Validation of Creatinine-Based Estimates of GFR When Evaluating Risk Factors in Longitudinal Studies of Kidney Disease
Xuelei Wang*,
Julia Lewis,
Lawrence Appel,
DeAnna Cheek,
Gabriel Contreras||,
Marquetta Faulkner¶,
Harold Feldman**,
Jennifer Gassman*,
Janice Lea,
Joel Kopple,
Mohammed Sika,
Robert Toto,
Tom Greene* for the AASK Investigators
* Cleveland Clinic Foundation, Quantitative Health Sciences, Cleveland, Ohio; Nephrology Clinical Trials Center, Vanderbilt University Medical Center, Nashville, Tennessee; ProHealth, Johns Hopkins Medical Institutions, Baltimore, Maryland; Pediatric Nephrology, Medical University of South Carolina, Charleston, South Carolina; || Division of Nephrology, University of Miami, Miami, Florida; ¶ Medicine/Research, Meharry Medical College, Nashville, Tennessee; ** Center for Clinical Epidemiology & Biostatistics, University of Pennsylvania, Philadelphia, Pennsylvania; Center for Hypertension & Renal Disease Research, Emory University, Atlanta, Georgia; Division of Nephrology and Hypertension, Harbor-UCLA Medical Center, Torrance, California; Division of Nephrology, University of Texas Southwestern Medical Center at Dallas, Dallas, Texas
Address correspondence to: Ms. Xuelei Wang, Cleveland Clinic Foundation, Department of Quantitative Health Sciences, Wb-4, 9500 Euclid Avenue, Cleveland, OH 44195. Phone: 216-445-4319; Fax: 216-445-2781; E-mail: wangx{at}ccf.org
Received for publication October 24, 2005.
Accepted for publication August 2, 2006.
Whereas much research has investigated equations for obtainingestimated GFR (eGFR) from serum creatinine in cross-sectionalsettings, little attention has been given to validating theseequations as outcomes in longitudinal studies of chronic kidneydisease. A common objective of chronic kidney disease studiesis to identify risk factors for progression, characterized byslope (rate of change over time) or time to event (time untila designated decline in kidney function or ESRD). The relationshipsof 35 baseline factors with eGFR-based outcomes were comparedwith the relationships of the same factors with iothalamateGFR (iGFR)-based outcomes in the African American Study of KidneyDisease and Hypertension (AASK; n = 1094). With the use of theAASK equation to calculate eGFR, results were compared betweentime to halving of eGFR or ESRD and time to halving of iGFRor ESRD (with effect sizes expressed per 1 SD) and between eGFRand iGFR slopes starting 3 mo after randomization. The effectsof the baseline factors were similar between the eGFR- and iGFR-basedtime-to-event outcomes (Pearson R = 0.99, concordance R = 0.98).Small but statistically significant differences (P < 0.05,without adjustment for multiple analyses) were observed forseven of the 35 factors. Agreement between eGFR and iGFR wassomewhat weaker, although still relatively high for slope-basedoutcomes (Pearson R = 0.93, concordance R = 0.92). Effects ofcovariate adjustment for age, gender, baseline GFR, and urineproteinuria also were similar between the eGFR and iGFR outcomes.Sensitivity analyses including death in the composite time-to-eventoutcomes or using the Modification of Diet in Renal Diseaseequation instead of the AASK equation provided similar results.In conclusion, the data from the AASK provide tentative supportfor use of outcomes that are based on an established eGFR formulausing serum creatinine as a surrogate for measured iGFR-basedoutcomes in analyses of risk factors for the progression ofkidney disease.
