Universal GFR determination based on two time points during plasma iohexol disappearance
2011; Elsevier BV; Volume: 80; Issue: 4 Linguagem: Inglês
10.1038/ki.2011.155
ISSN1523-1755
AutoresDerek K. Ng, George J. Schwartz, Lisa P. Jacobson, Frank J. Palella, Joseph B. Margolick, Bradley A. Warady, Susan L. Furth, Álvaro Muñoz,
Tópico(s)Hemodynamic Monitoring and Therapy
ResumoAn optimal measurement of glomerular filtration rate (GFR) should minimize the number of blood draws, and reduce procedural invasiveness and the burden to study personnel and cost, without sacrificing accuracy. Equations have been proposed to calculate GFR from the slow compartment separately for adults and children. To develop a universal equation, we used 1347 GFR measurements from two diverse groups consisting of 527 men in the Multicenter AIDS Cohort Study and 514 children in the Chronic Kidney Disease in Children cohort. Both studies used nearly identical two-compartment (fast and slow) protocols to measure GFR. To estimate the fast component from markers of body size and of the slow component, we used standard linear regression methods with the log-transformed fast area as the dependent variable. The fast area could be accurately estimated from body surface area by a simple parameter (6.4/body surface area) with no residual dependence on the slow area or other markers of body size. Our equation measures only the slow iohexol plasma disappearance curve with as few as two time points and was normalized to 1.73 m2 body surface area. It is of the form: GFR=slowGFR/[1+0.12(slowGFR/100)]. In a random sample utilizing a third of the patients for validation, there was excellent agreement between the calculated and measured GFR with low root mean square errors being 4.6 and 1.5 ml/min per 1.73 m2 for adults and children, respectively. Thus, our proposed simple equation, developed in a combined patient group with a broad range of GFRs, may be applied universally and is independent of the injected amount of iohexol. An optimal measurement of glomerular filtration rate (GFR) should minimize the number of blood draws, and reduce procedural invasiveness and the burden to study personnel and cost, without sacrificing accuracy. Equations have been proposed to calculate GFR from the slow compartment separately for adults and children. To develop a universal equation, we used 1347 GFR measurements from two diverse groups consisting of 527 men in the Multicenter AIDS Cohort Study and 514 children in the Chronic Kidney Disease in Children cohort. Both studies used nearly identical two-compartment (fast and slow) protocols to measure GFR. To estimate the fast component from markers of body size and of the slow component, we used standard linear regression methods with the log-transformed fast area as the dependent variable. The fast area could be accurately estimated from body surface area by a simple parameter (6.4/body surface area) with no residual dependence on the slow area or other markers of body size. Our equation measures only the slow iohexol plasma disappearance curve with as few as two time points and was normalized to 1.73 m2 body surface area. It is of the form: GFR=slowGFR/[1+0.12(slowGFR/100)]. In a random sample utilizing a third of the patients for validation, there was excellent agreement between the calculated and measured GFR with low root mean square errors being 4.6 and 1.5 ml/min per 1.73 m2 for adults and children, respectively. Thus, our proposed simple equation, developed in a combined patient group with a broad range of GFRs, may be applied universally and is independent of the injected amount of iohexol. Glomerular filtration rate (GFR) can be determined accurately by measuring the plasma clearance of a single intravenous injection of a contrast medium such as iohexol, calculated from plasma sampling at multiple time points over several hours1.Schwartz G.J. Furth S.L. Cole S.R. et al.Glomerular filtration rate via plasma iohexol disappearance: pilot study for chronic kidney disease in children.Kidney Int. 2006; 69: 2070-2077Abstract Full Text Full Text PDF PubMed Scopus (178) Google