Estimating glomerular filtration rate for the full age spectrum from serum creatinine and cystatin C
根据血清肌酐和胱抑素 C 估算全年龄范围的肾小球滤过率

Abstract 抽象的

INTRODUCTION 介绍

Serum creatinine (Scr)-based estimating glomerular filtration rate (eGFR) equations are commonly used and reported when Scr is measured. Despite the worldwide acceptance of isotope dilution mass spectrometry (IDMS)-standardized Scr assays, Scr-based eGFR equations are still relatively imprecise [1]. Also, different equations are proposed for children, adults and older adults as most equations lack continuity and accuracy across the full age spectrum.
在测量 Scr 时，通常使用和报告基于血清肌酐 (Scr) 的估算肾小球滤过率 (eGFR) 方程。尽管全世界都接受同位素稀释质谱 (IDMS) 标准化 Scr 测定，但基于 Scr 的 eGFR 方程仍然相对不精确 [1]。此外，针对儿童、成人和老年人提出了不同的方程，因为大多数方程在整个年龄范围内缺乏连续性和准确性。

We recently published a Scr-based full-age-spectrum (FAS_crea) equation [2] that has been validated in a large number of healthy and kidney–diseased white individuals (n = 6870) including 735 children, 4371 adults and 1764 older adults against measured GFR (mGFR) and using IDMS-equivalent Scr. The FAS_crea equation showed improved validity and continuity across the full age spectrum and was less biased and more accurate than the currently recommended Scr-based eGFR equations.
我们最近发表了一个基于 Scr 的全年龄谱 (FAS _crea ) 方程 [2]，该方程已在大量健康和患有肾病的白人 (n = 6870) 中得到验证，其中包括 735 名儿童、4371 名成人和 1764 名老年人对照测量的 GFR (mGFR) 并使用 IDMS 等效 Scr。 FAS _crea 方程在整个年龄范围内显示出更高的有效性和连续性，并且比目前推荐的基于 Scr 的 eGFR 方程偏差更小、更准确。

The FAS equation is based on three fundamental assumptions:
FAS 方程基于三个基本假设：

• The average GFR for healthy populations (children, adolescents and young adults) is equal to a value of 107.3 mL/min/1.73 m² after kidney function matures (around 2 years of age) until the age of 40 years. This assumption is also supported by the results of a recent meta-analysis in living kidney donors [3].
  健康人群（儿童、青少年和青壮年）肾功能成熟后（2岁左右）至40岁期间的平均GFR等于107.3 mL/min/1.73 m ² 年。最近对活体肾脏捐赠者进行的荟萃分析结果也支持了这一假设[3]。

• The age decline of GFR begins at around 40 years.
  GFR 的年龄下降从 40 岁左右开始。

• GFR and population-normalized Scr (Scr/Q_crea) are inversely related (Q_crea being the mean or median Scr concentration of the corresponding age-/sex-matched healthy population).
  GFR 和人群标准化 Scr (Scr/Q _crea ) 呈负相关（Q _crea 是相应年龄/性别匹配的健康人群的平均或中位 Scr 浓度）。

The equation is simple and intuitive and can be easily explained: when Scr/Q_crea deviates from ‘1’, the eGFR will deviate from the average value of 107.3 mL/min/1.73 m². Scr/Q_crea, for every healthy age-/sex-matched population, is normally distributed (Gaussian distribution) around the mean of ‘1’ (a consequence of the definition of Q_crea). It has been shown that the 2.5th percentile (Pct) = 0.67 and the 97.5th Pct = 1.33, or, equivalently, the standard deviation (SD) is 0.1683 [2].
该方程简单直观，易于解释：当 Scr/Q _crea 偏离“1”时，eGFR 将偏离平均值 107.3 mL/min/1.73 m ² 呈正态分布（高斯分布），均值“1”（Q _crea ).研究表明，第 2.5 个百分位数 (Pct) = 0.67，第 97.5 个百分位数 = 1.33，或者等效地，标准差 (SD) 为 0.1683 [2]。

Serum cystatin C (ScysC) is considered to be a potential alternative to Scr for estimating GFR [4], especially since a certified reference cystatin C material became available in 2010, allowing standardization of ScysC assays [5].
血清胱抑素 C (ScysC) 被认为是估算 GFR 时 Scr 的潜在替代品 [4]，特别是自 2010 年获得认证的参考胱抑素 C 材料问世以来，ScysC 测定得以标准化 [5]。

