## Abstract

The normalization of GFR to a standardized body-surface area of 1.73 m^{2} impedes comparison of GFR across individuals of different genders, heights, or weights. Ideally, GFR should be normalized to a parameter that best explains variation in GFR. Here, we measured true GFR by iohexol clearance in a representative sample of 1627 individuals from the general population who did not have diabetes, cardiovascular disease, or kidney disease. We also estimated total body water (TBW), extracellular fluid volume, lean body mass, liver volume, metabolic rate, and body-surface area. We compared two methods of normalizing GFR to these physiologic variables: (*1*) the conventional method of scaling GFR to each physiologic variable by simple division and (*2*) a method based on regression of the GFR on each variable. TBW explained a higher proportion of the variation in GFR than the other physiologic variables. GFR adjusted for TBW by the regression method exhibited less dependence on gender, height, and weight compared with the other physiologic variables. Thus, adjusting GFR for TBW by the regression method allows direct comparisons between individuals of different genders, weights, and heights. We propose that regression-based normalization of GFR to a standardized TBW of 40 L should replace the current practice of normalizing GFR to 1.73 m^{2} of body-surface area.

The GFR is arguably one of the most important parameters in human physiology and plays a fundamental role in nephrology. In both clinical practice and research, comparisons of GFR between and within subjects are of vital importance. Because GFR varies with weight and height, it is evident that GFR comparisons must include some adjustment for body size. The traditional adjustment method has been to divide GFR by body-surface area (BSA) and to standardize it to 1.73 m^{2}. This was first proposed in a study of urea clearance by McIntosh in 1928.^{1}

The conventional method has been repeatedly criticized, and it has been suggested that other physiologic variables may be more appropriate for adjusting GFR than BSA. Peters *et al.*^{2} showed that normalizing the GFR to the extracellular fluid volume (ECV) was more appropriate for children. In adults, some studies have concluded that ECV should replace BSA,^{2,3} and others have found BSA superior or similar to other parameters.^{4,5} A comparison among mammals of different sizes has supported the hypothesis that metabolic rate sets the level of GFR; thus, some researchers have proposed that metabolic rate should be used for normalization.^{6} Total body water (TBW), height, liver volume, and lean body mass have also been suggested as candidates for a normalizing factor.^{4,7} In practice, fluid volumes and metabolic rate are cumbersome to measure directly and would have to be estimated with equations based on anthropometric measures.

In normalizing GFR to body size, at least two issues must be considered. First, the adjustment must facilitate GFR comparisons among individuals by reducing differences that arise from differences in body size as much as possible. The physiologic variables that have been suggested as a basis for adjustment may differ in their abilities to explain interindividual variations in GFR. Second, statistically, there are theoretical problems associated with adjustments that simply divide GFR by a physiologic variable, *e.g.* the current practice of dividing GFR by BSA (the ratio method). Specific conditions must be met to avoid spurious correlations between such ratio variables and other independent variables.^{8} This problem was previously pointed out by Tanner in 1949^{9} and illustrated in a simulation study by Lowrie in 1999.^{10} An alternative method based on regression analysis has been proposed by Turner and Reilly,^{11} but to date this has received very little attention in the nephrological community.

The normalization of GFR has been studied only in small studies of selected subjects or in populations of potential kidney donors. Those results may not be valid for the general population. The purpose of this study was to explore the normalization issue in a representative sample of the general population drawn from the sixth population-based prospective survey conducted in Tromsø, Norway (Tromsø 6). In the Renal Iohexol Clearance Survey in Tromsø 6 (RENIS-T6), GFR was measured with a precise method in persons between 50 and 62 years without known diabetes, cardiovascular, or renal disease. Our first aim was to investigate the ability of different physiologic variables to explain variations in GFR. Our second aim was to compare the conventional ratio method and the Turner and Reilly regression method for adjusting GFR by the physiologic variables that we estimated with functions based on height and weight.

## RESULTS

The RENIS-T6 cohort consisted of a representative sample of 1627 subjects aged 50 to 62 years without diabetes, cardiovascular disease, or kidney disease from the general population. Table 1 shows the baseline measurements made in the main part of the population survey, Tromsø 6, and compares the included subjects to all eligible subjects. The statistically significant differences between groups were very small.

