Research Letter: Revisiting the application of an adult kidney failure risk prediction equation to children with chronic kidney disease

The Kidney Failure Risk Equation (KFRE) is a widely validated equation to predict end-stage kidney disease (ESKD) for adults with mild-to-moderate chronic kidney disease (CKD), developed in a geriatric cohort.¹ The KFRE was applied to the Chronic Kidney Disease in Children (CKiD) cohort, yielded good discrimination², and was recommended for pediatric practice³, despite heterogeneous CKD etiologies and progression in children. This analysis only presented limited assessment of calibration, which is the other metric, along with discrimination, necessary for instrument validation, and this deserves particular attention in the application of an adult instrument for children.

While discrimination summarizes the ability of the prognostic test to ascribe a higher risk score to those with the event compared to those without the event, calibration refers to the congruency between predicted and observed risk. Calibration performance is often underreported⁴ and poorly calibrated instruments, even with good discrimination, can misinform and negatively impact decision-making⁵. To quantify calibration of the KFRE in children with CKD, we used a formal statistical test (Greenwood Nam-D’Agostino (GND) goodness-of-fit⁶) in CKiD data enhanced by additional follow-up and observed ESKD events.

CKiD is a North American longitudinal cohort of children with CKD with a primary endpoint of ESKD, defined as kidney transplant or dialysis. We replicated the analytic structure in which the KFRE was first assessed², with an additional 214 participants, extended follow-up, and estimation of albuminuria using pediatric-based equations⁷.

The KFRE 2- and 5-year risk of ESKD based on the 4-variable and 8-variable equations were calculated at the first visit when eGFR⁸ <60 ml/min|1.73m² and all predictors were available. Albuminuria was measured centrally, and if unavailable, was estimated using validated equations⁷.

Calibration plots and the goodness-of-fit GND test for survival data evaluated calibration. Using g bins based on similar KFRE 2-year and 5-year probabilities of ESKD with at least 5 events per bin⁶, the GND test compares the predicted (expected) risk with the observed risk estimated by 1 - Kaplan-Meier (KM) failure probability for the gth bin at time t and incorporates the variance of KM_g(t). Under the null hypothesis, the test statistic follows a chi-square distribution with (g-1) degrees of freedom with α=0.05. Discrimination was quantified by the c-statistic. All analyses were conducted in R.4.0.

Table 1 presents clinical characteristics of the cohort. A total of 817 children (median age=10.6 years, IQR: 5.9, 1.4) with a median GFR of 44 ml/min|1.73m² (IQR: 33, 52) provided complete data to calculate 4-variable KFRE. Of these, 75% were followed >2.1 years, and 81 and 189 ESKD events by 2 and 5 years, respectively. 799 participants had complete data for 8-variable calculation. No deaths were observed within 5 years of follow-up.

Table 1.

Clinical characteristics of participants in the Chronic Kidney Disease in Children (CKiD) study. Median [interquartile range] or n (%).

Variable	CKiD participants n=817
4-variable KFRE predictors
Age, years	10.6 [5.9, 14.3]
Male sex	509 (62%)
U25 Estimated GFR, ml/min|1.73m2	44 [33, 52]
Albuminuriaa, mg/g	156 [35, 522]
Additional predictors for 8-variable KFRE b
Serum albumin, mg/dL	4.3 [4.1, 4.6]
Serum phosphate, mg/dL	4.5 [4.1, 5.0]
Serum bicarbonate, mmol/L	23 [20, 25]
Serum calcium, mg/dL	9.6 [9.3, 9.9]
Chronic kidney disease characteristics
Nonglomerular (congenital) CKD diagnosis	627 (77%)
Urine protein-creatinine ratio, mg/g	450 [180, 1310]
Nephrotic range proteinuria, >2000 mg/g	135 (17%)
Longitudinal data and outcomes
Median duration of follow-up, years	4.6 [2.1, 9.3]
ESKD within 2 years	81 (10%)
ESKD within 5 years	189 (23%)

^aWhen direct measured albuminuria was not available, albuminuria was estimated from total urine protein (489 of 817= 60%).

^b18 had missing serum biomarker levels and were excluded (n= 799).

Figure 1 presents the observed risk (1-KM(2) and 1-KM(5)) on KFRE predicted 2- and 5-year risk, for the 4-variable (Figure 1A and 1B) and 8-variable equations (Figure 1C and 1D), respectively. For the 2-year KFRE (4- and 8-variables), the KFRE overestimated observed risk, among those with higher KFRE scores. In the 5-year equation, the KFRE underestimated risk at lower predicted probabilities and overestimated risk at higher probabilities (Fig. 1B, 1D). For all four equations, the predicted KFRE risk was significantly different than the observed risk (p<0.001) indicating poor calibration. Similar results and inferences were observed in sensitivity analyses: stratified by glomerular/non-glomerular diagnoses and restricted to measured albuminuria only (Supplemental Material). Discrimination was high (c-statistic between 0.814 and 0.871).

Figure 1.

Calibration plots comparing the predicted probability of ESKD and the Kaplan-Meier failure probability within groups of KFRE predicted probabilities for 2-year and 5-year 4-variable equations (Figure 1A and 1B, respectively) and 8-variable equations (Figure 1C and 1D, respectively). The Greenwood Nam-D’Agostino (GND) test statistic and the c-statistic for each equation is reported.

The KFRE demonstrated poor calibration for both the 2-year and 5-year risk of ESKD in this external cohort. This was despite strong discrimination (which replicated previous results²) and underscores the distinction between calibration and discrimination as two necessary but disparate measures of validity. The KFRE predictors are key biomarkers related to CKD progression in both children and adults which explains why discrimination was high. Specifically, GFR is often used to decide to initiate the kidney replacement therapy process.

In addition to poor calibration, there are epidemiologic considerations when deciding to apply the KFRE to a pediatric CKD population. The interpretation of the KFRE age coefficient is that as age increases, the risk of ESKD decreases (i.e., 20% lower hazard per 10-year age increase). In marked contrast, pediatric patients with CKD are known to experience increasing ESKD risk with older age.⁹ The KFRE was also developed among older adults with CKD (average age: 70 years) with stark differences in etiology and natural history compared to a young pediatric CKD population with mostly congenital kidney or urinary tract diseases. Another structural incongruity is that the 8-variable KFRE includes absolute level of phosphorus, yet normative phosphorous levels differ substantially between children and adults.

Prognostic tools are critical for clinical management of CKD. Clinicians should therefore have confidence that equations they use are designed for, and specific to, their patient population, with both strong discrimination and calibration, especially for children. Despite valid application across adult populations, the KFRE had poor calibration in children with CKD but may be suitable if only discrimination were of interest. For pediatric clinical settings where calibration is necessary, we recommend pediatric-specific ESKD risk prediction calculators¹⁰.