In this article, we demonstrate that the last assumption (that GFR is inversely related to the normalized Scr biomarker) also applies to ScysC, if properly normalized. We show that the FAS_crea equation can be transformed into a ScysC-based FAS equation (FAS_cysC) and a combined Scr-/ScysC-based FAS equation (FAS_combi), by simply replacing the normalized Scr (Scr/Q_crea) by ScysC/Q_cysC or by the combination of Scr/Q_crea and ScysC/Q_cysC [i.e. the (weighted) average of Scr/Q_crea and ScysC/Q_cysC], where Q_cysC is the normalization factor for ScysC.
在本文中，我们证明了最后一个假设（GFR 与标准化 Scr 生物标志物成反比）也适用于 ScysC（如果正确标准化）。我们证明 FAS _crea 方程可以转换为基于 ScysC 的 FAS 方程 (FAS _cysC ) 和基于 Scr/ScysC 的组合 FAS 方程 (FAS _combi 或 Scr/Q _crea 的组合替换标准化 Scr (Scr/Q _crea ) 和ScysC/Q _cysC [即Scr/Q _crea 和 ScysC/Q _cysC 的（加权）平均值]，其中 Q _cysC 是 ScysC 的归一化因子。

In the first part of this study, we give a rationale for choosing the normalization factor Q_cysC for ScysC. Next, we validate the FAS_cysC and FAS_combi equation against mGFR and compare the performance of these equations with the currently recommended and most used eGFR equations (Schwartz_cysC [6], Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI_cysC) [4], Caucasian Asian Paediatric Adult Cohort equation (CAPA) [7], combined CKD-EPI_combi [4] and BIS2 [8]). Finally, we evaluate the performance of all FAS equations (by varying the weighting factors for the normalized biomarkers) in all age groups.
在本研究的第一部分中，我们给出了为 ScysC 选择归一化因子 Q _cysC 的基本原理。接下来，我们根据 mGFR 验证 FAS _cysC 和 FAS _combi 方程，并将这些方程的性能与当前推荐和最常用的 eGFR 方程进行比较 (Schwartz _cysC [6]、慢性肾脏病流行病学协作方程（CKD-EPI _cysC ）[4]、高加索亚裔儿科成人队列方程（CAPA）[7]、组合 CKD-EPI _combi [ 4] 和 BIS2 [ 8]）。最后，我们评估了所有年龄组中所有 FAS 方程的表现（通过改变标准化生物标志物的权重因子）。

MATERIALS AND METHODS 材料和方法

Overview of study design and participants
研究设计和参与者概述

We collected data from 11 cohorts, forming a representative sample of the general population and renal disease patients. For the same six cohorts (Saint-Etienne, Tromsø, Rochester and Minnesota for adults; Kent and Berlin for older adults [2]) that were used for the validation of the FAS_crea equation, we additionally collected the ScysC results. The other cohorts used in the previous validation did not have ScysC data available, and, therefore, we collected data of new cohorts. For children, adolescents and young adults (<21 years), one cohort came from the University Hospital in Leuven (n = 114), and one from Lyon (n = 695). Both cohorts contained children and adolescents with established renal pathologies. The data from Leuven contained single-time point measurements per child and the data from Lyon (n = 695) were from 259 children with serial measurements over a period of several years, but we used the first measurement only. We further collected data from a cohort of healthy and renal disease adults from Paris (n = 603), from Lyon (n = 598) and from the Chronic Renal Insufficiency Cohort (CRIC; n = 3939) [9], which we restricted to whites only (n = 1824) and to the first visit where all required variables were available (n = 674). All datasets were centralized by the first author for data analysis. This retrospective non-interventional study was approved by the Institutional Ethical Board of the University Hospital of Leuven, Belgium.
我们收集了 11 个队列的数据，形成了一般人群和肾病患者的代表性样本。对于用于验证 FAS _crea 方程的相同六个队列（成年人为圣艾蒂安、特罗姆瑟、罗切斯特和明尼苏达；老年人为肯特和柏林 [2]），我们还收集了ScysC 结果。先前验证中使用的其他队列没有可用的 ScysC 数据，因此，我们收集了新队列的数据。对于儿童、青少年和年轻人（<21 岁），一组来自鲁汶大学医院 (n = 114)，一组来自里昂 (n = 695)。两个队列均包含患有明确肾脏病变的儿童和青少年。鲁汶的数据包含每个儿童的单时间点测量结果，里昂的数据 (n = 695) 来自 259 名儿童，在几年内进行了连续测量，但我们仅使用了第一次测量。我们进一步收集了来自巴黎（n = 603）、里昂（n = 598）和慢性肾功能不全队列（CRIC；n = 3939）的健康和肾脏疾病成年人队列的数据[9]，我们将其限制为仅白人 (n = 1824) 和第一次访问时所有必需的变量均可用 (n = 674)。所有数据集均由第一作者集中进行数据分析。这项回顾性非干预性研究得到了比利时鲁汶大学医院机构伦理委员会的批准。