Scholar,2.Schwartz G.J. Abraham A.G. Furth S.L. et al.Optimizing iohexol plasma disappearance curves to measure the glomerular filtration rate in children with chronic kidney disease.Kidney Int. 2010; 77: 65-71Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar using an open two-compartment (slope–intercept) mathematical model for the plasma disappearance curve. The protocols to measure GFR in the Multicenter AIDS Cohort Study (MACS) and Chronic Kidney Disease in Children (CKiD) study involved four venous blood samples after a single bolus injection of iohexol. To properly estimate the two compartments, referred to hereafter as 'fast' for the first compartment, and 'slow' for the second compartment, two of the four blood samples were collected within ∼30 min of the injection (for the fast compartment) and the other two were obtained ≥2 h after the injection (for the slow compartment). The ratio of the injected amount of iohexol to the area under the disappearance curve is a direct measure of GFR. This 'gold-standard' protocol is time intensive and requires multiple blood draws, thereby increasing complexity of large epidemiologic studies.2.Schwartz G.J. Abraham A.G. Furth S.L. et al.Optimizing iohexol plasma disappearance curves to measure the glomerular filtration rate in children with chronic kidney disease.Kidney Int. 2010; 77: 65-71Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar,3.Work D.F. Schwartz G.J. Estimating and measuring glomerular filtration rate in children.Curr Opin Nephrol Hypertens. 2008; 17: 320-325Crossref PubMed Scopus (30) Google Scholar An optimal GFR measurement should minimize the number of blood draws, procedural invasiveness, burden to study personnel, and cost. Restricting sampling to only the slow compartment of the model has been proposed in adults4.Brochner-Mortensen J.A. A simple method for the determination of glomerular filtration rate.Scand J Clin Lab Invest. 1972; 30: 271-274Crossref PubMed Scopus (774) Google Scholar,5.Fleming J.S. Zivanovic M.A. Blake G.M. et al.Guidelines for the measurement of glomerular filtration rate using plasma sampling.Nucl Med Commun. 2004; 25: 759-769Crossref PubMed Scopus (225) Google Scholar and children.2.Schwartz G.J. Abraham A.G. Furth S.L. et al.Optimizing iohexol plasma disappearance curves to measure the glomerular filtration rate in children with chronic kidney disease.Kidney Int. 2010; 77: 65-71Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar,6.Brochner-Mortensen J.A. Haahr J. Christoffersen J. A simple method for accurate assessment of the glomerular filtration rate in children.Scand J Clin Lab Invest. 1974; 33: 139-143Crossref Google Scholar GFR equations to quantify a universal relationship between the one-compartment (slow) and the two-compartment (slow + fast) plasma disappearance models have been published, based on diverse, but small, study samples (combining adults and children) representing different clinical populations (that is, varying levels of renal function).7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar, 8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar, 9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar Thus, the purpose of the current study was to develop a formula to determine the two-compartment GFR for studies where samples in the fast compartment are not collected. To accomplish this, we used iohexol-based studies that measured both the slow disappearance curve and the fast disappearance curve in two large-scale, clinically disparate populations. Our analysis includes large populations with a broad range of GFRs and thus should provide a strong basis for a universally applicable equation. The protocol for measuring GFR in the MACS and CKiD study used a two-compartment, four blood sample model of plasma iohexol disappearance to calculate GFR (see Materials and Methods). Two GFR values were calculated: one GFR based on the slow compartment only (GFR0,2) and the other GFR based on both the fast and slow compartments (GFR2,2; see Variables subsection). As there is a close relationship between GFR0,2 and GFR2,2, two approaches have been proposed to estimate GFR2,2 from GFR0,2; this estimate is denoted hereafter as GFR^2,2 . These approaches are: (1) the classical Brochner-Mortensen equation4.Brochner-Mortensen J.A. A simple method for the determination of glomerular filtration rate.Scand J Clin Lab Invest. 