The GFR is regarded as the best overall index of renal functionin patients with chronic kidney disease (CKD) (1). However,because measurement of GFR is expensive and logistically difficult,serum creatinine (SCr) often is used as an alternative (2,3).SCr is an imperfect indicator of GFR because it is influencedby creatinine generation and tubular secretion, both of whichvary between individuals and within individuals over time. Inan attempt to overcome this drawback, several equations havebeen developed to estimate GFR from SCr in conjunction withdemographic factors (4–7). The most widely used is theModification of Diet in Renal Disease (MDRD) equation, whichwas developed by applying linear regression to enrollees inthe MDRD Study (5,6). A related equation was developed specificallyfor black individuals by applying similar methods to relatemeasured GFR, estimated by the clearance of I125-iothalamate,to SCr, gender, and age at the baseline evaluation of the AfricanAmerican Study of Kidney Disease and Hypertension (AASK) (7).
To date, estimating equations for GFR have been derived andvalidated almost exclusively using cross-sectional data sets(4–18). Whereas limited work has been done to evaluatethe association between longitudinal changes in creatinine-basedestimates of GFR and contemporaneous longitudinal changes iniothalamate GFR (iGFR), including studies in lung transplantrecipients (19) and Pima Indians with type 2 diabetes (20),the validity of creatinine-based outcomes to identify risk factorsin longitudinal studies has not been examined comprehensively.Nonetheless, longitudinal changes in creatinine-based estimatesof GFR are used routinely as outcomes in randomized, clinicaltrials and cohort studies (7,21–24).
We previously reported that despite subtle differences, themain conclusions of the randomized treatment group comparisonsof the AASK were similar between outcomes that were based onestimated GFR (eGFR) using the AASK equation and outcomes thatwere based on iGFR (25). This report extends this work by examiningthe concordance of the relationships of 35 potential risk factorswith eGFR-based outcomes versus the corresponding relationshipsof the same factors with iGFR-based outcomes. When iGFR is viewedas a reference standard, this analysis can be viewed as evaluatingthe validity of eGFR-based outcomes as surrogate end pointsin longitudinal studies in which the research objective is toidentify risk factors for the progression of renal disease.
Both slope-based and time-to-event outcomes have been used instudies of renal disease progression. Slope-based analyses evaluatethe average progression rate in all patients, whereas time-to-eventanalyses are more sensitive to large, clinically important declinesin renal function (26). Because the suitability of eGFR as asurrogate for iGFR may differ between these approaches, we investigatedthe validity of eGFR for both slope and the time-to-event endpoints.
Patients and Renal Function Measurements
The AASK was a randomized clinical trial of black individualswho had hypertension (n = 1094), were aged 18 to 70 yr, andhad a GFR between 20 and 65 ml/min per 1.73 m2. Participantswere randomly assigned according to a 3 x 2 factorial designto one of three antihypertensive drug regimens (first-line therapywith a calcium channel blocker [amlodipine], blocker [metoprolol],or an angiotensin-converting enzyme inhibitor [ramipril]) andto two levels of BP control (mean arterial pressure 92 versus102 to 107 mmHg). On the recommendation of the Data Safety andMonitoring Board, the amlodipine intervention was terminatedapproximately 1 yr before the end of the trial.
The GFR was assessed by renal clearance of 125I-iothalamatetwice at baseline, at 3 and 6 mo, then every 6 mo thereafter.For this report, iGFR was standardized to body surface areaby multiplication by 1.73/(body surface area), where body surfacearea was computed using the patient’s weight at the timeof the GFR measurement. SCr was measured centrally using therate-Jaffe method with an alkaline picrate assay (normal range0.7 to 1.4 mg/dl) twice during baseline, at 3 and 6 mo, thenat 6-mo intervals during follow-up. A total of 10,679 iGFR and11,130 SCr measurements were obtained during the trial (excludingthose in the amlodipine group after September 2000). To facilitatecomparisons between analyses that were based on iGFR and SCr,the data set was restricted to 9742 matched pairs of iGFR andSCr measurements that were obtained within 8 wk of each otherwhen evaluating time-to-event outcomes and to 8529 of thesematched pairs that remained after exclusion of the second baselinemeasurement. Each of the SCr measurements was used to computeeGFR using the AASK equation (7) eGFR = 329 x SCr–1.096x age–0.294 x (0.736 if female).
