Measurement uncertainty in derived (calculated) biological quantities: Impact on clinical interpretation

Measurement uncertainty (MU) is essential for interpreting laboratory results. While MU is often reported for directly measured quantities, it is rarely considered for derived (calculated) ones, despite their widespread clinical use. This study assessed the impact of MU on interpretation of derived quantities by comparing directly measured and calculated results.

Following ISO/TS 20914:2019 and GUM guidelines, MU was estimated for directly measured and derived biological quantities. Ionized magnesium (iMg) was analyzed as a case, comparing direct measurement with regression-based estimates. The approach was extended to estimated glomerular filtration rate (eGFR), low-density lipoprotein cholesterol (cLDL, direct enzymatic vs. Friedewald), free testosterone (direct vs. Vermeulen calculation), and the anion gap (AG, incorporating calculated bicarbonate). Clinical interpretation was evaluated by comparing coverage intervals with biological reference intervals and clinical decision limits.

Direct iMg measurement at 0.520 mmol/L yielded a relative expanded uncertainty (U, k = 2) of 4.1 %. Regression-derived values showed U up to 21.4 %. For eGFR, U ranged from 3.8 % to 5.5 %. At 63 mL/min/1.73 m², coverage intervals overlapped the 60 mL/min/1.73 m² decision limit, altering chronic kidney disease staging. Direct cLDL measurement (2.54 mmol/L) had U = 4.8 %, while Friedewald calculation (2.60 mmol/L) showed U = 4.8 %; both overlapped therapeutic decision limits. Free testosterone measurement (0.221 nmol/L) had U = 13.9 %, whereas Vermeulen-derived values (0.210 nmol/L) reached 24.1 %. For AG, an abnormal value (28.2 mmol/L) remained pathological, but values of 20.3 or 14.0 mmol/L overlapped the 18 mmol/L limit, producing indeterminate classification.

MU significantly influences the interpretation of derived laboratory quantities, particularly near decision limits. Systematic reporting of MU, in line with international recommendations, would enable more reliable interpretation, improve patient safety, and reduce misclassification in clinical decision-making.

MU, measurement uncertainty; eGFR, estimated glomerular filtration rate, cLDL, substance concentration of LDL-cholesterol in serum; fTes, substance concentration of free testosterone in serum; AG, anion gap; iMg, substance concentration of ionized magnesium in serum; tMg, substance concentration of (total) magnesium in serum; Alb, mass concentration of albumin in serum; IP, substance concentration of inorganic phosphate in serum; PaCO₂, partial pressure of carbon dioxide in arterial blood; BRI, biological reference interval; y, derived quantity; u_c(y), combined standard uncertainty for derived quantity y; x_i, measured quantity or empirical constant i; x_j, measured quantity or empirical constant j; [Formula: see text] , correlation coefficients between quantities x_i and x_j; ∂y∂x_i, sensitivity coefficient for the measured or empirical constant i; ∂y∂x_j, sensitivity coefficient for the measured or empirical constant j; u_cal, uncertainty associated with the assigned value of the end-user calibrator; u_Rw, uncertainty related to the intermediate precision; u_b, uncertainty associated with any correction factors related to bias; IFU, Instructions for Use; CI, confidence interval; u_ciMg, Combined uncertainty related to the iMg; UiMg, Expanded uncertainty related to the iMg.