1972; 30: 271-274Crossref PubMed Scopus (774) Google Scholar that has been used typically in clinical guidelines5.Fleming J.S. Zivanovic M.A. Blake G.M. et al.Guidelines for the measurement of glomerular filtration rate using plasma sampling.Nucl Med Commun. 2004; 25: 759-769Crossref PubMed Scopus (225) Google Scholar and epidemiological research;2.Schwartz G.J. Abraham A.G. Furth S.L. et al.Optimizing iohexol plasma disappearance curves to measure the glomerular filtration rate in children with chronic kidney disease.Kidney Int. 2010; 77: 65-71Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar and (2) a new equation based on theoretical underpinnings by Fleming7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar and Brochner-Mortensen and Jodal.8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar,9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar In this study, we aimed to develop a formula to estimate the fast component in GFR2,2 not measured in GFR0,2 (that is, missing fast area). Once such a formula was developed, we derived the corresponding formula to determine GFR2,2 based on GFR0,2, and we position our proposed equation in the context of the recently improved principles.7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar, 8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar, 9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar The MACS and CKiD studies provided an excellent opportunity to develop a universal equation because the GFR-measuring protocols were nearly identical (except for the time of the last blood sample: 240 min in the MACS and 300 min in CKiD) and included the same central biochemistry laboratory (principal investigator GJS, University of Rochester Medical Center, Rochester, NY) and the same data coordinating center (co-principal investigators AM and LPJ, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD), although the two populations studied were extremely different. Agreement between GFR^2,2 and GFR2,2 within each study population, therefore, would assess the appropriateness of a truly universal equation. Such a robust equation would highlight any common dynamics between these two disparate groups and permit future iohexol GFR studies in any population to accurately determine GFR using only two plasma samples. Table 1 presents descriptive statistics of the 527 adult men from the MACS and the 514 children from the CKiD cohort who were studied. In the CKiD data set, 63% of subjects underwent one GFR2,2 study, 36% had two studies, and 1% had three studies (with repeated studies at ∼1-year intervals), yielding a total of 820 GFR2,2 studies. The two cohorts differed substantially in most characteristics shown in Table 1. The MACS subjects were adult men with a median age of 51 years, and the CKiD subjects were children (62% male) with a median age of 11 years. Human immunodeficiency virus (HIV) infection was an exclusion criterion for CKiD, but 70% of the MACS subjects were HIV infected. In CKiD, a cohort of children with chronic kidney disease, 21% had glomerular kidney disease.Table 1Descriptive statistics (percent or median (interquartile range)) of clinical and demographic characteristics of the MACS and CKiD populations at baselineCharacteristicMACS (n=527)CKiD (n=514)Age (years)50.9 (46.0, 57.1)11.1 (7.7, 14.7)Male100%62%Race White57%66% Black35%23% Other8%12%Height (m)1.76 (1.71, 1.80)1.40 (1.20, 1.58)Weight (kg)80.7 (72.6, 90.4)36.3 (23.7, 54.8)BMI (kg/m2)26.2 (23.9, 28.8)18.3 (16.2, 22.0)BSA (m2)2.00 (1.87, 2.14)1.19 (0.89, 1.57)HIV infected70%0%Serum creatinine (mg/dl)0.92 (0.79, 1.08)1.30 (1.00, 1.80)GFR2,2 (ml/min per 1.73 m2)109.2 (94.9, 125.2)44.0 (32.8, 56.0)Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; HIV, human immunodeficiency virus; MACS, Multicenter AIDS Cohort Study. Open table in a new tab Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; HIV, human