Background Few studies are available on how to optimize time points for sampling and how to estimate effects of analytical uncertainty when glomerular filtration rate (GFR) is calculated. Methods We explored the underlying regression mathematics of how analytical variation of a kidney filtration marker affects 1-compartment, slope-and-intercept GFR calculations, using 2 or 3 time points following a bolus injection, and used this to examine the results from 731 routine 3-point iohexol plasma clearance measurements. Results GFR calculations inflated analytical uncertainty if the time points were taken too late after the bolus injection and too close after each other. The uncertainty in GFR calculation was, however, the same as the analytical uncertainty if optimal time points were used. The middle of the 3 samples was of little value. The first sample should be taken as early as possible after the distribution phase. Sampling before the patient specific half-life of the kidney filtration marker resulted in an exponential error inflation whereas no error inflation was seen when sampling occurred later than 2 half-lives. Theoretical GFR uncertainty could be lowered 2.6-fold if individually optimized time points for sampling had been used in our 731 clearance measurements. Using Taylor expansions to approximate the moments of transformed random variables, the uncertainty of an individual GFR measurement could be calculated in a simple enough way to be applicable by laboratory software. Conclusions We provide a theoretical foundation to select patient-optimal time points that may both limit errors and allow calculation of GFR uncertainty.

中文翻译：

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估算肾小球滤过率测量的分析误差

背景 在计算肾小球滤过率 (GFR) 时，关于如何优化采样时间点以及如何估计分析不确定性的影响的研究很少。方法 我们使用推注后的 2 或 3 个时间点探索了肾脏滤过标志物的分析变异如何影响 1 室、斜率和截距 GFR 计算的基本回归数学，并用它来检查 731 例程的结果3 点碘海醇血浆清除率测量。结果 如果时间点在快速注射后太晚并且彼此太接近，则 GFR 计算会夸大分析不确定性。然而，如果使用最佳时间点，GFR 计算的不确定性与分析不确定性相同。3个样本中间的价值不大。第一个样本应在分发阶段后尽早采集。在肾滤过标记物的患者特定半衰期之前取样导致指数误差膨胀，而当取样发生在 2 个半衰期之后时，没有观察到误差膨胀。如果在我们的 731 清除测量中使用了单独优化的采样时间点，则理论 GFR 不确定性可以降低 2.6 倍。使用泰勒展开来近似转换后的随机变量的矩，单个 GFR 测量的不确定性可以以一种足够简单的方式计算，以供实验室软件应用。结论 我们为选择患者最佳时间点提供了理论基础，这些时间点既可以限制错误又可以计算 GFR 不确定性。