A Machine Learning Approach to Estimate the Glomerular Filtration Rate in Intensive Care Unit Patients Based on Plasma Iohexol Concentrations and Covariates



This work aims to evaluate whether a machine learning approach is appropriate to estimate the glomerular filtration rate in intensive care unit patients based on sparse iohexol pharmacokinetic data and a limited number of predictors.


Eighty-six unstable patients received 3250 mg of iohexol intravenously and had nine blood samples collected 5, 30, 60, 180, 360, 540, 720, 1080, and 1440 min thereafter. Data splitting was performed to obtain a training (75%) and a test set (25%). To estimate the glomerular filtration rate, 37 candidate potential predictors were considered and the best machine learning approach among multivariate-adaptive regression spline and extreme gradient boosting (Xgboost) was selected based on the root-mean-square error. The approach associated with the best results in a ten-fold cross-validation experiment was then used to select the best limited combination of predictors in the training set, which was finally evaluated in the test set.


The Xgboost approach yielded the best performance in the training set. The best combination of covariates comprised iohexol concentrations at times 180 and 720 min; the relative deviation from these theoretical times; the difference between these two concentrations; the Simplified Acute Physiology Score II; serum creatinine; and the fluid balance. It resulted in a root-mean-square error of 6.2 mL/min and an r2 of 0.866 in the test set. Interestingly, the eight patients in the test set with a glomerular filtration rate < 30 mL/min were all predicted accordingly.


Xgboost provided accurate glomerular filtration rate estimation in intensive care unit patients based on two timed blood concentrations after iohexol intravenous administration and three additional predictors.

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  1. 1.

    Kellum JA, Lameire N, Aspelin P, Barsoum RS, Burdmann EA, Goldstein SL, et al. Kidney disease: improving global outcomes (KDIGO) acute kidney injury work group. KDIGO clinical practice guideline for acute kidney injury. Kidney Int Suppl. 2012;2:1–138.

    Article  Google Scholar 

  2. 2.

    Kirwan CJ, Philips BJ, Macphee IAM. Estimated glomerular filtration rate correlates poorly with four-hour creatinine clearance in critically ill patients with acute kidney injury. Crit Care Res Pract. 2013;2013:406075.

    PubMed  PubMed Central  Google Scholar 

  3. 3.

    Soveri I, Berg UB, Björk J, Elinder C-G, Grubb A, Mejare I, et al. Measuring GFR: a systematic review. Am J Kidney Dis. 2014;64:411–24.

    Article  Google Scholar 

  4. 4.

    Bröchner-Mortensen J. A simple method for the determination of glomerular filtration rate. Scand J Clin Lab Invest. 1972;30:271–4.

    Article  Google Scholar 

  5. 5.

    Benz-de Bretagne I, Le Guellec C, Halimi JM, Gatault P, Barbet C, Alnajjar A, et al. New sampling strategy using a Bayesian approach to assess iohexol clearance in kidney transplant recipients. Ther Drug Monit. 2012;34:289–97.

    CAS  Article  Google Scholar 

  6. 6.

    Taubert M, Ebert N, Martus P, van der Giet M, Fuhr U, Schaeffner E. Using a three-compartment model improves the estimation of iohexol clearance to assess glomerular filtration rate. Sci Rep. 2018;8:17723.

    CAS  Article  Google Scholar 

  7. 7.

    Riff C, Besombes J, Gatault P, Barbet C, Büchler M, Blasco H, et al. Assessment of the glomerular filtration rate (GFR) in kidney transplant recipients using Bayesian estimation of the iohexol clearance. Clin Chem Lab Med. 2020;58:577–87.

    CAS  Article  Google Scholar 

  8. 8.

    Åsberg A, Bjerre A, Almaas R, Luis-Lima S, Robertsen I, Salvador CL, et al. Measured GFR by utilizing population pharmacokinetic methods to determine iohexol clearance. Kidney Int Rep. 2020;5:189–98.

    Article  Google Scholar 

  9. 9.