The mean follow-up period from randomization to the final iGFR–SCrpair was 3.6 yr. The protocol and procedures were approved bythe institutional review board at each center, and all participantsgave written informed consent. Additional details regardingthe trial have been presented elsewhere (27–29).
Outcomes
For time-to-event analyses, we compared the effects of the baselinerisk factors on the time from randomization to the two compositeoutcomes defined by (1) a 50% reduction in iGFR from the meanof two baseline values or ESRD or (2) a 50% reduction in eGFRfrom the mean of two baseline eGFR measurement or ESRD. Forslope-based analyses, the statistical models evaluated the rateof change in iGFR and eGFR separately in the first 3 mo (acutephase) and the subsequent period after 3 mo (chronic phase)because the study interventions were known to lead to hemodynamicchanges in renal function that differed from their hypothesizedlong-term effects. The data presentation of this report is limitedto the chronic phase, which may reflect long-term disease progressionbetter.
Potential Baseline Risk Factors
A total of 38 potential baseline variables were selected bythe investigators before the analyses of the data for examinationas potential risk factors for the progression of renal disease(30). Two of the selected factors, pulse pressure and mean arterialpressure, were excluded from this report because they are mathematicalfunctions of systolic and diastolic BP, which also were selected.A third factor, baseline iGFR, was excluded because it is acomponent of the outcome variable in analyses of iGFR slope.The remaining 35 factors are listed in Table 1. For categoricalfactors, the reference group was defined by consensus of theinvestigators as the category that best represents the absenceof the potential risk factor. With the exception of hematocrit,which was obtained locally, the remaining serum and urine biochemistrymeasurements were obtained at a central laboratory (ClevelandClinic Research Laboratory, Cleveland, OH). BP measurementswere taken as the average of two seated values by a random zerosphygmomanometer. Demographic information and medical historieswere obtained by patient interview and chart review.
Table 1. Patient characteristics of 35 selected baseline risk factorsa
Statistical Analyses Assessment of Agreement on a Patient Basis.
The eGFR- and iGFR-based time-to-event outcomes were comparedusing two-way contingency tables and the statistic for time-to-eventoutcomes (31). The eGFR and iGFR slopes were compared for individualpatients using the following measures:
Mean eGFR slope –mean iGFR slope (to assess bias)
Pearson correlation of eGFRslope with iGFR slope (to assessprecision)
Concordance correlationof eGFR slope with iGFR slope (to assessagreement)
Root meansquare error (rMSE) of iGFR slope that cannot be accountedforby a linear regression of iGFR slope on eGFR slope (to assessprecision)
The concordance correlation (32) is a measure of agreement thatadjusts the Pearson correlation downward if there is a systematicbias between the measures being compared. The rMSE is an estimateof the variability in the iGFR slopes that cannot be explainedby the eGFR slopes. Measures 2 through 4 were adjusted for randomizedtreatment group. For patient-level analyses the chronic eGFRand iGFR slopes were computed using least squares regressionsof each patient’s eGFR or iGFR measurements versus follow-uptime under a two-slope segmented model, with separate slopesin months 0 through 3 and in the remainder of follow-up.
Assessment of Agreement between Effects of Covariates.
The 35 baseline risk factors were scaled to have unit SD tofacilitate comparisons of effects for different regression coefficients.For the time-to-event outcomes, separate Cox proportional hazardsanalyses were applied to relate the eGFR and iGFR compositeoutcomes to each baseline factor, and robust sandwich variance-covarianceestimators were used to account for the dependence of the outcomesin the same patient (33). For the slope-based outcomes, iGFRand eGFR were analyzed separately using the two-slope mixed-effectsmodels (34,35) with fixed-effects terms to estimate the meaneffects of baseline factors and randomized treatment group onthe intercept and acute and chronic slopes and with random interceptsand acute and chronic slopes to represent deviations of individualpatients around the group means. A two-band Toepolitz errorstructure was used to account for autocorrelation in neighboringGFR measurements (36). Robust sandwich estimates were used toestimate SE and the correlation between the regression coefficientslinking the eGFR and iGFR slopes to the respective baselinecovariates (37).
