PANC-BKF: A Mechanistically Constrained Longitudinal Biomarker Framework for Prediagnostic Pancreatic Cancer Risk Estimation

Description PANC-BKF (Pancreatic Cancer Biomarker Kinetic Formula) is a proposed mathematical and computational framework for investigating whether longitudinal biomarker trajectories can reveal persistent changes in biological dynamics before the clinical diagnosis of pancreatic ductal adenocarcinoma (PDAC). The framework integrates four main components: (1) a mechanistically motivated reaction–advection–diffusion model for biomarker dynamics; (2) an observation model designed to account for measurement noise, irregular sampling, patient-specific baselines, missing data, and relevant clinical confounders; (3) a sequential Kinetic Transition Index (KTI) based on mixture likelihood-ratio processes to quantify evidence for changes in biomarker dynamics; and (4) a separate landmark survival model for estimating absolute PDAC risk over specified time horizons. The manuscript develops mathematical results concerning aggregate biomarker dynamics, source–clearance non-identifiability, sequential false-transition control under explicit assumptions, evidence accumulation, detection delay, measurement-error propagation, and risk-model stability. Synthetic experiments examine the behavior of the proposed framework under stable benign, inflammatory, and simulated malignant trajectories. The central hypothesis is that persistent changes in multivariate biomarker dynamics may provide additional predictive information beyond individual biomarker measurements. This hypothesis remains to be evaluated using appropriately designed longitudinal human cohorts with measurements collected before clinical diagnosis. Research status and limitations: This is a preliminary theoretical and computational research manuscript shared as a preprint. It has not undergone peer review, and the proposed framework has not been validated on independent human prediagnostic cohorts. The synthetic results do not establish clinical diagnostic accuracy, early-detection performance, or clinical utility. PANC-BKF is a research framework, not a validated diagnostic test. Further work is required to independently audit the mathematical derivations and statistical assumptions, establish computational reproducibility, compare the framework with appropriate baseline methods, and assess its performance using independent longitudinal clinical data. This preprint documents the current formulation of PANC-BKF to support scientific discussion, methodological evaluation, and future research into longitudinal biomarker modeling for pancreatic cancer.