Inverse Breakpoint Analysis: A Scale-Invariant Physics-Inspired Metrological Audit for Sanitary Big Data

Abstract: Classical inferential statistics and p-value hypothesis testing in healthcare big data repositories suffer from severe structural limitations, notably p-hacking, asymptotic N-bias, and the frequent violation of independent and identically distributed (i.i.d.) assumptions due to intra-patient longitudinal dependencies, hospital clustering, and epidemiological shockwaves. To overcome these failures, we introduce an Inverse Breakpoint Analysis, a scale-invariant, physics-inspired metrological audit framework. Our analysis treats discrete clinical event counts not as abstract probabilities, but as physical informational mass. Grounded in Garwood exact discrete limits and Wilson-Hilferty approximations, the framework extends our previous work on stress testing indices for Big health data and establishes three rigorous thresholds: a pure mass saturation limit, a baseline tolerance band, and a structural signal threshold. Through the use of these three parameters, our inverse break-point analysis eliminates false-positive artifacts induced by massive repository sizes while preventing under-powering in small cohorts. Ultimately, the framework demonstrates that percentage-based thresholds are kinematic artifacts of scale, whereas absolute excess discrete mass serves as the sole physical invariant for healthcare data validation. We validated this approach with numerous illustrative examples.