These analytic methods first were used to relate the time-to-eventand slope outcomes individually to each of the 35 standardizedbaseline covariates, with adjustment for randomized treatmentassignment. The effects of the baseline factors on the eGFRand iGFR outcomes were compared by (1) plotting the regressioncoefficients (transformed to hazard ratios (HR) for the time-to-eventoutcomes) for the eGFR outcome versus the iGFR outcome, withthe line of identity indicating perfect agreement; (2) presentingthe Pearson and concordance correlations between the effectsof the 35 covariates on the eGFR and iGFR outcomes; and (3)presenting the rMSE of the effects of the 35 covariates on iGFRthat cannot be accounted for by a linear regression on the effectson eGFR. Because observational analyses usually are performedwith adjustment for major nonmodifiable demographic factorsand previously identified risk factors, these analyses wererepeated with gender, age, baseline iGFR, and baseline proteinuria(defined as the log-transformed urine protein-to-creatinineratio) as covariates.
Several sensitivity analyses were conducted to evaluate therobustness of the results. First, because death is a competingrisk for the occurrence of the renal events, the comparisonsof the time-to-event outcomes were repeated after addition ofdeath as an component of the eGFR and iGFR composites. Second,because SCr is a component of eGFR, summary statistics thatevaluated the agreement of the eGFR- and iGFR-based outcomeswere recomputed after deletion of baseline SCr from the baselinerisk factors. Third, the analyses that compared the effectsof the baseline factors on the eGFR and iGFR outcomes were repeatedusing the MDRD formula in place of the AASK equation to calculateeGFR. Fourth, the comparisons of the time-to-event outcomeswere repeated for doubling of SCr in places of 50% reductionin GFR.
Patient Characteristics at Baseline
The 35 potential baseline risk factors are summarized in Table 1.The mean (±SD) age was 54.6 ± 10.7 yr, and 61%were male. Average prestudy duration of hypertension was 14.2± 10.1 yr, and baseline systolic and diastolic BP were150 ± 24 and 96 ± 14 mmHg, respectively. MeanGFR was 46 ± 13 ml/min per 1.73 m2.
Patient-Level Association for Time-to-Event and Slope Outcomes
Of 1094 AASK participants, 280 experienced a halving of iGFRor ESRD, and 240 experienced a halving of eGFR or ESRD. Thetwo event outcomes agreed for 1020 (93%) of the participants( = 0.81). A total of 74 (7%) participants reached one outcomebut not the other (Table 2). The greater rate of iGFR eventscompared with eGFR events may reflect, in part, a higher variabilityof iGFR measurements (3).
Table 2. Patient-level association for time-to-event outcomesa
A total of 1012 patients with at least two follow-up GFR measurementswere included in patient-level slope analyses. There were onlyminimal biases in the eGFR slope estimates (0.10 ml/min per1.73 m2/yr for the chronic slopes). The Pearson R and concordanceR between chronic eGFR and iGFR slopes were 0.62 and 0.60, respectively.Because of a greater precision of slopes that were estimatedover a longer follow-up period, participants with >18 moof follow-up time had a better patient-level agreement betweenchronic eGFR and iGFR slopes than did patients with shorterfollow-up (Figure 1, Table 3).
Figure 1. Agreement of chronic slopes on a patient basis. Shown is the association between the estimated GFR (eGFR) and the iothalamate GFR (iGFR) slopes during the chronic phase of the study starting 3 mo after randomization. Slopes are expressed in ml/min per 1.73 m2/yr and computed by the least squares method. The areas of the plot symbols are proportional to the SE of the slope estimates.
