Reducing bias in estimated blood volume: A robust approach to calibration of the Nadler formula

The Nadler formula is widely used for blood-volume estimation but exhibits systematic proportional bias that compromises clinical accuracy. A calibrated formula was developed and validated using Passing-Bablok regression. A published dataset of 90 patients with directly measured blood volumes was randomly partitioned into training and test sets. Passing-Bablok regression on the training set derived calibration coefficients, which were applied to the internal test set. Validation used Passing-Bablok regression, concordance correlation coefficient and robust Bland-Altman analysis. Five-fold cross-validation assessed generalisability. Training set analysis demonstrated significant proportional bias. After calibration, the internal test set showed elimination of proportional bias and excellent concordance with measured blood volume. Five-fold cross-validation confirmed robust and consistent performance across all data partitions. An independent external cohort of 201 healthy men showed improved agreement after calibration, once a documented haematocrit-conversion difference between the two reference methods was accounted for, supporting generalisability beyond the initial Retzlaff dataset. Passing-Bablok regression-based calibration successfully eliminated systematic bias in the Nadler formula, achieving high concordance with radioisotope-measured blood volume in internal validation. The simple linear calibration maintains clinical simplicity while addressing a critical limitation of the original formula. A preliminary external validation in an independent historical cohort of 201 men supported this generalisability; further validation in contemporary, mixed-sex cohorts is recommended before widespread clinical implementation.