immunodeficiency virus; MACS, Multicenter AIDS Cohort Study. Table 2 presents the plasma disappearance parameters by study cohort and by training data set (for model development using a 2/3 random sample) and validation data set (for evaluation of agreement between observed and estimated GFR using the remaining 1/3 random sample). All parameters were significantly different between the cohorts except for the injected iohexol, which was ∼3200 mg by the common protocol. As expected, randomization yielded similar parameters for the training and validation data sets for each cohort. For CKiD, these parameters indicated renal insufficiency. In contrast, most of the MACS had normal renal function: 81% of these subjects had a GFR2,2 ≥90 ml/min per 1.73 m2.Table 2Median (interquartile range) of plasma disappearance parameters of iohexol studies for the training and validation data sets from the MACS and CKiD populationsTraining data set (2/3 random sample)Validation data set (1/3 random sample)MACS (n=350)CKiD (n=546)P-valueaWilcoxon rank-sum test comparing MACS and CKiD in training data set; bold indicates statistically significant (P<0.05).MACS (n=177)CKiD (n=274)Iohexol injection (mg)3180 (3151, 3243)3190 (3156, 3223)0.4263185 (3127, 3223)3192 (3160, 3228)Fast areabBased on plasma samples at 10 and 30min after iohexol injection. (mg min/ml)3.2 (2.6, 3.9)5.7 (4.0, 8.1)<0.0013.4 (2.8, 4.1)5.3 (3.7, 8.2)Slow areacBased on plasma samples at 120 and 240min for MACS and 120 and 300min for CKiD after iohexol injection. (mg min/ml)21.9 (18.6, 25.5)107.6 (73.9, 156.2)<0.00121.3 (18.7, 25.0)97.5 (63.8, 142.8)GFR0,2d(Iohexol injection/slow area) × (1.73/BSA). (ml/min per 1.73 m2)125.3 (105.5, 149.0)45.3 (33.4, 59.2)<0.001128.3 (110.0, 150.1)47.7 (36.2, 63.6)GFR2,2e(Iohexol injection/total area) × (1.73/BSA). (ml/min per 1.73 m2)108.6 (93.8, 126.2)42.9 (32.0, 54.8)<0.001112.1 (96.3, 124.9)45.4 (34.6, 58.6)Abbreviations: CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter Aids Cohort Study.a Wilcoxon rank-sum test comparing MACS and CKiD in training data set; bold indicates statistically significant (P<0.05).b Based on plasma samples at 10 and 30 min after iohexol injection.c Based on plasma samples at 120 and 240 min for MACS and 120 and 300 min for CKiD after iohexol injection.d (Iohexol injection/slow area) × (1.73/BSA).e (Iohexol injection/total area) × (1.73/BSA). Open table in a new tab Abbreviations: CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter Aids Cohort Study. The left side of Table 3 shows the regression coefficients and R2 for the univariate regressions with the dependent variable being the fast area in the log scale. All variables showed substantial associations with the fast area. In particular, the fast area was inversely proportional to body surface area (BSA; that is, coefficient of BSA was close to, and not statistically different from, –1). Furthermore, there was a strong positive relationship between the slow and fast areas, with the slow area explaining close to 34% of the variability in fast area. Given the strong relationship between the fast area and BSA, we explored the predictive power of variables in Table 3 on the variability of the fast area unexplained by BSA. The right side of Table 3 shows that none of the predictors explain the variability of residuals of the regression of fast area on BSA. In particular, the strong univariate association between slow and fast area completely disappeared when the dependent variable was BSA-adjusted fast area (regression coefficient=-0.018 (P=0.194), R2=0.2%). Further evidence of the lack of association between the fast and slow area conditional on BSA is the fact that the R2=34% observed in the overall univariate relationship between the fast and slow area reduced to 0.6, 0.1, 0.7, and 1.6% in four strata defined by quartiles of BSA.Table 3Univariate linear regression models used to determine the percent of explained variance of BSA-unadjusted and BSA-adjusted fast area for the combined MACS (n=350) and CKiD (n=546) training data setIndependent variableaAll variables except gender in