Time-varying coefficient of determination to quantify the explanatory power of biomarkers on longitudinal GFR among children with chronic kidney disease

Abstract

Purpose: Coefficients of determination (R2) for continuous longitudinal data are typically reported as time constant, if they are reported at all. The widely used mixed model with random intercepts and slopes yields the total outcome variance as a time-varying function. We propose a generalized and intuitive approach based on this variance function to estimate the time-varying predictive power (R2) of a variable on outcome levels and changes.

Methods: Using longitudinal estimated glomerular filtration rate (eGFR) from the Chronic Kidney Disease in Children Study, linear mixed models characterized the R2 for two chronic kidney disease (CKD) risk factors measured at baseline: a traditional marker (proteinuria) and a novel marker (fibroblast growth factor 23 [FGF23]).

Results: Time-varying R2 divulged different disease processes by risk factor and diagnoses. Among children with glomerular CKD, time-varying R2 for proteinuria had significant upward trends, suggesting increasing power to predict eGFR change, but crossed with FGF23, which was higher up to 2.5 years from baseline. In contrast, among those with nonglomerular CKD, proteinuria explained more than FGF23 at all times, and time-varying R2 for each risk factor was not substantially different from time-constant estimates.

Conclusions: Proteinuria and FGF23 explained substantial eGFR variability over time. Time-varying R2 can characterize predictive roles of risk factors on disease progression, overcome limitations of time-constant estimates, and are easily derived from mixed effects models.

Keywords: Chronic kidney disease; Coefficient of determination; Epidemiologic methods; Fibroblast growth factor; Glomerular filtration rate; Pediatrics; Proteinuria.

Copyright © 2018 Elsevier Inc. All rights reserved.

Figures

Figure 1.

Total variance and R-square as a function of time for mixed effects models for children with a glomerular CKD diagnosis. Figure 1a presents estimates of total eGFR variance for four mixed models in Table 2a. Figure 1b presents time-varying R-square values for mixed models (random intercepts and slopes; Table 2a) and time-constant R-square values based on mixed models with random intercepts only in Table 3.

Figure 2.

Total variance and R-square as a function of time for mixed effects models for children with a non-glomerular CKD diagnosis. Figure 2a presents estimates of total eGFR variance for four mixed models in Table 3a. Figure 2b presents time-varying R-square values for mixed models (random intercepts and slopes; Table 2b) and time-constant R-square values based on mixed models with random intercepts only in Table 3.