Decision-theoretic recruitment and validation planning for depression surveys: An illustrative Chinese application

Background Survey planning must balance recruitment losses against uncertainty in screening yield, diagnostic accuracy and survey design. This study examined how these considerations determine invitation requirements and diagnostic-validation allocation. Methods A Beta planning distribution used 170 PHQ-9-positive results among 1,045 Chinese community participants and an effective sample size of 100. Asymmetric recruitment loss selected conditional and joint-distribution invitation targets. A separate cost-plus-variance Bayes criterion jointly allocated survey clusters and independent reference-positive and reference-negative validation samples. Parameter uncertainty and future-data performance were evaluated by integration and simulation. Results With an illustrative underplanning-to-overplanning loss ratio of 3, conditional planning selected a screening-positive proportion of 0.1862 and 4,794 screening invitations. Integrating design uncertainty increased this target to 5,346. Current-prevalence planning required 9,247 conditional invitations or 11,866 under joint parameter uncertainty when diagnostic accuracy was known within each scenario. The original validation sample imposed a reference-point half-width floor of 0.0292, exceeding the 0.020 target. Under specified relative costs, the joint allocation used 21,708 invitations and 240/4,538 reference-positive/reference-negative validation participants. Its prior-predictive width attainment was 53.15%, compared with 0.03% when nearly the same budget retained the original validation sample. Increasing the precision valuation fourfold raised attainment to 10,000/10,000 simulations, with 95.31% coverage. Uncorrected specificity shifts produced substantial bias despite larger samples. Conclusions At k = 3, the loss-based rule selected a screening-positive planning proportion of 0.1862, reducing conditional invitation requirements by 39.38% relative to p = 0.5. Joint survey–validation allocation improved simulated precision at comparable assumed cost. These findings support allocating recruitment and diagnostic-validation resources jointly when planning current-prevalence surveys.