In total, we collected data on mGFR, Scr, ScysC, age, gender, height and weight for n = 6132 participants (n = 368 children aged between 1 and 18 years; n = 4295 adults aged between 18 and 70 years and n = 1469 older adults aged ≥70 years).
总的来说，我们收集了 n = 6132 名参与者的 mGFR、Scr、ScysC、年龄、性别、身高和体重的数据（n = 368 名 1 至 18 岁的儿童；n = 4295 名 18 至 70 岁的成年人，n = 1469 名年龄≥70 岁的老年人）。

We further used a separate cohort (n = 1333) from the Berlin Initiative Study [8] of apparently healthy older subjects to study the age dependency of the ScysC distribution. This cohort was obtained from 2069 subjects (2069 baseline samples and 1693 follow-up samples) aged >70 years (Berlin residents), which we reduced to a subset of 1333 individuals who were defined as apparently healthy; i.e. no history of myocardial infarction, no history of stroke, not on dialysis, not deceased between first and second follow-up study visit, no albuminuria (ACR <30 mg/g), arterial blood pressure <160/90 mmHg.
我们进一步使用来自柏林倡议研究 [8] 的一个单独的队列 (n = 1333)，该队列由明显健康的老年受试者组成，以研究 ScysC 分布的年龄依赖性。该队列来自年龄 > 70 岁（柏林居民）的 2069 名受试者（2069 名基线样本和 1693 名随访样本），我们将其减少到 1333 名被定义为表面健康的个体的子集；即无心肌梗塞病史、无中风病史、未进行透析、在第一次和第二次随访研究访视期间未死亡、无蛋白尿（ACR <30 mg/g）、动脉血压<160/90 mmHg。

Methods 方法

The new FAS equation(s)
新的 FAS 方程

mGFR, Scr and cystatin C assays
mGFR、Scr 和胱抑素 C 检测

A summary of the methods used in the different collaborating centres is given in Tables 1 and 2. Direct GFR measurements were obtained with different reference methods as described previously [2, 10]. Scr was measured with an enzymatic assay, equivalent to IDMS, or directly with IDMS, or recalculated to the enzymatic assay, in all centres. ScysC was measured with the calibrated particle-enhanced nephelometric (PENIA) method of Siemens in Saint-Etienne, Berlin and partially in Lyon. The ScysC measurements for the CRIC Study were done with the non-calibrated PENIA assay of Siemens, but calculated back to the certified reference material, as previously described [4]. The non-calibrated PENIA assay of Siemens was also used in Rochester, Kent, and partially in Lyon, and the results were recalculated to the certified reference standard, using the multiplication factor in Rochester [11] and in Lyon and Kent [12], according to the manufacturer’s specifications. Tromsø used the non-calibrated (with back calculation) and Leuven used the calibrated particle-enhanced turbidimetric (PETIA, Tina quant®) assay of Roche (Tables 1 and 2).
表 1 和表 2 总结了不同合作中心使用的方法。直接 GFR 测量是使用先前所述的不同参考方法获得的 [2, 10]。在所有中心，Scr 均采用相当于 IDMS 的酶测定法进行测量，或直接使用 IDMS 进行测量，或根据酶测定法重新计算。 ScysC 采用西门子在圣艾蒂安、柏林和里昂的校准颗粒增强散射比浊法 (PENIA) 进行测量。 CRIC 研究的 ScysC 测量是使用西门子的非校准 PENIA 测定完成的，但计算回经过认证的参考材料，如前所述 [4]。西门子的非校准 PENIA 测定法也在罗切斯特、肯特以及里昂的部分地区使用，并且使用罗切斯特 [11] 以及里昂和肯特 [12] 的倍增因子将结果重新计算为经过认证的参考标准，根据制造商的规格。特罗姆瑟使用未校准（带反算），鲁汶使用罗氏的校准颗粒增强比浊法（PETIA、Tina quant®）测定法（表 1 和表 2）。

eGFR equations eGFR 方程

The new FAS_cysC equation and the FAS_combi equation were compared and validated against mGFR and against the currently available and recommended eGFR equations listed in Table 3.
新的 FAS _cysC 方程和 FAS _combi 方程针对 mGFR 以及表 3 中列出的当前可用和推荐的 eGFR 方程进行了比较和验证。

