Functional reference limit: objectively defining the physiological relationship between serum vitamin D and parathyroid hormone

A functional reference limit is defined as the point of inflection (a ‘breakpoint’), representing a change in the statistical relationship, between two biologically related biomarkers. We describe a statistical framework to objectively define functional reference limits using the homoeostatic relationship between serum 25-hydroxy vitamin D (vitamin D) and parathyroid hormone as a proof of concept. Vitamin D (the independent variable) and parathyroid hormone (the dependent variable) measurements were extracted from the Melbourne Pathology laboratory information system database. A scatter plot of the biomarker pair was first generated to visually assess the presence of an inflection point (breakpoint). Following this, the measurements were grouped into fixed concentration intervals of 500, 800 and 1000 and normalised to ensure the range of values were identical for both biomarkers. The normalised data were split into two (left and right) frames, and two weighed linear regressions were fitted in a sliding manner along the concentration range to search for the optimal fit for both regressions, as determined by the smallest mean squared of residual. Using this approach, the optimal functional reference limit for vitamin D, where the breakpoint for parathyroid hormone was found at 28 nmol/L with 800 fixed concentration intervals and a mean squared of residual of 0.0022. This approach uses several statistical procedures to improve the fitting of the weighted linear regressions to objectively identify the functional reference limit. An Excel tool of this approach is available (Supplementary File 1).