Methods for characterizing differences in longitudinal glomerular filtration rate changes between children with glomerular chronic kidney disease and those with nonglomerular chronic kidney disease

Abstract

The rate of decline of glomerular filtration rate (GFR) in children with chronic kidney disease (CKD) can vary, even among those with similar diagnoses. Classic regression methods applied to the log-transformed GFR (i.e., lognormal) quantify only rigid shifts in a given outcome. The generalized gamma distribution offers an alternative approach for characterizing the heterogeneity of effect of an exposure on a positive, continuous outcome. Using directly measured GFR longitudinally assessed between 2005 and 2010 in 529 children enrolled in the Chronic Kidney Disease in Children Study, the authors characterized the effect of glomerular CKD versus nonglomerular CKD diagnoses on the outcome, measured as the annualized GFR ratio. Relative percentiles were used to characterize the heterogeneity of effect of CKD diagnosis across the distribution of the outcome. The rigid shift assumed by the classic mixed models failed to capture the fact that the greatest difference between the glomerular and nonglomerular diagnosis' annualized GFR ratios was in children who exhibited the fastest GFR declines. Although this difference was enhanced in children with an initial GFR level of 45 mL/minute/1.73 m(2) or less, the effect of diagnosis on outcome was not significantly modified by level. Generalized gamma models captured heterogeneity of effect more richly and provided a better fit to the data than did conventional lognormal models.

Figures

Figure 1.

A) Lognormal cumulative distribution functions of annualized glomerular filtration rate (GFR) ratios based on random intercepts and random-slopes mixed models for 420 children with nonglomerular chronic kidney disease (black dashed curve) and 109 children with glomerular chronic kidney disease (black solid curve) from the Chronic Kidney Disease in Children Study, 2005–2010. Diagnosis-specific empirical cumulative distributions of annualized GFR ratios are shown as thin black step curves. B) Diagnosis-specific generalized gamma cumulative distribution functions superimposed on diagnosis-specific empirical cumulative distributions of annualized GFR ratios (shown as thin black step curves).

Figure 2.

Generalized gamma (GG)-modeled relative percentiles of annualized glomerular filtration rate (GFR) ratio in children with glomerular chronic kidney disease (CKD) versus children with nonglomerular CKD, Chronic Kidney Disease in Children Study, 2005–2010 (n = 529). The solid black curve represents ratio estimates (95% confidence intervals are shown as vertical brackets at highlighted percentiles) of percentiles of GG(0.003, 0.132, 2.100) for children with glomerular diagnosis to percentiles of GG(−0.014, 0.109, 0.782) for children with nonglomerular diagnosis. For comparison, the estimated relative percentile (and 95% confidence interval) in annual change in GFR for children with glomerular CKD versus those with nonglomerular CKD using a random intercepts and slopes linear mixed model with log-transformed GFR as the outcome is shown on the right side of the figure (and as thin, dashed lines). The nonglomerular CKD reference group is indicated by the horizontal dashed line at 1.0.

Figure 3.

A) Generalized gamma cumulative distribution functions of annualized glomerular filtration rate (GFR) ratios for 212 children with nonglomerular chronic kidney disease (dashed curve) and 45 children with glomerular chronic kidney disease (solid curve) with a baseline GFR level of 45 mL/minute/1.73 m2 of less from the Chronic Kidney Disease in Children Study, 2005–2010. Diagnosis-specific empirical cumulative distributions of annualized GFR ratios are shown as thin gray step curves. B) Generalized gamma cumulative distribution functions of annualized GFR ratios for 208 children with nonglomerular chronic kidney disease (black dashed curve) and 64 children with glomerular chronic kidney disease (black solid curve) with a baseline GFR level greater than 45 mL/minute/1.73 m2. Diagnosis-specific empirical cumulative distributions of annualized GFR ratios are shown as thin black step curves.

Figure 4.

Baseline glomerular filtration rate (GFR) level-specific generalized gamma (GG)-modeled relative percentiles of annualized GFR ratio in children with glomerular chronic kidney disease (CKD) versus children with nonglomerular CKD, Chronic Kidney Disease in Children Study, 2005–2010 (n = 529). The 2 solid curves provide ratio estimates and 95% confidence intervals of GG-based percentiles of glomerular to nonglomerular children: GG(0.047, 0.121, 3.002) and GG(−0.013, 0.117, 0.903) for children with baseline GFR less than or equal to 45 mL/minute/1.73 m2 (shown in gray) and GG(−0.036, 0.137, 1.450) and GG(−0.017, 0.098, 0.602) for children with baseline GFR greater than 45 mL/minute/1.73 m2 (shown in black). For comparison, the estimated relative differences in and 95% confidence intervals for annual change in GFR for children with glomerular CKD versus those with nonglomerular CKD with baseline GFR less than or equal to 45 mL/minute/1.73 m2 and for children with baseline GFR greater than 45 mL/minute/1.73 m2 using a random intercepts and slopes linear mixed model with log-transformed GFR as the outcome are shown on the right side of the Figure (as thin dashed lines). The nonglomerular CKD reference group is indicated by the horizontal dashed line at 1.0.