Table 3. Patient-level association of chronic slopes between eGFR and iGFRa
Association of Estimated Effects of Baseline Risk Factors without Covariate Adjustment Figure 2 plots the effects of the 35 baseline factors on theeGFR time-to-event outcome versus the effects of the same factorson the iGFR-based time-to-event outcome. The abbreviations ofeach factor are defined in Table 1. The proximity of the plottedpoints to the line of identify indicates that the observed effectsof the factors were similar between the iGFR- and eGFR-basedoutcomes, with Pearson R = 0.99 and concordance R = 0.98.
Figure 2. Agreement of effects of baseline factors on eGFR- and iGFR-based composite end points. Plotted are the hazard ratios (HR) of the eGFR composite outcome (vertical axis) versus the HR of the iGFR composite outcome (horizontal axis) associated with each of the 35 baseline factors. The line of identity indicates perfect agreement. HR are expressed per 1-SD increases in each factor. The color of the symbols indicates which factors were significantly related to the respective composite end points at the 5% level; triangles indicate factors whose effects on the eGFR and iGFR composites differ at the 5% level. Pearson R = 0.99, concordance R = 0.98, and root mean square error (rMSE) = 0.039 (log HR per 1 SD).
Twelve factors were statistically significant predictors ofboth the iGFR and eGFR time-to-event outcomes. Four factorshad a significant effect on eGFR but not on iGFR; none had asignificant effect on iGFR but not eGFR. Statistically significant(but generally small) differences between the two time-to-eventoutcomes were observed for seven of the 35 factors: Years ofhypertension, age, diastolic BP, SCr, triglycerides, no highschool education, and proteinuria. The largest discrepancies(with a >15% difference in the HR [per 1-SD increase]) occurredfor proteinuria and age. Expressed in units that are relevantto each factor, doubling of proteinuria had an HR of 1.60 (95%confidence interval [CI] 1.51 to 1.70) for iGFR versus 1.73(95% CI 1.62 to 1.84) for eGFR and a 10-yr increase in age withan HR of 0.78 (95% CI 0.70 to 0.87) for iGFR versus 0.67 (95%CI 0.60 to 0.75) for eGFR.
During the chronic phase, the Pearson and concordance R relatingthe eGFR and iGFR slope outcomes were 0.93 and 0.92, respectively(Figure 3). Eight factors were observed to be significant predictorsof both chronic slope outcomes, and four factors each had significanteffects on eGFR but not on iGFR or iGFR but not eGFR. Six ofthe 35 factors had significantly different effects on the chroniciGFR and eGFR slopes, including SCr, diastolic BP, gender, height,urine volume, and triglyceride level. The largest discrepancywas observed for gender, with female gender associated witha 0.40 ± 0.22 ml/min per 1.73 m2/yr steeper iGFR slopebut a 0.087 ± 0.20 ml/min per 1.73 m2/yr less steep eGFRslope.
Figure 3. Agreement of effects of baseline factors on eGFR and iGFR slopes. Plotted are the effects of each of the 35 baseline risk factors on the chronic eGFR slope (vertical axis) and on the chronic iGFR slope (horizontal axis). Effects are expressed per 1-SD increases in the baseline factors. Plot symbols are defined as in Figure 2. Pearson R = 0.93, concordance R = 0.92, and rMSE = 0.105 ml/min per 1.73 m2/yr per 1 SD.
Effect of Covariate Adjustment on Agreement between the Effects of Baseline Factors on iGFR- and eGFR-Based Outcomes Figure 4 plots the effects of the baseline factors on the eGFR-basedtime-to-event outcome versus the effects of the same factorson the iGFR-based time-to-event outcome without and with adjustmentfor age, gender, baseline GFR, and proteinuria. The interconnectingblack lines describe the effect of covariate adjustment; linesthat are parallel to the line of identity indicate similar effectsof adjustment on the two outcomes. Covariate adjustment hadsimilar effects on the two time-to-event outcomes, in both casesreducing the variation in estimated effects among the risk factors.As a result of this reduced variation, The Pearson and concordanceR declined from 0.99 to 0.95 and from 0.98 to 0.93, respectively,after covariate adjustment. However, the stable rMSE indicatethat covariate adjustment did not reduce the precision withwhich estimates of effects on the iGFR composite could be estimatedfrom the eGFR composite.
