Combining Bayesian and Frequentist Inference for Laboratory-Specific Performance Guarantees in Copy Number Variation Detection

Targeted amplicon panels are widely used in oncology diagnostics, but providing per-gene performance guarantees for copy number variant (CNV) detection remains challenging due to amplification artifacts, process-mismatch heterogeneity, and limited validation sample sizes. While Bayesian CNV callers naturally quantify per-sample uncertainty, translating this into the frequentist population-level guarantees required for clinical validation, coverage rates, false-positive bounds, and minimum detectable copy-number changes, is a fundamentally different inferential problem. We show empirically that even robust Bayesian credible intervals, including coarsened posteriors and sandwich-adjusted intervals, are severely miscalibrated on panels with small amplicon counts per gene. To address this, we propose a hybrid framework that evaluates Bayesian posterior functionals on validation samples and models the resulting squared losses with a Gamma distribution, yielding tolerance intervals with valid frequentist coverage. Three components make the method practical under real-world constraints: (1) imputation that removes the influence of true CNV-positive samples without requiring known ground truth, (2) regularization to address small sample variability, and (3) evidence-based stratification on the log model evidence to accommodate non-exchangeable noise profiles arising from process mismatch. Evaluated on two targeted amplicon panels using leave-one-out cross-validation, the proposed method achieves single-digit mean absolute coverage error across all genes under both process-matched and unmatched conditions, whereas Bayesian comparators exhibit mean absolute errors exceeding 60\% on clinically relevant genes such as ERBB2.