Uncertainty Quantification of Antibody Measurements: Physical Principles and Implications for Standardization

Abstract

Harmonizing serology measurements is critical for identifying reference materials that permit standardization and comparison of results across different diagnostic platforms. However, the theoretical foundations of such tasks have yet to be fully explored in the context of antibody thermodynamics and uncertainty quantification (UQ). This has restricted the usefulness of standards currently deployed and limited the scope of materials considered as viable reference material. To address these problems, we develop rigorous theories of antibody normalization and harmonization, as well as formulate a probabilistic framework for defining correlates of protection. We begin by proposing a mathematical definition of harmonization equipped with structure needed to quantify uncertainty associated with the choice of standard, assay, etc. We then show how a thermodynamic description of serology measurements (i) relates this structure to the Gibbs free-energy of antibody binding, and thereby (ii) induces a regression analysis that directly harmonizes measurements. We supplement this with a novel, optimization-based normalization (not harmonization!) method that checks for consistency between reference and sample dilution curves. Last, we relate these analyses to uncertainty propagation techniques to estimate correlates of protection. A key result of these analyses is that under physically reasonable conditions, the choice of reference material does not increase uncertainty associated with harmonization or correlates of protection. We provide examples and validate main ideas in the context of an interlab study that lays the foundation for using monoclonal antibodies as a reference for SARS-CoV-2 serology measurements.