Statistical analysis 统计分析

The performance statistics are presented as constant bias (mean of eGFR–mGFR) and proportional bias (mean of eGFR/mGFR), root mean square error (RMSE) of prediction, Lin’s concordance correlation coefficient (Lin’s CCC, which is a measure of both correlation and agreement as it evaluates the degree to which pairs of observations fall on the identity line), P10 and P30 (the percentage of subjects within 10% and 30% of mGFR), for the different age groups, total and in subgroups according to mGFR <60 and ≥60 mL/min/1.73 m². McNemar’s test is used to compare P30 among equations.
性能统计数据以恒定偏差（eGFR–mGFR 的平均值）和比例偏差（eGFR/mGFR 的平均值）、预测均方根误差 (RMSE)、Lin 的一致性相关系数 (Lin 的 CCC，这是两者的度量) 的形式呈现。相关性和一致性，因为它评估了观察对落在同一线上的程度）、P10 和 P30（mGFR 10% 和 30% 范围内的受试者百分比），对于不同年龄组、总数和亚组，根据mGFR <60 且≥60 mL/min/1.73 m ² 。 McNemar 检验用于比较方程之间的 P30。

RESULTS 结果

Description of the cohorts
群组描述

Summary statistics for the patient characteristics of the 11 cohorts are given in Tables 4 and 5, and are described in Supplementary data.
表 4 和表 5 给出了 11 个队列的患者特征的汇总统计数据，并在补充数据中进行了描述。

Rationale for Q_cysC values for ScysC
ScysC 的 Q _cysC 值的基本原理

To define normalization factors for ScysC we searched the literature for normal reference ranges and we investigated whether these ranges depend on age or gender differences. We realized that the literature before the year 2010 was based on non-standardized cystatin C assays, but, in general, ScysC is independent of age (up to age 70 years) and gender in children, adolescents and adults [14–16], although there might be small differences between sexes and races [17]. We used the value of 0.82 mg/L as the normalization factor, as it is the middle of the normal reference interval for children, adolescents and adults up to ∼70 years (and in line with the manufacturer’s information on reference ranges) [8, 18]. The ScysC-based CKD-EPI equation normalized ScysC by 0.80 for both males and females [4], a value that is close to the proposed value of 0.82 in this study. The new CAPA equation does not have a gender factor in the equation, suggesting that the same Q_cysC normalization constant can be used for both sexes [7]. For older adults, we could not find normal reference ranges in the literature. In our dataset of 1333 apparently healthy older persons aged >70 years from the Berlin Initiative Study, we modelled Q_cysC as a linear function of age: Q_cysC=0.01704 × Age – 0.3384 = 0.863 + 0.01704 × (Age – 70) (R²=0.919; see Figure 1). At the age of 67.5 years, the corresponding value of Q_cysC=0.82. Therefore, we defined the Q_cysC normalization factor for cystatin C as 0.82 mg/L until the age of 70 years and then Q_cysC gradually (and linearly) increases (Figure 1). The mode of the ScysC distribution (Figure 2) of the n = 1333 apparently healthy subjects was 0.95 mg/L. Based on this analysis, and for the sake of simplicity, we fixed Q_cysC to 0.82 mg/L for all ages <70 years and to 0.95 mg/L for older ages.
为了定义 ScysC 的标准化因子，我们在文献中搜索了正常参考范围，并研究了这些范围是否取决于年龄或性别差异。我们意识到 2010 年之前的文献基于非标准化的半胱氨酸蛋白酶抑制剂 C 测定，但一般来说，ScysC 与儿童、青少年和成人的年龄（最高 70 岁）和性别无关[14-16]，尽管性别和种族之间可能存在细微差异[17]。我们使用 0.82 mg/L 的值作为标准化因子，因为它是 70 岁以下儿童、青少年和成人正常参考区间的中间值（并且与制造商关于参考范围的信息一致）[8， 18]。基于 ScysC 的 CKD-EPI 方程将男性和女性的 ScysC 归一化为 0.80 [4]，该值接近本研究中建议的 0.82 值。新的 CAPA 方程中没有性别因素，这表明相同的 Q _cysC 归一化常数可用于两种性别 [7]。对于老年人，我们在文献中找不到正常的参考范围。在柏林倡议研究中 1333 名年龄 > 70 岁、表面健康的老年人的数据集中，我们将 Q _cysC 建模为年龄的线性函数：Q _cysC =0.01704 × 年龄 – 0.3384 = 0.863 + 0.01704 ×（年龄 – 70）（R ² =0.919；见图 1）。 67.5岁时，对应的Q _cysC 值=0.82。因此，我们将胱抑素 C 的 Q _cysC 标准化因子定义为 0.82 mg/L，直至 70 岁，然后 Q _cysC 逐渐（线性）增加（图 1）。 n = 1333 名表面健康受试者的 ScysC 分布众数（图 2）为 0.95 mg/L。 基于此分析，为了简单起见，我们将所有年龄 <70 岁的 Q _cysC 固定为 0.82 mg/L，将较大年龄的 Q _cysC 固定为 0.95 mg/L。

