<p>Specificity-recalibrated planning values.</p>

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.</p> <p>Conclusions</p><p>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.</p></div>