natural logarithmic scale.Dependent variableBSA-unadjusted fast areabDependent variable is the natural log of the observed fast area.BSA-adjusted fast areacDependent variable is the residual of the regression of fast area on BSA (log scale).Regression coefficientR2Regression coefficientR2BSA (m2)-1.02355.9%——Slow area (mg min/ml)0.35933.6%-0.0180.2%GFR0,2 (ml/min per 1.73 m2)-0.31512.2%0.0410.5%Height (m)-2.07556.4%-0.0820.2%Weight (kg)-0.67054.6%-0.006<0.1%BMI (kg/m2)-1.18732.2%0.1280.8%Age (years)-0.43049.9%-0.0220.3%Male gender0.3356.6%0.0320.1%Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter AIDS Cohort Study.a All variables except gender in natural logarithmic scale.b Dependent variable is the natural log of the observed fast area.c Dependent variable is the residual of the regression of fast area on BSA (log scale). Open table in a new tab Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter AIDS Cohort Study. Figure 1a shows that the relationship between fast area and BSA (R2=56%) is given by fast area=6.46 × (BSA)−1.023. More importantly, Figure 1b shows that once the variability of fast area due to BSA has been accounted for, there is no additional information from the slow area (R2=0.2%). Hence, the fast area depends on BSA, but not on the slow area once BSA has been taken into account. Not only does the fast area not depend on the slow area once BSA has been taken into account, but the relationship between the fast area and BSA can be simplified to fastarea=6.4/BSA and we can derive an equation to determine GFR2,2 in terms of GFR0,2. Specifically, by simply dividing both sides of the above equation by the slow area and multiplying and dividing the right-hand side of the equation by 1.73 × I (where I is the injected amount of iohexol), the equation becomes fastarea/slowarea=(6.4/(1.73×I))×GFR0,2. As by protocol, I is close to 3200 and has very low variability (see Table 2), 6.4/(1.73 × I) is equal to 0.00116 (which hereafter we round to 0.0012). In addition, the ratio of fast to slow area is simply (GFR0,2/GFR2,2) – 1. Hence, (GFR0,2/GFR2,2)−1=0.0012×GFR0,2 which, solving for GFR2,2, yields our proposed equation for GFR^2,2 from GFR0,2 as follows: GFR^2,2=GFR0,2/[1+0.12(GFR0,2/100)] or, in short, GFR^=slowGFR/[1+0.12(slowGFR/100)] This equation is of the same form as the one proposed by Fleming7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar and simpler than the one proposed by Brochner-Mortensen and Jodal.9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar More importantly, the form of the equation is consonant with the theoretical and physiological considerations put forward by these authors. Figure 2 plots the data for (GFR0,2/GFR2,2) – 1 (y axis) on GFR0,2 (x axis) and it indicates that the equation including the simple proportionality factor of 0.12 not only fits the data well for both cohorts but also explains 75% of the variability for the combined training data set. For the validation data sets of each study population (1/3 random sample), Table 4a and b describes the agreement of GFR2,2 (measured) and the GFR^2,2 (estimated) from four different GFR0,2-based equations. The equations evaluated included the original Brochner-Mortensen equations for adult4.Brochner-Mortensen J.A. A simple method for the determination of glomerular filtration rate.Scand J Clin Lab Invest. 1972; 30: 271-274Crossref PubMed Scopus (774) Google Scholar and pediatric6.Brochner-Mortensen J.A. Haahr J. Christoffersen J. A simple method for accurate assessment of the glomerular filtration rate in children.Scand J Clin Lab Invest. 1974; 33: 139-143Crossref Google Scholar populations; those published by Brochner-Mortensen and Jodal8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar and Fleming;7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar and our proposed equation.Table 4Agreement of the estimated GFR (GFR^2,2) based on two-point GFR from the slow curve only (GFR0,2) and selected models with the observed four-point GFR (GFR2,2) in the (a) MACS (n=177) and (b) CKiD (n=274) validation data setsModel of GFR^2,2 as a function of GFR0,2 and BSASourceBias ratio (95% CI)Ratio of s.d.'s (95% CI)Correlation (95% CI)RMSE% of GFR^2,2 within 5% of GFR2,2(a)MACS validation data set (n=177)Original Brochner-MortensenC1 (GFR0,2/100) + C2 (GFR0,2/100)2C1=98.31; C2=–0.1218Brochner-Mortensen4.Brochner-Mortensen J.A. A simple method for the determination of glomerular filtration rate.Scand J Clin Lab Invest. 