Hierarchical biomarker thresholding: a model-agnostic framework for stability

Many biomarker pipelines require patient-level decisions aggregated from instance-level (cell/patch) scores. Thresholds tuned on pooled instances often fail across sites due to hierarchical dependence, prevalence shift, and score-scale mismatch. We present a selection-honest framework for hierarchical thresholding that makes patient-level decisions reproducible and more defensible. At its core is a risk decomposition theorem for selection-honest thresholds. The theorem separates contributions from (i) internal fit and patient-level generalization, (ii) operating-point shift reflecting prevalence and shape changes, and (iii) a stability term that penalizes sensitivity to threshold perturbations. The stability component is computable via patient-block bootstraps mapped through a monotone modulus of risk. This framework is model-agnostic, reconciles heterogeneous decision rules on a quantile scale, and yields monotone-invariant ensembles and reportable diagnostics (e.g. flip-rate, operating-point shift).