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

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.