    Salmon Gandonnière C, Helms J, Le Tilly O, Benz-de Bretagne I, Bretagnol A, Bodet-Contentin L, et al. Glomerular hyper- and hypofiltration during acute circulatory failure: iohexol-based gold-standard descriptive study. Crit Care Med. 2019;47:e623–e629629.

    Article  Google Scholar 

  10. 10.

    Badillo S, Banfai B, Birzele F, Davydov II, Hutchinson L, Kam-Thong T, et al. An introduction to machine learning. Clin Pharmacol Ther. 2020;107:871–85.

    Article  Google Scholar 

  11. 11.

    Chen T, Guestrin C. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining—KDD’16. August 13-17, 2016: 785–94. https://doi.org/10.1145/2939672.2939785. Available online from https://arxiv.org/abs/1603.02754 [cs.LG]. Accessed 3 Aug 2020

  12. 12.

    Friedman JH. Multivariate adaptive regression splines: the annals of statistics. Inst Math Stat. 1991;19:1–67.

    Google Scholar 

  13. 13.

    Le Gall JR, Lemeshow S, Saulnier F. A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study. JAMA. 1993;270:2957–63.

    Article  Google Scholar 

  14. 14.

    Castagnet S, Blasco H, Vourc’h P, Benz-De-Bretagne I, Veyrat-Durebex C, Barbet C, et al. Routine determination of GFR in renal transplant recipients by HPLC quantification of plasma iohexol concentrations and comparison with estimated GFR. J Clin Lab Anal. 2012;26:376–83.

    CAS  Article  Google Scholar 

  15. 15.

    Gower JC. A general coefficient of similarity and some of its properties. Biometrics. 1971;27:857–71.

    Article  Google Scholar 

  16. 16.

    Templ M, Kowarik A, Meindl B. Statistical disclosure control for micro-data using the R Package sdcMicro. J Stat Softw. 2015;67:1–36.

    Article  Google Scholar 

  17. 17.

    Ryu JY, Kim HU, Lee SY. Deep learning improves prediction of drug-drug and drug-food interactions. Proc Natl Acad Sci USA. 2018;115:E4304–E43114311.

    CAS  Article  Google Scholar 

  18. 18.

    Sheridan RP, Wang WM, Liaw A, Ma J, Gifford EM. Extreme gradient boosting as a method for quantitative structure–activity relationships. J Chem Inf Model. 2016;56:2353–60.

    CAS  Article  Google Scholar 

  19. 19.

    Daunhawer I, Kasser S, Koch G, Sieber L, Cakal H, Tütsch J, et al. Enhanced early prediction of clinically relevant neonatal hyperbilirubinemia with machine learning. Pediatr Res. 2019;86:122–7.

    Article  Google Scholar 

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The authors are grateful to K. Poole for manuscript editing.

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Corresponding author

Correspondence to Jean-Baptiste Woillard.

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No external funding was used in the preparation of this article.

Conflict of Interest

Jean-Baptiste Woillard, Charlotte Salmon Gandonnière, Alexandre Destere, Stephan Ehrmann, Hamid Merdji, Armelle Mathonnet, Pierre Marquet, and Chantal Barin-Le Guellec have no conflicts of interest that are directly relevant to the content of this article.

Ethics Approval

The study protocol was approved by the regional ethics institutional review board (Comité de Protection des Personnes Tours Ouest-1: 2013-R49).

Data Availability

The data that support the findings of this study are available from Charlotte Salmon Gandonnière upon reasonable request (charlotte.salmon.gandonniere@gmail.com).

Code Availability

The code is available under request (Rmarkdown html file).

Authors′ Contributions

JBW conceived and design the analysis, perform the analysis, JBW and CBLG wrote the paper, CSG, SE, HM, AM conceived and design the study and collected the data, AD, PM and CBLG contributed to the analysis.

Consent to participate

All patients and/or relatives submitted written informed consent before study inclusion.

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Woillard, JB., Salmon Gandonnière, C., Destere, A. et al. A Machine Learning Approach to Estimate the Glomerular Filtration Rate in Intensive Care Unit Patients Based on Plasma Iohexol Concentrations and Covariates. Clin Pharmacokinet 60, 223–233 (2021). https://doi.org/10.1007/s40262-020-00927-6

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