Fail-closed conformal multiresolution error control for conservative three-dimensional dose remapping in synthetic phantoms

Abstract

Conservative dose remapping can be formulated by transporting mass and deposited energy across nonmatching grids, but fixed high-sampling calculations use the same work for easy and difficult cases. We developed conformal multiresolution error control (CoMERC), a fail-closed multilevel quasi-Monte Carlo (QMC) controller for reference-relative target-cell allocation error in a fixed piecewise-constant source model with known deformation. Two randomized nested replicates were evaluated at a probe level of 4 and candidate levels of 8 and 16. Four endpoints were controlled jointly: reference-mass-weighted global, high-gradient, and density-gradient-threshold root-mean-square error, plus eligible-cell maximum absolute error. A split-conformal multiplier was calibrated from 240 synthetic cases, frozen, and evaluated on 400 independent cases from the same generator and 120 cases from a prespecified shifted generator. In the primary set, joint coverage was 394/400 (98.50%; one-sided 95% lower limit, 97.06%), 388/400 cases (97.00%; lower limit, 95.18%) received an output, and 0/388 released outputs exceeded any tolerance (one-sided 95% upper limit, 0.769%). Final actions were level 8 for 190 cases, level 16 for 198, and ABSTAIN for 12. The frozen policy implied mean relative production-sample work of 0.5844 compared with always running both randomized replicates through level 16; the prespecified 95th-percentile bootstrap upper limit was 0.6194. All seven primary gates passed. In the shifted-generator set, 113/120 cases were released and one released output exceeded a tolerance. CoMERC provided marginal finite-sample error control and lower modeled production-sample work in the locked synthetic population, but not patient-level, registration-level, conditional-on-release, or clinical safety validation.