Author: Qian Sun, PhD, Assistant Professor of Pathology, William Beaumont School of Medicine, Oakland University
Low-density lipoprotein cholesterol (LDL-C), a key cardiovascular disease marker, is often estimated by the Friedewald or Martin equation. However, the calculated LDL-C in this way is less accurate in patients with low LDL-C levels or hypertriglyceridemia (triglyceride [TG] levels ≥400 mg/dL). Dr. Qian Sun and her colleagues developed a new equation to calculate LDL-C for these patients based on a large set of blood lipid test results (1).
The study used a de-identified dataset from 8,656 fasting patients tested on multiple occasions at the National Institutes of Health Clinical Center between January 1, 1976, and June 2, 1999. The dataset included results of β-quantification for LDL-C, a reference test method. Test results of LDL-C (n = 18715) and other lipids were randomly divided into equally sized training and validation datasets. Using TG and non-high-density lipoprotein cholesterol as independent variables, multiple least squares regression was used to establish an equation for very low-density lipoprotein cholesterol [VLDL-C] (Equation 1). Based on Equation 1, another equation for LDL-C was established (Equation 2).
Equation 1
Equation 2
The New equations were tested against the internal validation dataset, as well as multiple external datasets of either β-quantification LDL-C results or direct LDL-C test results.
Compared with β-quantification, the new equation was more accurate than other LDL-C equations: slope, 0.964; root mean square error (RMSE) = 15.2 mg/dL; R2 = 0.9648; vs Friedewald equation: slope, 1.056; RMSE = 32 mg/dL; R2 = 0.8808; vs Martin equation: slope, 0.945; RMSE = 25.7 mg/dL; R2 = 0.9022. Particularly, for patients with hypertriglyceridemia, compared with β-quantification, the new equation: mean absolute difference (MAD) = 24.9 mg/dL; vs Friedewald equation: MAD = 56.4 mg/dL; vs Martin equation: MAD = 44.8 mg/dL. The new equation was able to achieve same-level accuracy when calculating the LDL-C level with TG levels up to 800 mg/dL as the Friedewald equation did with TG levels less than 400 mg/dL. It could result in 35% fewer misclassifications, which were defined as patients with hypertriglyceridemia (TG levels, 400-800 mg/dL) categorized into different LDL-C treatment groups.
The new equation can be readily implemented by clinical laboratories with no additional costs compared with the standard lipid panel. It will allow for more accurate calculation of LDL-C level in patients with low LDL-C levels and/or hypertriglyceridemia (TG levels, ≤800 mg/dL) and thus should improve the use of LDL-C level in cardiovascular disease risk management. So far, the major reference laboratories LabCorp and Mayo Clinic Lab have adopted this new equation.
Recognizing the limitation of the conventional Friedewald equation in hypertriglyceridemic individuals and its inaccuracy in the low range of LDL-C, cardiology societies in both the US and Europe have recommended alternative LDL-C calculations (2). In addition to the equation introduced in this article, the Martin equation that can be licensed from John Hopkins uses table search to report estimated LDL-C derived from ultracentrifugation measurement (3). Both can be considered to fill in the vacancy left behind after the future retirement of the Friedewald equation.
计算正常以及高甘油三酯血症患者低密度脂蛋白胆固醇的一个新方程
低密度脂蛋白胆固醇 (LDL-C) 是一种关键的心血管疾病标志物，通常通过 Friedewald 或 Martin公式进行估算。然而，在LDL-C水平较低或高甘油三酯血症（甘油三酯[TG]水平≥400毫克/分升）的患者中，通过这种方式计算的LDL-C不够准确。这些患者需要更准确的 LDL-C计算公式。
孙倩博士和她的同事们根据大量的血脂检测结果，开发了一个新的公式来计算上述患者的LDL-C (1)。LDL-C 的β定量结果来自于 1976年1月1日至 1999年6月2日期间在美国国立卫生研究院临床中心多次测试的 8656 名空腹患者的去识别数据集（β-定量是LDL-C 的参考测试方法）。LDL-C (n = 18715) 和其他脂质的测试结果被随机分为大小相等的训练数据集和验证数据集。使用 TG 和非高密度脂蛋白胆固醇作为自变量，使用多元最小二乘回归建立极低密度脂蛋白胆固醇 [VLDL-C] 的公式（公式 1）。基于公式1，建立了 LDL-C 的另一个公式（公式2）。
公式 1
公式2
针对内部验证数据集以及 β-定量的 LDL-C 结果或直接 LDL-C 测试结果的多个外部数据集对公式进行了测试。
与β-定量相比，新公式比其他LDL-C计算公式更准确：斜率，0.964；RMSE (均方根误差) = 15.2 mg/dL；R2 = 0.9648；对比Friedewald 公式：斜率，1.056；RMSE = 32 mg/dL；R2 = 0.8808；对比Martin公式：斜率，0.945；RMSE = 25.7 mg/dL；R2 = 0.9022。特别是对于高甘油三酯血症患者：MAD (平均绝对差) = 24.9 mg/dL；对比Friedewald公式：MAD = 56.4 mg/dL；对比 Martin公式：MAD = 44.8 mg/dL。在TG水平高达 800 mg/dL 时去计算 LDL-C 水平，新方程能够达到与Friedewald公式在 TG水平低于 400 mg/dL时所做的相同水平的准确性。 它可以减少 35% 的错误分类，错误分类被定义为高甘油三酯血症（TG水平，400-800 mg/dL）患者被分类到不同的 LDL-C治疗组。
与标准血脂检测相比，新公式可以很容易地由临床实验室实施，无需额外费用。新公式可以更准确地计算低 LDL-C水平和/或高甘油三酯血症（TG水平≤800 mg/dL）患者的 LDL-C水平，这应该有助于改善LDL-C水平在心血管疾病风险管理中的应用。到目前为止，主要参考实验室LabCorp和 Mayo Clinic Lab都采用了这个新的LDL-C计算公式。
认识到传统 Friedewald 公式在高甘油三酯血症个体中的局限性及其在低水平LDL-C内的不准确性，美国和欧洲的心脏病学会都推荐了替代的 LDL-C计算方法 (2)。除了本文介绍的公式外，Martin公式（可以从John Hopkins获得使用许可）通过表格搜索来估算基于超速离心测量的LDL-C数值 (3)。两者都可以被考虑用来填补未来Friedewald公式退役后留下的空缺。
Acknowledgements
We thank Dr. Jing Cao for revising the article.
References
1. Sampson M, Ling C, Sun Q, Harb R, Ashmaig M, Warnick R, et al. A New Equation for Calculation of Low-Density Lipoprotein Cholesterol in Patients With Normolipidemia and/or Hypertriglyceridemia. JAMA Cardiol 2020;5:540-8.
2. Langlois MR, Nordestgaard BG, Langsted A, Chapman MJ, Aakre KM, Baum H, et al. Quantifying atherogenic lipoproteins for lipid-lowering strategies: consensus-based recommendations from EAS and EFLM. Clin Chem Lab Med 2020;58:496-517.
3. Sajja A, Park J, Sathiyakumar V, Varghese B, Pallazola VA, Marvel FA, et al. Comparison of Methods to Estimate Low-Density Lipoprotein Cholesterol in Patients With High Triglyceride Levels. JAMA Netw Open 2021;4:e2128817.