Uncertainty quantification of antibody measurements: Physical principles and implications for standardization

Harmonizing serology measurements (i.e., rendering them interchangeable) is critical for comparing results across different diagnostics platforms, developing associated reference materials, and thereby informing medical decisions. However, the theoretical foundations of such tasks have yet to be fully explored in terms of antibody thermodynamics and uncertainty quantification (UQ). In the context of SARS-CoV-2, for example, this has restricted the usefulness of standards currently deployed, limited the scope of materials considered as viable standards, and ultimately decreased confidence in serology. To address these problems, we develop rigorous theories of antibody normalization and harmonization. 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 an optimization-based normalization (not harmonization!) method that validates consistency between the behavior of a reference material and biological samples. A key result of these analyses is that under physically reasonable conditions, the choice of reference material does not increase uncertainty associated with harmonization. We validate main ideas via an interlab study that considers monoclonal antibodies as a reference for SARS-CoV-2 serology measurements and discuss connections to correlates of protection.