Figure 4. Effect of covariate adjustment on estimated effects of baseline factors on eGFR- and iGFR-based composite end points. Plotted are the HR of the eGFR composite outcome (vertical axis) versus the HR of the iGFR composite outcome (horizontal axis) associated with each of 32 baseline factors. HR are expressed per 1-SD increases in the indicated baseline factors. HR are displayed without (red circles) and with (green circles) adjustment for age, gender, baseline GFR, and baseline proteinuria. The solid black lines indicate the effect of covariate adjustment on the HR associated with the two outcomes. The Pearson and concordance R declined from 0.99 to 0.95 and from 0.98 to 0.93, respectively, after covariate adjustment. rMSE changed from 0.036 to 0.045 (log HR per 1 SD). Labels are provided for factors significantly associated (P < 0.05) with one or both outcomes without covariate adjustment.
The effect of covariate adjustment was smaller for slope-basedoutcomes (Figure 5). With covariate adjustment, the PearsonR remained unchanged at 0.89, concordance R changed from 0.87to 0.86, and the rMSE changed from 0.095 to 0.093 ml/min per1.73 m2/yr per 1-SD change in the predictor variables.
Figure 5. Effect of covariate adjustment on estimated effects of baseline factors on eGFR and iGFR slopes. Plotted are the effects of each of the 32 baseline risk factors on the chronic eGFR slope (vertical axis) and on the chronic iGFR slope (horizontal axis). Effects are expressed per 1-SD increases in the baseline factors. Estimated effects are displayed without (red circles) and with (green circles) adjustment for age, gender, baseline GFR, and baseline proteinuria. The solid black lines indicate the effect of covariate adjustment. With covariate adjustment, Pearson R changed from 0.89 to 0.89, concordance R changed from 0.87 to 0.86, and rMSE changed from 0.095 to 0.093 ml/min per 1.73 m2/yr per 1 SD. Labels are provided for factors significantly associated (P < 0.05) with one or both outcomes without covariate adjustment.
Sensitivity Analyses
Of 1094 AASK participants, 354 had an event of halving of iGFR,ESRD, or death, and 317 had an event of halving of eGFR, ESRD,or death. The two event outcomes agreed for 1025 (94%) of thepatients. The Pearson and concordance R of observed effectsof the 35 factors relating the expanded iGFR and eGFR compositeswere both equal to 0.99.
Deleting SCr from the analyses had only minimal effects on theresults, with relative changes in the Pearson and concordanceR of <1% in all analyses.
The agreement of the eGFR-based outcomes with iGFR-based outcomeswas similar when the MDRD equation was used in place of theAASK equation. When eGFR was computed by the MDRD equation,the Pearson and the concordance R between the effects of the35 baseline factors on the eGFR and iGFR time-to-event compositeswere 0.99 and 0.98 and were 0.91 and 0.90, respectively, betweenthe chronic eGFR and iGFR slopes. The Pearson and concordanceR were 0.99 and 0.98, respectively, between the composite ofdoubling of SCr or ESRD and the composite of halving of iGFRor ESRD.
