Improved correction formulas to estimate iohexol clearance from simple models

To the editor,

Measuring glomerular filtration rate by iohexol plasma clearance has become a preferred method in clinical practice and research [1–9], but ambiguities remain regarding the choice of pharmacokinetic modeling when evaluating iohexol concentration. We recently showed that a three-compartment pharmacokinetic model provides better iohexol clearance estimates than the two-compartment approach in elderly subjects in the Berlin Initiative Study (BIS) [7, 8]. However, implementation of the presented model in clinical and research practice is complicated by the required technical expertise and the complexity of Bayesian software [7]. A viable alternative could be the use of correction formulas which rely on traditional one- or two-compartment models and correct the obtained clearance estimates for the bias introduced by the omission of compartments [9–14]. Well-known examples for established correction formulas are the Bröchner-Mortensen (BM) equation [12] and the further simplified Chantler (Ch) formula [14] based on a one-compartment model, which have recently been shown to perform well in iohexol data from the BIS [9]. Such an evaluation remains to be carried out based on a three-compartment model, which is the subject of this letter.

Data from the BIS, including 546 individuals with data obtained up to 300 min post-injection, were evaluated [7, 8]. One-, two-, and three-compartment models were used to estimate iohexol clearance (CL1, CL2, and CL3), respectively. CL1 was estimated based on the slow component of iohexol concentrations 120 to 300 min post-dose, CL2 was estimated based on the protocol by Schwartz et al. [11] as carried out in the BIS [8], and CL3 was estimated using the empirical Bayes approach based on the three-compartment model [7]. Equations resembling the BM and Ch formulas were then fitted to correct CL1 and CL2 results, using CL3 as the reference (Table 1) [12, 14]. A leave-one-out cross-validation [15] was utilized to assess the bias and root mean squared error (RMSE), as well as to evaluate Lin’s concordance correlation coefficient (CCC) [16] and the relative total deviation index (TDI) for a range of coverage probabilities (CP) [17]. A TDI ≤ 10% for a CP of 90% (TDI₉₀) and an at least substantial CCC of ≥ 0.95 were considered optimal. R 4.2.1 [18] and NONMEM 7.4.2 [19] were used as statistical software.

Table 1.

Performance of correction formulas based on leave-one-out cross-validation, comparing iohexol clearance estimates obtained from different correction formulas to reference clearance values from three-compartment model

Nr.	Equation	Bias (mL/min) mean (95% CI)	Relative bias (%) mean (95% CI)	RMSE (mL/min)	CCC	TDI90 (%)
1 (BM)	$\text{CL=0.872}\times \text{CL1-0.000560}\times {\text{CL1}}^2$	− 0.0949 (− 0.428 to 0.238)	− 0.103 (− 0.616 to 0.411)	3.97	0.974	10.6
2 (Ch)	$\text{CL=0.824}\times \text{CL1}$	− 0.357 (− 0.698 to − 0.016)	− 0.953 (− 1.50 to − 0.409)	4.08	0.974	11.5
3 (BM)	$\text{CL=0.894}\times \text{CL2+0.0000246}\times {\text{CL2}}^2$	− 0.0415 (− 0.288 to 0.205)	− 0.0331 (− 0.411 to 0.344)	2.94	0.986	7.71
4 (Ch)	$\text{CL=0.896}\times \text{CL2}$	− 0.0313 (− 0.277 to 0.214)	− 0.0022 (− 0.378 to 0.374)	2.92	0.986	7.68

CL iohexol clearance estimates obtained from different correction formulas, CL1 one-compartment clearance estimates, CL2 two-compartment clearance estimates, BM Bröchner-Mortensen–like equation, Ch Chantler–like equation, CI confidence interval, RMSE root mean square error, CCC Lin’s concordance correlation coefficient, TDI₉₀ total deviation index for a coverage probability of 90%

BM- and Ch-like equations performed similarly well (Table 1), with an absolute bias < 1 mL/min, an RMSE between 2.92 and 4.08 mL/min, and a substantial concordance for all equations. The TDI₉₀ goal was achieved with Eqs. 3 and 4 based on two compartments, while it was missed with Eqs. 1 and 2 based on one compartment. Differences between BM-like and Ch-like equations were negligible with equations based on two compartments, while the BM-like equation provided a notably lower absolute bias than the Ch-like equation in the case of one compartment (− 0.0949 versus − 0.357 mL/min). In summary, our evaluation demonstrates that correction formulas in conjunction with one- or two-compartment models can provide adequate clearance estimates with only a minimal loss in accuracy and precision compared to a three-compartment model. When one-compartment estimates are available, the BM-like correction formula might be a good choice, while the simple Ch-like formula might be sufficient if two-compartment estimates are available. This provides the means to efficiently estimate iohexol clearance in settings where complexities and costs associated with the implementation of a Bayesian model are prohibitive. Whether the slight loss of accuracy and precision compared to the three-compartment model is acceptable depends on the clinical context and should therefore be judged on a case-by-case basis. Further validation in diverse patient populations is required, and the evaluation of additional, potentially non-linear correction formulas might provide further improvements.

Author contribution

Conception and design: MT, QD. Acquisition of data: ES, NE, MvdG. Analysis and/or interpretation of data: QD, MT. Manuscript drafting: QD, MT, UF. Revision and final approval of manuscript: all authors.

Funding

Open Access funding enabled and organized by Projekt DEAL. Qian Dong received a scholarship from the China Scholarship Council (CSC) for support of her PhD studies (scholarship number 202008320388).

Availability of data and materials

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Disclaimer

The funder had no role in design, collection, analysis, and interpretation of data, and writing and publication of the manuscript.