FIGURE 1 图1

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(a) The linear relationship between median (solid black circles) ScysC and age for the n = 1333 apparently healthy Berlin Initiative Study participants (grey circles). (b) Histogram for ScysC measurements of n = 1333 apparently healthy older adults.
(a) n = 1333 名表面健康的柏林倡议研究参与者（灰色圆圈）的中位数（实心黑色圆圈）ScysC 与年龄之间的线性关系。 (b) n = 1333 名表面健康的老年人的 ScysC 测量直方图。

FIGURE 2 图2

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RMSE as a function of the weighting factor α for children [based on Q(height)], adults and older adults. The total RMSE for all n = 6132 measurements is also shown. For children the FAS_cysC equation has smaller RMSE than the FAS_crea equation. For adults there is a slightly smaller RMSE for the single biomarker FAS_crea equation compared with the single marker FAS_cysC equation. For older adults there is no real preference for the value of α. For all age groups the RMSE is minimal for α  ≈ 0.5 (= combined FAS equation).
RMSE 是儿童 [基于 Q（身高）]、成人和老年人的权重因子 α 的函数。还显示了所有 n = 6132 次测量的总 RMSE。对于儿童，FAS _cysC 方程的 RMSE 小于 FAS _crea 方程。对于成人，与单标记 FAS _cysC 方程相比，单生物标记 FAS _crea 方程的 RMSE 稍小。对于老年人来说，对于 α 的值没有真正的偏好。对于所有年龄组，RMSE 最小，α ≈ 0.5（= 组合 FAS 方程）。

Performance results of the different equations
不同方程的性能结果

The performance statistics for the three FAS equations for the different age groups are presented in Tables 6–8. The FAS_crea equation [for children in two versions, based on Q_crea(age) and Q_crea(height)] is compared with the relevant Scr-based recommended equations (Schwartz for children, CKD-EPI for adults, BIS1 for older adults). The FAS_cysC equation is compared with the ScysC-based Schwartz equation (for children), the CAPA equation (for all ages) and ScysC-based CKD-EPI equation (for adults). Finally, the FAS_combi equation is compared with the combined CKD-EPI equation (for adults and older adults) and the combined BIS2 equation for older adults. To our knowledge, there is no combined equation for children available yet (based on the certified reference material). Tables 6–8 are presented for all subjects within each age group, but also for subgroups according to the mGFR threshold of 60 mL/min/1.73 m².
表 6-8 列出了不同年龄组的三个 FAS 方程的表现统计数据。 FAS _crea 方程[针对两个版本的儿童，基于 Q _crea （年龄）和 Q _crea （身高）] 与相关 Scr-基于推荐方程（儿童为 Schwartz，成人为 CKD-EPI，老年人为 BIS1）。将 FAS _cysC 方程与基于 ScysC 的 Schwartz 方程（针对儿童）、CAPA 方程（针对所有年龄段）和基于 ScysC 的 CKD-EPI 方程（针对成人）进行比较。最后，将 FAS _combi 方程与组合 CKD-EPI 方程（针对成人和老年人）以及针对老年人的组合 BIS2 方程进行比较。据我们所知，目前还没有适用于儿童的组合方程（基于经过认证的参考材料）。表 6-8 列出了每个年龄组内的所有受试者，也列出了根据 60 mL/min/1.73 m ² mGFR 阈值的亚组。