1972; 30: 271-274Crossref PubMed Scopus (774) Google Scholar0.967(0.961, 0.973)0.937(0.909, 0.965)0.978(0.971, 0.984)6.4962.7%GFR0,2/[1+ B0 × (GFR0,2/100)B1 × BSAB2] B0=0.185; B1=1, B2=–0.3Brochner-Mortensen and Jodal8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar,9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar0.972(0.967, 0.978)0.960(0.934, 0.986)0.979(0.972, 0.984)5.8066.1%GFR0,2/[1+B0 × (GFR0,2/100)B1] B0=0.17; B1=1Fleming7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar0.953(0.947, 0.959)0.941(0.916, 0.967)0.979(0.972, 0.984)7.4949.7%MACS and CKiD proposed equation GFR0,2/[1+B0 × (GFR0,2/100)B1] B0=0.12; B1=1Training set CKiD + MACS 2/3 random sample (n=896)1.005(1.000, 1.011)0.987(0.962, 1.013)0.980(0.972, 0.985)4.5979.1%(b)CKiD validation data set (n=274)Original Brochner-MortensenC1 (GFR0,2/100) + C2 (GFR0,2/100)2C1=101.0; C2=–0.17Brochner-Mortensen et al.6.Brochner-Mortensen J.A. Haahr J. Christoffersen J. A simple method for accurate assessment of the glomerular filtration rate in children.Scand J Clin Lab Invest. 1974; 33: 139-143Crossref Google Scholar0.983(0.980, 0.986)0.968(0.959, 0.976)0.996(0.995, 0.997)2.0491.2%GFR0,2/[1+ B0 × (GFR0,2/100)B1 × BSAB2] B0=0.185; B1=1, B2=–0.3Brochner-Mortensen and Jodal8.Jodal L. Brochner-Mortensen J. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 305-313Crossref PubMed Scopus (54) Google Scholar,9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar0.978(0.975, 0.981)0.984(0.976, 0.992)0.996(0.995, 0.997)1.9286.5%GFR0,2/[1+B0 × (GFR0,2/100)B1] B0=0.17; B1=1Fleming7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar0.980(0.978, 0.983)0.983(0.974, 0.991)0.996(0.995, 0.997)1.8790.9%MACS and CKiD proposed equation GFR0,2/[1+B0 × (GFR0,2/100)B1] B0=0.12; B1=1Training set CKiD + MACS 2/3 random sample (n=896)1.004(1.001, 1.006)1.005 (0.996, 1.013)0.996(0.995, 0.997)1.4696.0%Abbreviations: BSA, body surface area; CI, confidence interval; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter AIDS Cohort Study; RMSE, root mean square error.Bold indicates statistically significantly different from 1 (that is, P<0.05). Open table in a new tab Abbreviations: BSA, body surface area; CI, confidence interval; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter AIDS Cohort Study; RMSE, root mean square error. Bold indicates statistically significantly different from 1 (that is, P<0.05). The original Brochner-Mortensen equations showed significant underestimation of GFR2,2 in the MACS (bias: -3.3%, 95% confidence interval (CI): -3.9, -2.7%) and in the CKiD (-1.7%, 95% CI: -2.0%, -1.4%). The equations also produced significant underdispersion in both populations and higher root mean square errors (RMSEs) and lower percentages of GFR^2,2 within 5% of GFR2,2 than those of our proposed equation. Although these estimates were statistically significant, the effect size was relatively small. The equations proposed by Brochner-Mortensen and Jodal9.Brochner-Mortensen J. Jodal L. Reassessment of a classical single injection n51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance.Scand J Clin Lab Invest. 2009; 69: 314-322Crossref PubMed Scopus (24) Google Scholar and Fleming7.Fleming J.S. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.Nucl Med Commun. 2007; 28: 315-320Crossref PubMed Scopus (28) Google Scholar each yielded a slight systematic underestimation and underdispersion in both populations. Our proposed equation, based upon the MACS and CKiD, showed good agreement in each validation data set. In the MACS data set, there was no significant bias or difference in dispersion associated with GFR^2,2 compared with GFR2,2. In the CKiD data set, there was a minor, but significant, overestimation (bias: +0.4%, 95% CI: 0.1%, 0.6%) and no significa
Referência(s)