To find the best predictor of GFR from gender, age, weight, and height, multiple linear regression analyses were performed with unadjusted GFR (uGFR) in ml/min as the dependent variable (Table 2). Age, gender, height, and weight were independently associated with uGFR (*P* < 0.0001). Because of colinearity, weight and height were not included in the same model. The model that incorporated weight (Model 2) had a higher coefficient of determination (R^{2}) than the model that incorporated height (Model 3) (0.437 *versus* 0.356). All of the possible interactions between the independent variables were tested. Only the interaction between gender and weight was significant (*P* = 0.004), but its partial R^{2} was only 0.004. No nonlinear effects were found when the same variables were explored in generalized additive models. When the continuous variables in Model 2 were log-transformed, all of the independent variables remained statistically significant, and R^{2} was 0.404.

Physiologic variables were estimated with published equations (Table 3). To explore their ability to explain variation in uGFR, the fit of separate linear regression analyses with uGFR as the dependent variable and each of the physiologic variables and age as the independent variables were analyzed (Table 4). The analyses were performed both with and without log-transformed variables. For the untransformed variables, all of the intercepts were different form zero (*P* < 0.05), which means that uGFR was not strictly proportional to any of the physiologic variables. For both untransformed and log-transformed variables, TBW had the highest R^{2}. Although the 95% confidence intervals overlapped, these differences in R^{2} between TBW and each of the other physiologic variables were statistically different with the bootstrap method (*P* < 0.05). Lean body mass and metabolic rate had R^{2} values similar to that of TBW. The differences in root-mean-square error exhibited the same pattern as R^{2}.

The models with log-transformed variables in Table 4 were used to create adjusted GFRs according to the regression method of Turner and Reilly.^{11} Another set of adjusted GFRs was created by simply dividing the uGFR by each of the physiologic variables (the ratio method). We then determined the effects of gender and either height or weight on each adjusted GFR variable (Table 5). The adjusted GFR variables were regressed on gender and on height or weight in age-adjusted models. For the ratio method, all of the adjusted GFR variables were associated with both gender and either weight or height (*P* < 0.05), except metabolic rate, which was not associated with gender (Model 2). For the Turner and Reilly regression method, all of the adjusted GFR variables were associated with both gender and height or weight (*P* < 0.05), except TBW and lean body mass. Neither TBW nor lean body mass adjustments depended on gender or weight (Model 3). For TBW, the regression coefficients for gender and height in Model 4 were smaller than the corresponding coefficients for the other physiologic variables. The regression coefficients in Table 5 were standardized estimates to facilitate comparison across physiologic variables.

GFRs normalized to either BSA or TBW by the two methods were compared according to body-mass index (BMI) for different genders (Table 6). In this table, GFR was normalized to the population means of BSA (1.9 m^{2}) and TBW (39.2 L) to facilitate comparisons, rather than to a BSA of 1.73 m^{2} and a TBW of 40 L. GFR adjusted for TBW by the Turner and Reilly regression method did not differ across the BMI categories for either of the genders. The other adjusted variables varied across BMI categories for one or both genders (*P* < 0.05).

## DISCUSSION

When assessing GFR, we want to be able to decide whether a person has a normal GFR, and if not, to measure the deviation from normal. However, the concept of “normality” in physiology is no less problematic than in other areas of medicine. Conceivably, more detailed knowledge of renal physiology and homeostatic mechanisms would reveal constant relationships between GFR and other physiologic parameters, which would help settle the issue; however, we are far from attaining that knowledge. Currently, our best option is to use statistical methods to adjust GFR for factors that clearly affect variation.

The physiologic variables investigated in this study were only able to explain 30 to 45% of the variation in uGFR (Table 4). Some of the residual variation was caused by day-to-day, within-person variability of iohexol-clearance measurements; this measurement has been found to have a coefficient of variation of about 5.5% in other studies,.^{12,13} In this study, we found that TBW was superior to BSA and the other physiologic variables in explaining the variation in uGFR, as expressed by R^{2} (*P* < 0.05) (Table 4). In addition to the ECV equation developed by Silva *et al.*,^{14} we tested an alternative equation developed by Bird *et al.*^{15} that resulted in an even lower R^{2} (not shown).

The traditional and almost universally used method for adjusting GFR has been to scale uGFR by simply dividing by a variable, *e.g.* uGFR/BSA or uGFR/TBW. The problem with this method is that it assumes strict proportionality between GFR and the physiologic variable, *i.e.* it assumes an intercept of zero in a regression of uGFR on the physiologic variable. We found that the intercepts were statistically different from zero for all of the investigated physiologic variables (upper part of Table 4). As a consequence, the ratio method assigned inappropriately-high adjusted GFR values in subjects with, for example, low TBW and inappropriately-low adjusted GFR values in subjects with high TBW, even when their uGFRs could be considered normal, relative to their TBWs (Figure 1). The example in Figure 1 was calculated for the mean age in the RENIS-T6 cohort. Because age was an independent predictor of uGFR in the untransformed analyses, the intercept in Figure 1 varied with age, which made the ratio method even more problematic.