Using the AASK equation (7) to obtain eGFR from SCr, the estimatedeffects of 35 potential baseline risk factors on eGFR-basedoutcomes were found to have good overall agreement with theestimated effects of the same factors on iGFR-based outcomes.This was especially true for time-to-event outcomes, definedas composites of ESRD with a 50% reduction in either iGFR oreGFR (Figure 2). The Pearson and concordance correlations relatingthe effects of the 35 factors on the eGFR and iGFR compositeswere equal to 0.99 and 0.98, indicating that 96 to 98% of thevariance of the effects of the 35 factors on iGFR could be accountedfor by the effects of these factors on eGFR. Both outcomes identifiedthe same factors as the strongest predictors of faster progression(higher urine proteinuria, SCr, serum urea nitrogen, serum phosphorus,and serum triglycerides) and the same predictors of slower progression(higher serum albumin and serum hematocrit and greater age).Agreement was somewhat weaker, although still relatively high,for the mean slope after 3 mo, with Pearson and concordancecorrelations of 0.93 and 0.92, respectively. For both slope-basedoutcomes, higher proteinuria and SCr were the strongest predictorsof faster progression, and higher serum albumin and greaterage were the strongest indicators of slower progression.
The identification of proteinuria as the strongest predictorof progression for both eGFR- and iGFR-based outcomes is consistentwith previous reports from the AASK describing the dominantrole of proteinuria in predicting progression despite a lowbaseline median urine protein/creatinine ratio of 0.08 (30,38).The inverse relationship of age with progression may reflectthat for a given entry GFR, older patients, on average, mayhave had their disease progress over a longer time period, inwhich case younger age would act as a marker for more rapidlyprogressive disease.
Although there generally was good agreement between the eGFR-and iGFR-based outcomes, discordant results were observed inspecific cases. At the 5% significance level, seven of the 35factors exhibited differences in their effects on the eGFR andiGFR time-to-event outcomes, and six factors exhibited differencesfor the slope outcomes. As shown in Figures 2 and 3, most ofthese differences were small compared with the magnitudes ofthe treatment effects, and some may be spurious as a resultof the number of factors considered.
The predictor variables of commonly used equations for estimationof GFR include a term approximating the reciprocal of SCr (SCr–1.096for the AASK equation), age, gender, and, in some cases, raceand weight. Among these factors, race and gender are constantover time, and in adults, changes in age and weight usuallyare too small during a follow-up period of several years tohave a large effect on the computed eGFR. Hence, when assessinglongitudinal change, similar results would be expected irrespectiveof which equation is used. In sensitivity analyses, the estimatedeffects of the 35 baseline factors on the eGFR slope and time-to-eventoutcomes were similar for the AASK and MDRD equations. In addition,the estimated effects on doubling of SCr, which often is usedas an end point in randomized, clinical trials, were similarto the estimated effects on the halving of eGFR with the AASKequation. Hence, the results of this report apply also to time-to-eventoutcomes that are based on the doubling of SCr and to otherequations for eGFR that stipulate an approximately reciprocalrelationship of GFR with SCr.
Although the focus of this article is the agreement betweenresults that are given by eGFR- and iGFR-based outcomes, italso is of interest to compare results between the slope-basedand time-to-event outcomes. Some differences are notable; forexample, a comparison of Figures 2 and 3 indicates that highervalues of baseline weight and baseline body mass index wereassociated with steeper iGFR and eGFR slope but were not significantlyassociated with the iGFR or eGFR time-to-event outcomes.
Because the effects of potential risk factors usually are evaluatedin observational studies after adjustment for key covariates,we also examined the effect of covariate adjustment for age,gender, and baseline proteinuria and GFR. Adjustment for thesefactors reduced the variation in the estimated effects of theremaining factors on both the eGFR and iGFR time-to-event outcomes(Figure 4). However, the changes in the estimated effects thatresulted from covariate adjustment were similar for the eGFR-and iGFR-based slope outcomes. In contrast to the time-to-eventanalyses, covariate adjustment resulted in only minimal changesin the estimated effects on GFR slope (Figure 5). Covariateadjustment seems to have had a greater effect on time-to-eventthan slope-based outcomes because a number of the baseline factorswere strongly associated with the baseline GFR, which was morestrongly related to the time-to-event outcomes than to the slopeoutcomes.
