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Licensed Unlicensed Requires Authentication Published by De Gruyter July 19, 2023

Uncertainty in measurement and the renal tubular reabsorption of phosphate

  • Ian Farrance ORCID logo EMAIL logo , Robert Frenkel and Kay Weng Choy



The ratio of tubular maximum reabsorption of phosphate to glomerular filtration rate (TmP/GFR) is used to evaluate renal phosphate transport. TmP/GFR is most probably calculated using the formula described by Kenny and Glen or obtained from the nomogram described by Walton and Bijvoet. Even though the calculation itself is well described, no attention has been given to its measurement uncertainty (MU). The aim of this study is to provide a procedure for evaluating the MU of the Kenny and Glen formula; a procedure which is based on the Evaluation of measurement data – Guide to the expression of uncertainty in measurement (GUM).


TmP/GFR is a quantity value calculated from the input of measured values for serum (plasma) phosphate and creatinine, plus measured values of urine phosphate and creatinine. Given the measurement uncertainty associated with these input quantities, the GUM describes the mathematical procedures required to determine the uncertainty of the calculated TmP/GFR. From a medical laboratory perspective, these input uncertainties are the standard deviations of the respective internal quality control estimates for serum and urine phosphate, plus serum and urine creatinine.


Based on representative measurements for the input quantities and their associated standard uncertainties, the expanded relative uncertainty for a calculated TmP/GFR is approximately 3.0–4.5 %.


With the continued relevance of the TmP/GFR procedure and the use of creatinine clearance as an estimate of GFR, the addition of an uncertainty estimate is important as an adjunct to this diagnostic procedure.

Corresponding author: Ian Farrance, Discipline of Laboratory Medicine, School of Health and Biomedical Sciences, RMIT University, Bundoora, VIC, 3083, Australia, E-mail:

  1. Research funding: None declared.

  2. Author contributions: All authors contributed equally to the design and development of the study. All authors reviewed and edited the manuscript and approved the final version for publication. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors state no conflict of interest.

  4. Informed consent: Not applicable.

  5. Ethical approval: Not applicable.


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Received: 2023-05-06
Accepted: 2023-06-29
Published Online: 2023-07-19
Published in Print: 2023-11-27

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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