Current guidelines provide separate equations to calculate
for adults and children, but the present analysis shows that a universal equation is applicable indiverse populations. The literature often cautions that equations to calculate
are appropriate only in populations similar to those in which they were developed. In the present study, two large studies of different populations, demographically diverse and with a broad range of renal function, underwent essentially the same iohexol GFR2,2
measurement protocols; this allowed us to develop an equation suitable for both populations. Crucial findings for the proposed universal equation were that the fast area was inversely proportional to BSA and that the BSA-adjusted fast area was independent of the slow area. Thus, BSA was a key consideration when evaluating the common dynamic between these two populations, and must routinely be accounted for when measuring GFR.
The simple relationship between the fast area and BSA allowed the derivation of a simple equation to calculate
, as measured by an iohexol-based GFR protocol. To confirm this derivation, a direct regression analysis was performed on the data in . Indeed, the slope (= 1.025) was not significantly different from 1 (95%CI: 0.987, 1.063), and the intercept (i.e., at GFR0,2
= 100 ml/min|1.73m2
) was equal to 0.117. Our proposed equation provides an accurate and reliable GFR measurement from as few as two blood samples collected between 120 minutes and 300 minutes after injection of iohexol. This modification of the iohexol-based protocol represents an important reduction in study burden for subjects and personnel, and should facilitate GFR measurements in large-scale clinical and epidemiological studies.
Our analysis assessed the agreement between GFR2,2
of our proposed equation as well as of previously published equations [4
]. While the previously published equations showed good agreement, our proposed equation was even better: RMSEswere4.59 and 1.46 ml/min|1.73m2
for the MACS and CKiD validation datasets, respectively. Furthermore, our proposed equation had the highest proportion of
within 5% of the GFR2,2
(79% for MACS and 96% of CKiD).
Importantly, the equation
is consistent in form with the equations proposed by Brochner-Mortensen & Jodal [8
] and Fleming [7
] and coheres with the theoretical principles discussed by these authors. Specifically, using the general expression:
the Brochner-Mortensen & Jodal [8
]equation corresponds to B0
= 0.185, B1
= 1 and B2
= −0.3; the Fleming [7
] equation corresponds to B0
= 0.17, B1
= 1 and B2
= 0; and our proposed equation corresponds to B0
= 0.12, B1
= 1 and B2
Another feature of our proposed equation is that it is invariant with respect to the injected amount of iohexol. Indeed, the relationship describing GFR0,2 and the ratio of GFR0,2 to GFR2,2 in is not dependent on the dose of iohexol and the equation with0.12 provided an excellent fit to the data. In contrast, the constant of 6.4 relating fast area to BSA is directly proportional to the dose of iohexol and in general, if fast area = c / BSA, c will be equal to 0.00116 × 1.73 × I, where c= 6.4 for I= 3200. Thus, our proposed equation may be applicable to other iohexol protocols (with variations in amounts of iohexol injection), while the estimation of fast area by 6.4/BSA is specific to this protocol (i.e., when I=3200 mg).
The difference between the Fleming equation and our equation was meaningful: the Fleming equation had relatively high RMSE in our study populations and it systematically underestimated GFR2,2
, although this underestimation was modest (about 2% in the CKiD and 5% in the MACS). This slight discrepancy may be due to differences in the exogenous clearance markers used (i.e., iohexol versus 51
Cr-EDTA); however, previous studies have shown comparable GFR measurement performance with either marker [10
]. It is also possible that this discrepancy may be due to other factors altogether (i.e., study design or model development).
The relationship between fast area and BSA determined in and depicted in (R2
= 56%) may be re-expressed to form the basis of our proposed equation whose fit to the data is depicted in (R2
= 75%). Given that the fast area depends solely on BSA, we compared our proposed equation with the agreement in an equation that directly imputes the fast area as inversely proportional to BSA:
This equation yielded RMSEs of 5.81 and 1.48 ml/min|1.73m2
in the MACS and CKiD, respectively; which, for the MACS, was 27% higher than the RMSE of 4.59 of our proposed equation (
as a function of GFR0,2
). Since the main assumption from the analysis is that the fast area depends only on BSA, the proposed equation does not take into account the between-subject variability in the fast area among those with the same BSA. Despite this limitation, the assumption works well because the fast area does not contribute much to the overall GFR2,2
As a secondary analysis, we also investigated how a previously published Brochner-Mortensen-like equation that was developed exclusively in the CKiD population [2
] performed when applied separately to the validation datasets in the two studies. In the CKiD validation dataset, there was no significant bias or difference in dispersion, and a very high correlation (r= 0.998, 95%CI: 0.995, 0.997) between
. This was expected since the equation was derived in the same clinical population. However, when the equation was applied to the MACS validation dataset, the measures of agreement were much poorer: there was significant underestimation (bias= −2.6%, p< 0.01), shrinking of dispersion (ratio of SDs= 0.932, p< 0.01) and lower correlation (r= 0.978, 95%CI: 0.971, 0.984) than had been observed in the CKiD validation dataset. This finding highlights a limitation of developing an equation within a specific population and then applying it to a different one. As such, a limitation of our study is the lack of adult female subjects studied, with whose data we could have assessed the validity of the proposed equation. Nevertheless, ours is the only study that has developed an accurate iohexol
equation using two disparate, large-scale cohorts (total n= 1347) that underwent essentially identical GFR protocols.
Although the fast area can be estimated from the body surface area, it should be noted that the intercept and slope of the fast curve cannot be determined with our method. Determination of these parameters (needed for measures like the extracellular volume [13
]) would require collecting samples within 60 minutes of iohexol injection. Another limitation to our method is that our data did not take into account obese or edematous subjects, populations for which it is unclear whether our approach will work. However, in spite of the substantial differences in weight and BMI between the two study populations (i.e., MACS men with a median BMI of 26 kg/m2
versus CKiD children being overweight relative to their height), the analysis showed excellent agreement in each population.
In conclusion, due to the fast area being dependent on BSA but not on the slow area, determination of GFR using only the slow component showed a remarkable consistency between the MACS and CKiD populations. A simple equation was derived from a training dataset that included both cohorts and showed excellent agreement when applied to validation sets from both studies. Using this validated equation, GFR can be accurately measured across populations with diverse demographics and renal function using only the slow iohexol plasma disappearance curve with as few as two time points.