A geometric tensor-based computational framework for harmonizing thyroid function tests across laboratories with...

Thyroid function tests (TFT) - notably free thyroxine (FT4) and thyrotropin (TSH) - are fundamental to the diagnosis and monitoring of thyroid disorders. However, different frames of reference from variations in laboratory assays calibrations for TFT result in inconsistent normative ranges that hinder direct comparison and trending, leading to clinical misinterpretations and inefficient longitudinal follow-up.

Using differential geometry and tensor calculus, we formulate inter-laboratory harmonization as a coordinate transformation between laboratory coupled FT4-TSH measurements spaces defined on a common differentiable physiological manifold endowed with metric tensor describing its reference range geometry, with polynomial mappings serving as local approximations of the transformation. Predictive performance of the transformation was evaluated using leave-one-out cross-validation and Bland-Altman agreement analysis.

Via a training TFT dataset, the coefficients of the mapping polynomial were computed. Both affine and quadratic mappings demonstrated excellent goodness-of-fit (R² > 0.998). However, LOOCV indicated that the affine model yielded lower prediction error than the quadratic model for the small training dataset sample, suggesting greater stability of affine mapping when paired datasets are limited. Bland-Altman analysis showed that predicted and observed values were generally in agreement.

In practice, affine mappings may offer greater robustness when calibration datasets are small in clinics, whereas higher-order models may be advantageous for larger datasets in hospital laboratories. This geometric framework provides a principled approach for reference interval harmonization across analytical platforms while preserving physiological structure of the FT4-TSH relationship, facilitating automated assay alignment in healthcare establishments.