The analytic criteria that were used in this report are in somerespects analogous to individual- and trial-level criteria thatwere proposed recently in the statistical literature on thevalidation of surrogate end points for randomized, clinicaltrials (39–41). An intermediate end point is regardedas a good surrogate on the individual level when the surrogateis strongly associated with the true clinical end point forindividual patients and on the trial level when the treatmenteffects on the true end point can be predicted accurately fromthe treatment effects on the intermediate end point. Similarly,the analyses of Figure 1 and Table 2 examine the validity ofeGFR-based outcomes as surrogates for iGFR-based outcomes atthe individual level. The analyses of Figures 2 through 5 evaluatewhether effects of baseline factors on the iGFR-based outcomescan be predicted accurately from the effects of the same factorsin the eGFR-based outcomes and are analogous to the trial-levelcriterion in that both approaches evaluate whether effects onthe target clinical end point can be predicted accurately fromeffects on the surrogate.
The consideration of large numbers of potential risk factorsin the longitudinal cohort setting increases the burden of prooffor validation of a surrogate end point, because one has toconsider, for each factor, whether that factor may affect thesurrogate independent of the target outcome. In this study,we have addressed this issue by including a wide range of potentialrisk factors that cover as many domains as possible in our assessmentof validity. Nonetheless, it is impossible to eliminate completelythe risk that new potential risk factors that were not includedin previous validation studies may behave differently with respectto the difference between eGFR and iGFR than those consideredin previous validation studies.
There are several limitations in the scope of our analyses.First, because relationships of potential risk factors withprogression may differ between populations, the results fromthis report of a single study should be interpreted cautiouslyuntil confirmed in other studies. Second, we have consideredthe validity of eGFR-based outcomes for identification of baselinerisk factors that are measured before the follow-up period;it remains to be seen whether eGFR performs similarly well forevaluation of the effects of changes in risk during the follow-upperiod. Third, although the iothalamate-based estimate of GFRused as the target end point in this study is regarded as arigorous method for estimating GFR in practice, iothalamateclearance may differ from inulin clearance, which is regardedas a truer "gold standard." It has been estimated that up to10% of iothalamate is secreted, and it is possible that newrisk factors could alter iGFR by altering iothalamate handlingby the kidney. We have not addressed in this article the associationof iGFR- and eGFR-based outcomes with the occurrence of renalfailure, which is the clinical end point of greatest interest.Fourth, we have limited the slope-based analyses to GFR itself,without log transformation. The log transformation expresseschange in GFR on a percentage basis, which accords more closelywith the time-to-event outcomes that are based on halving ofGFR. However, because mean GFR declined faster at lower GFRlevels in the AASK (25), the log transformation introduces otheranalytic complications that are beyond the scope of this article.Finally, the measures of agreement that are presented in associationwith Figures 2 through 5 pertain to the estimated effects ofthe baseline factors on eGFR- and iGFR-based outcomes that wereobserved in the study cohort rather than to the true effectsin the target population. Methods for evaluating the relationshipsamong the true effects are the subject of a separate statisticalmanuscript in preparation.
The data from the AASK provide tentative support for the useof outcomes that are based on eGFR, as determined by standardequations from SCr, as surrogates for corresponding outcomesthat are based on measured GFR for analyses of risk factorsin longitudinal studies of the progression of kidney disease.As with other applications of surrogate end points, the useof eGFR-based outcomes to investigate new risk factors thathave not been previously studied requires an extrapolation beyondexisting data and should be done with appropriate caution.
Footnotes
Published online ahead of print. Publication date availableat www.jasn.org.
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Top
Abstract
Introduction
blocker [metoprolol], or an angiotensin-converting enzyme inhibitor [ramipril]) and to two levels of BP control (mean arterial pressure 
92 versus 102 to 107 mmHg). On the recommendation of the Data Safety and Monitoring Board, the amlodipine intervention was terminated approximately 1 yr before the end of the trial. 
statistic for time-to-event outcomes (31). The eGFR and iGFR slopes were compared for individual patients using the following measures:
