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Am J Kidney Dis. 2019 Jan;73(1):82-89. doi: 10.1053/j.ajkd.2018.07.009. Epub 2018 Sep 21.

Using All Longitudinal Data to Define Time to Specified Percentages of Estimated GFR Decline: A Simulation Study.

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Arbor Research Collaborative for Health, University of Michigan, Ann Arbor, MI. Electronic address:
Arbor Research Collaborative for Health, University of Michigan, Ann Arbor, MI.
Arbor Research Collaborative for Health, University of Michigan, Ann Arbor, MI; Department of Internal Medicine, University of Michigan, Ann Arbor, MI.
Department of Biostatistics, University of Michigan, Ann Arbor, MI.



The standard method to calculate time to the event of a specified percentage decline in estimated glomerular filtration rate (eGFR) uses 2 eGFR assessments, 1 at baseline and 1 at the event time. However, event times may be inaccurate due to eGFR variability and restriction of events to study visit times. We propose a novel method for calculating time to a specified percentage decline in eGFR that uses all available longitudinal eGFR assessments.


Simulation study and comparison of methods in 2 observational cohorts.


Simulation data and study participants in the Nephrotic Syndrome Study Network (NEPTUNE) and Clinical Phenotyping and Resource Biobank Core (C-PROBE).


Analytical method for calculating time to a specified percentage decline in eGFR: standard 2-point method versus a regression method incorporating all available longitudinally assessed eGFR assessments.


Time to percentage decline in eGFR.


A 2-point method used only the baseline eGFR and first eGFR below the decline threshold. The comparison method used ordinary linear regression incorporating all longitudinal eGFR assessments to define the baseline measure and 40% decline threshold. Time to a 40% decline in eGFR was defined as the time when the regression line crossed the decline threshold. The 2 outcome calculation methods were compared using simulations to assess the accuracy of estimated event times and power to detect event time differences between groups. Comparison of event times calculated using each method was also implemented using data from NEPTUNE and C-PROBE.


The regression method incorporating all eGFR assessments was more accurate than the 2-point method in estimating event times in simulation analyses, particularly when eGFR variability was high, there was a greater correlation among successive eGFR values, or there were more missing data. This method was also more powerful in detecting differences between groups. Using NEPTUNE and C-PROBE data, the standard method estimated a more rapid rate of events, some likely representing transient reductions in kidney function, and was less likely to give accurate estimates in the presence of nonlinear eGFR trajectories.


Computations required for our proposed method currently limit its use to research rather than clinical applications.


A regression method using all longitudinal eGFR values to estimate time to a percentage decline in eGFR increases accuracy and power over traditional methods, representing a potential improvement in the ability to discover treatment or biomarker effects on kidney disease progression.


Estimated glomerular filtration rate (eGFR); eGFR trajectory; kidney disease progression; kidney function; longitudinal data; percent eGFR decline; simulations; time-to-event outcome

[Available on 2020-01-01]

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