Creatinine Linearity – Connecting the Dots Has Never Been So Complicated

Prediction. My least favorite part of the chronic kidney disease (CKD) clinic visit.

“No crystal ball.”

“I’m not in a position to guess.”

“Only God knows the answer to that.”

These are all lines I have used to warn patients that my predictions can be informative, but aren’t foolproof. My ability to advise if they will see dialysis in their lifetime (and if so, when?) lends itself to establishing the urgency of planning and reinforcing the importance of follow-up and adherence. It is also an important idea in clinical trial design. A recent study by Weldegiorgis et al that was published in AJKD offers insights into linearity in CKD progression – namely as a consideration in CKD trial design.

The pace of glomerular filtration rate (GFR) loss has long been a topic of debate, and it should be. The historical paradigm was that the decay of GFR was a steady, linear model of decline. In 1976, Mitch et al published a paper that helped to establish this paradigm. It was a small study of only 34 patients, but with 31 of those progressing linearly, it suggested that linearity was the rule, not the exception. We all have anecdotes about cases that behaved very differently, with some patients accelerating rapidly, preempting our ability to plan for dialysis, or conversely, we have also seen patients who are referred after a period of decline only to stabilize.

Accounting for the frequency of non-linear CKD trajectories within clinical trials is tricky. If we trust that decline is linear, then we could argue to shorten trial length, reduce the number of patients required to conduct such trials, and improve generalizability. If the trajectory is commonly nonlinear, then including patients who were destined to have a non-linear decline in the evaluation of the efficacy of a trial intervention may falsely inform our analysis of the intervention.

While anecdotal challenges to the idea of linearity abound, perhaps the best developed challenge was borne out of the African American Study of Kidney Disease and Hypertension (AASK). Li et al published an analysis in 2012 that evaluated the probability of nonlinear eGFR trajectory among about 850 patients included in the trial over a period of 9 years. Using similar methodology as the present study (briefly discussed below), that analysis determined that nonlinearity was common, with 41.6% of patients exhibiting a high probability of nonlinear CKD progression, or a long period of nonprogression.  Importantly, these were patients without diabetes, eGFR 20-65 mL/min, and relatively low protein to creatinine ratios. This led to cautions around trial design, emphasizing the importance of analytical methods to address those nonlinear patients and reemphasizing the importance of hard end points for analysis.

In the Weldegiorgis et al analysis, six large randomized controlled trials that maintained individual patient measurements of serum creatinine with at least two years of follow-up were included, with the longest median follow-up of 3.8 years (much less than the AASK analysis). The individual trials in this study included three trials of patients with diabetic CKD (BENEDICT, RENAAL, and IDNT) and three trials that included nondiabetic CKD (REIN, ROAD, ESBARI). The individual trials, as well as their main inclusion and exclusion criteria, can be found in Table 1 below:

Table 1 from Weldegiorgis et al, AJKD © National Kidney Foundation.

Comparison of the trial specific baseline characteristics is also instructive and can be found in Table 2 below:

Values for continuous variables given as mean ± standard deviation or median [interquartile range]; for categorical variables, as count (percentage). a) Albuminuria (μg/min).
b) Proteinuria (mg/d). Table 2 from Weldegiorgis et al, AJKD © National Kidney Foundation.

While the most potent variance between the trials is the included population (diabetic versus nondiabetic), the fact that BENEDICT, comprising about a third of the diabetic cohort, was composed of patients with a higher median eGFR and lower proteinuria should not be overlooked – more on that below. The presence of ACE or ARB should also be noted, though this was comparable between studies.

The analysis itself – and I am simplifying here – uses mathematical modelling to simulate uncertainty in GFR between measurements, generating a library of smooth GFR curves for each individual patient. From this library, we can compute how likely the GFR trajectory was to be either linear or nonlinear for that individual. These probabilities were then analyzed for different patient cohorts: first each study, then within a specific group (diabetic or nondiabetic), as well as for the entire cohort. The authors then used linear regression models to evaluate patient-specific details to determine which were likely to contribute to nonlinear decline. Weldegiorgis et al defined nonlinearity as  +/-  3 mL/min deviation from slope.

In the regression analyses, several factors associated with probability of a non-linear decline.  These included:

  • diagnosis of type 2 diabetes
  • higher baseline eGFR
  • male sex
  • steeper eGFR slopes
  • non-RAAS-inhibitor treatment assignment.

The probability of nonlinearity among all included patients was 0.26 (IQ: 0.13-0.48); notably, the probability of nonlinearity for the individual trials was always <0.31. This is substantially lower than the AASK analysis suggested. There are a variety of ways to present the data from the primary analysis, but it is well captured in Table 3 below:

Note: Values given as median [interquartile range], count (percentage), or mean ± standard deviation.. Table 3 from Weldegiorgis et al, AJKD © National Kidney Foundation.

Here you can see that the probability of nonlinearity was greater for the diabetic studies than the nondiabetic studies. That said, with median probabilities that were – on the whole – low, the authors conclude that most patients will behave linearly. Within the context of the broader literature, their analysis is similar with estimates of linearity drawn from other cohorts.  I previously mentioned the differences in BENEDICT versus the other two diabetic trials (less proteinuria, higher starting eGFR perhaps suggesting a lower likelihood of decline), but those differences did not bear out into a difference in the likelihood of nonlinearity between BENEDICT and RENAAL/IDNT.

As for the difference between the AASK analysis and this study, as the authors’ note, the difference in follow-up interval is important. The fact that 9 years of follow-up were available for AASK gave significantly more time for deviation from linearity to be detected. With a much shorter follow-up available for these samples, the time available to detect nonlinearity was smaller. Since these authors limit their conclusions to within the context of trial design, it seems reasonable to offer these results in support of eGFR slope as a clinical trial outcome. How this may  help me in counseling folks in clinic remains to be seen.

We need more of these types of analyses. Randomized controlled trials are cumbersome and expensive.  Could some of the encumbrance be addressed by changing the end points we choose? Absolutely, but only through supportive analyses will We – and here I mean the Royal “We” – accept those as conclusions worth pushing into our clinics.

– Post prepared by Ed Gould, AJKDBlog Contributor. Follow him @paininthekidney.

To view Weldegiorgis et al (subscription required), please visit

Title: Longitudinal Estimated GFR Trajectories in Patients With and Without Type 2 Diabetes and Nephropathy
Authors: M. Weldegiorgis, D. de Zeeuw, L. Li, H.-H. Parving, F.F. Hou, G. Remuzzi, T. Greene, and H.J.L. Heerspink
DOI: 10.1053/j.ajkd.2017.08.010



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