Theta: a multivariate normative statistic applied to amyloid β panel data in familial Alzheimer’s disease

Abstract Biomarker ratios often outperform individual biomarkers in complex, multifactorial diseases. In Alzheimer’s disease, bivariate ratios may fail to capture the complex stoichiometry of amyloid β (Aβ) processing. We extended the ratio concept into a multivariate framework and performed experiments on Aβ peptide data from four familial Alzheimer’s disease cohorts (8 controls, 223 PSEN1 mutation carriers). We define “theta” as a multivariate statistic quantifying the angular divergence of each subject’s peptide profile from a homeostatic norm. Performance was benchmarked against established Aβ ratios using AUC and precision–recall AUC. Theta consistently outperformed benchmarks across datasets, achieving near-perfect discrimination (AUC 0.999, PR AUC 0.964). Established ratios like Aβ42/40 and Aβ37/42 showed markedly lower precision–recall performance (0.201–0.410). Pairwise comparisons confirmed theta’s superiority. Theta leverages the full multi-peptide Aβ profile, treating it as a unified geometric entity in the spirit of systems-level thinking, addressing the inherent limitations of simple pairwise ratios. Its consistent performance across diverse PSEN1 mutations underscores its robustness and suggests utility for early and precise detection of pathogenic shifts. Additional validation in human biospecimens is needed, and the framework may extend to sporadic Alzheimer’s disease and broader multivariate modelling challenges such as differential diagnosis.