It has been argued that the error associated with the BSA ratio method is too small to justify changing the method.^{16} However, the error may be larger for individuals with atypical body sizes.^{17} The alternative method proposed by Turner and Reilly on the basis of regression analysis overcomes some of the problems associated with the ratio method, because it completely removes variation associated with the variable used to adjust the GFR. The TBW-regression adjustment of GFR was less dependent on gender, height, and weight than the other physiologic variables (Table 5). Moreover, the BSA adjustment depended on one or more of gender, height, and weight in both the ratio and the regression methods.

We modified Turner and Reilly's method by using the log-transformed linear regression analyses as the starting point (lower part of Table 4).^{11} We implemented this transformation because the untransformed variables can give negative values for the adjusted variable when uGFR is very low. Log-transformed variables avoid this problem because the subtraction of a negative residual is equivalent to division when the antilogarithm is performed. The fits of the untransformed and transformed models for TBW were not significantly different, as estimated by R^{2} (Table 4). An additional justification for using log transformation was the recognition of the general assumption that the error in GFR measurement depends on the magnitude of GFR. We also modified the Turner and Reilly method by including an adjustment for log(age) in the regression. However, the final, simplified equation for the TBW adjustment was independent of age, because the age terms canceled out.

Our findings indicated that using TBW to adjust the uGFR with the regression method of Turner and Reilly had clear advantages over other methods. Daugirdas *et al.*^{4} reached a different conclusion in their study of 1551 potential kidney donors. BSA and TBW were not analyzed in the regression method of Turner and Reilly, but after adjusting for age and race, they found that GFR/BSA did not depend on gender, but GFR/TBW was markedly higher in women than men. However, the investigated donor population may not have been representative of the general population, because the GFR of the included women was similar to that of the men (106 *versus* 104 ml/min per 1.73 m^{2}). In contrast, there was a clear gender difference in BSA-adjusted GFR in this study (Table 1).

In 1952, McCance and Widdowson^{18} suggested that TBW was the correct variable for adjusting GFR; however, there is a lack of studies on the relationship between GFR and TBW in the literature. Some authors compared BSA and ECV for adjusting the GFR. In fact, the uGFR/ECV is a particularly attractive adjustment, because the uGFR/ECV is approximately identical to the slope of the terminal exponential of the plasma clearance curve after a bolus injection of a filtration marker.^{19} In contrast to the single-sample method used in this study, uGFR and ECV can be measured in the same procedure, when GFR is measured by a single-injection, multi-sample method. Visser *et al.*^{3} found that GFR/ECV did not depend on gender, BSA, or height in regression analyses but that GFR/BSA depended on gender. That study was performed in healthy volunteers and potential kidney donors. In contrast, White and Strydom^{5} found that uGFR/BSA and uGFR/ECV produced essentially the same result in 110 patients with uGFRs between 10 and 160 ml/min. Peters *et al.*^{2} argued that normalization to ECV was more appropriate for children than for adults, but they included patients with reduced GFR. None of those studies considered the regression method of Turner and Reilly as an alternative to using the ratio method. The diverging results may have been caused by differences between the investigated populations. To our knowledge, this study is the first to examine this issue in a representative sample from the general population.

An important limitation of this study was that it relied on estimates, instead of direct measurements, of the physiologic variables. The estimates were all on the basis of age, gender, weight, and/or height, and whereas the BSA equation used only weight and height, the TBW equation included gender and age as well. Direct measurement of the physiologic variables, with the possible exception of ECV, is so complicated and costly that estimation from anthropometric measures is currently the only feasible method in clinical practice and epidemiologic research. Watson's equation for TBW has been validated.^{20,21} When we repeated the analyses with Chumlea's equation for estimating TBW, the results were very similar to those obtained with Watson's equation (not shown). Nevertheless, some caution should be observed in the conclusion that TBW was the best variable for the adjustment of GFR. The fits of the models for TBW, metabolic rate, and lean body mass showed only small differences, and physiologically, there is a high correlation between these variables and ECV. However, TBW, metabolic rate, and lean body mass were clearly different compared with BSA for adjusting GFR; this supports the recommendations that adjustment by BSA should be abandoned.

Another limitation was that this study only included middle-aged Caucasians. However, age did not influence the effects of gender, height, and weight on uGFR within the studied age interval because the interactions of these variables with age were not statistically significant. But although basal physiologic relationships can be expected to be invariant across age and ethnicity, our study should be replicated in general populations with other characteristics. Also, our analyses were on the basis of the assumption that variation in GFR caused by gender, height, and body weight in healthy persons in a representative sample of the general population is without biologic significance. Whereas this assumption is usually made about GFR, it is difficult to prove. When investigating effects of variation in GFR, the possibility that the relationship between GFR and body fluid volumes may be different in patient populations, for example as in obese patients, should be kept open. The best approach in such cases may be to use absolute GFR in ml/min as an explanatory variable and to adjust for both TBW and ECV.

The results of our study supported the recommendation that the practice of using GFR/BSA scaled to 1.73 m^{2} should be abandoned and should be replaced with a TBW adjustment of uGFR by the regression method of Turner and Reilly. The regression method is somewhat more complicated than the ratio method, but uGFR currently requires a computer calculation; thus, the calculations could be automated. In practice, we suggest that the measured, unadjusted GFR should be adjusted to the corresponding GFR in a person with 40 L of TBW (Table 7). This standard individual was chosen because the mean TBW of men and women is approximately 40 L.^{21} The algorithm for calculating the adjusted variable with this method is given in Table 7. One of the advantages of this method is that when TBW was used to adjust GFR with the regression method, we observed almost identical values across gender and BMI categories (Table 6). One of the problems with GFR/BSA has been that it assigned inappropriately low values to individuals with high BMI, which resulted in potential confounding by BMI in studies of GFR and cardiovascular disease.^{22}

We conclude that using BSA to adjust uGFR, either by the ratio method or by the regression method of Turner and Reilly, did not remove dependencies on gender, weight, or height. We found that more of the variation in uGFR could be explained by TBW than by BSA. Furthermore, when TBW estimated from gender, age, height, and weight was used to adjust GFR by the regression method, the dependencies on gender, weight, and height were removed. Therefore, we propose a new calculation that adjusts the uGFR to a standardized TBW of 40 L (GFR40) instead of the current practice of using uGFR/BSA standardized to a BSA of 1.73 m^{2}.

## CONCISE METHODS

### Subjects

The Tromsø Study is a series of population-based prospective surveys in the municipality of Tromsø, North Norway (current population, 65,000). Our RENIS-T6 cohort was an ancillary part of the sixth Tromsø study. In the main part of the Tromsø 6 study, a representative sample of 12,984 adults from the general population participated between October 2007 and December 2008. The invited population included a 40% random sample of individuals aged 50 to 59 years and all individuals aged 60 to 62 years (5464 total subjects in all). A total of 3564 individuals between 50 and 62 years of age completed the main part of Tromsø 6 (65%). Of these, 739 reported a previous history of myocardial infarction, angina pectoris, stroke, diabetes mellitus, or renal disease. The remaining 2825 eligible subjects were invited to participate in RENIS-T6. Of the 2107 individuals that responded positively, 12 were excluded because of an allergy to contrast media, iodine, or latex; 65 were excluded for other reasons; and 48 did not appear for their appointments. A total of 1982 subjects remained for potential inclusion, but only 1632 were investigated, according to a predefined target. Later, five participants were excluded because the iohexol-clearance measurements were technical failures. Accordingly, a total of 1627 participants were included in the RENIS-T6 cohort for this study.

This study was approved by the Norwegian Data Inspectorate and the Regional Ethics Committee of North Norway. All of the subjects provided written consent.

### Measurements

uGFR was measured as single-sample plasma clearance of iohexol at the Clinical Research Unit at the University Hospital of North Norway. This method has been validated against gold standard methods for measuring GFR.^{23–29} The subjects were instructed to avoid large meals with meat and nonsteroid anti-inflammatory drugs for 2 days before the investigation. The measurements were performed after fasting and abstinence from nicotine. The subjects were reminded to avoid restricting water intake. A Teflon catheter was placed in an antecubital vein, and blood was drawn for a null sample and for creatinine measurements. Five milliliters of iohexol (Omnipaque, 300 mg I/ml; Amersham Health, London, UK) was injected, and the syringe was weighed before and after the injection. The catheter was flushed with 30 ml of isotonic saline and used for iohexol analysis samples.^{27} The optimal time for measuring iohexol concentration after injection was calculated by Jacobsson's method on the basis of the GFR estimated from creatinine.^{30} To ensure complete distribution of iohexol in the extracellular fluid volume, the shortest sampling time was set at 180 minutes. The exact time from injection to sampling was measured in minutes with a different stop watch for each subject.

