-to-treat), including those who moved away or refused, so the program is not flattered by attrition.