The serum iohexol concentration was measured by HPLC, as described previously by Nilsson-Ehle.^{31} The coefficient of variation was 3.0% for the analysis during the study period. The external quality control was provided by Equalis (Equalis AB, Uppsala, Sweden).

The GFR was calculated with the formulas described by Jacobsson.^{30} Extrarenal iohexol clearance was ignored, in accordance with the practice of other authors. Further details about the iohexol analysis and the method for calculating GFR have been described previously.^{32}

Plasma-creatinine analyses were performed on the Hitachi modular model with an enzymatic method that has been standardized against isotope dilution mass spectroscopy (CREA Plus; Roche Diagnostics, GmbH, Mannheim, Germany). Estimated GFR was calculated as ml/min per 1.73 m^{2} with the recalibrated four-variable Modification of Diet in Renal Disease equation,^{33} as follows: 175 × (creatinine/88.4)^{−1.154} × age^{−0.203} × 1.212 (if African American) × 0.742 (if female). Creatinine was expressed in μmol/L.

### Statistical Methods

The comparison of differences between included and eligible persons in Table 1 was performed with quantile regression adjusted for age. The medians and interquartile ranges of characteristics of all eligible persons were weighted according to the age and gender stratifications of RENIS-T6. The baseline measurements from the main part of Tromsø 6 were used for these comparisons.

A multiple linear regression analysis was performed with uGFR as the dependent variable and age, gender, weight, and height as the independent variables. All of the possible interactions between the independent variables were tested. Nonlinear effects of the same variables were explored in generalized additive models.

Physiologic variables were estimated on the basis of equations from the literature (Table 3).^{7,14,20,34–36} uGFR was regressed on each variable in separate linear regression analyses. Regressions on height and body weight were included for comparison. All of the analyses were adjusted for age. The analyses were performed both with and without log transformation (natural logarithms) of the dependent and independent variables. The fit of each model was judged by root-mean-square error and R^{2}. The bootstrap method was used to estimate 95% confidence intervals of these statistics and the differences between fits from 2000 resamples of the original observations.^{37}

For each physiologic variable, adjusted GFRs were created by two methods. In the ratio method, uGFRs were adjusted by dividing by the physiologic variable, *e.g.* uGFR/metabolic rate. In the Turner and Reilly regression method, uGFR was regressed on age and each physiologic variable, with log transformation of the variables.^{11} For each subject, the residual from this regression (Figure 2) was added to the expected log(uGFR) for a person of the same age, with the logarithm of the physiologic variable set at the population mean. Then the adjusted GFR was the antilogarithm, according to the equation: adjusted GFR = exp[log(uGFR) − (*a* + *b* × log(*P*) + *c* × log(age)) + (*a* + *b* × log(mean *P*) + *c* × log(age))], where *P* is the physiologic variable, *a* is the intercept, and *b* and *c* are the regression coefficients in the regression of log(uGFR) on log(P) and log(age). The mean *P* is the arithmetic mean of *P* in the RENIS-T6 cohort. This equation simplifies to: adjusted GFR = exp[log(uGFR) − *b* × (log(*P*) − log(mean *P*))]; this equation does not depend on age.

Finally, multiple linear regression models were performed to study how the adjusted GFR created from each physiologic variable by the ratio method and by Turner and Reilly's regression method depended on gender, weight, and height. These analyses were adjusted for age. All of the analyses were performed with SAS, version 9.2 (SAS Institute, Cary, NC). Statistical significance was set at *P* < 0.05.

## DISCLOSURES

None.

## Acknowledgments

We thank Britt-Ann Winther Eilertsen, Bjørg Skog Høgset, Saskia van Heusden, and the rest of the staff at the Clinical Research Unit (University Hospital of North Norway) for performing the study; Harald Strand and the staff at the Department of Medical Biochemistry (University Hospital of North Norway) for HPLC analyses of iohexol; Inger Sperstad and Ingrid Dorthea Sandstad (Clinical Research Centre, University Hospital of North Norway) for database support; and Tom Wilsgaard, Sriharan Sivasingarajah, and Kurt Jøran Nyland (Department of Community Medicine, University of Tromsø) for identifying eligible subjects from the Tromsø 6 cohort.

## Footnotes

Published online ahead of print. Publication date available at www.jasn.org.

- Copyright © 2011 by the American Society of Nephrology