The Friedewald formula strikes back

The Friedewald formula introduced in 1972 is based on total cholesterol, high-density lipoprotein cholesterol (HDL-C), and very low-density lipoprotein cholesterol (VLDL-C) for estimating low-density lipoprotein cholesterol (LDL-C) concentration and is still the most popular method used in clinical laboratories worldwide [1]. Since VLDL-C is not measured directly, it is estimated by dividing triglycerides (TG) by 2.2 (mmol/L) or 5 (mg/dL). However, this estimation is increasingly inaccurate as TG concentrations rise above 2.3 mmol/L (200 mg/dL) and in chylomicronemia because it overestimates VLDL-C and, consequently, underestimates LDL-C particularly at low LDL-C concentrations, potentially leading to undertreatment [2]. To account for this, the equation is not used at TG >4.5 mmol/L (400 mg/dL) and in non-fasting samples. In Type 3 hyperlipidemia (dysbetalipoproteinemia) characterized by cholesterol-enriched VLDL remnant particles, VLDL-C is underestimated [1].

To overcome the aforementioned limitations, newer LDL-C calculations including the Martin-Hopkins equation and Sampson equation have been proposed as alternatives. Instead of a fixed ratio for the estimation of VLDL-C, an adjustable TG:VLDL-C factor based on the patient’s TG and non-HDL-C derived from a 180-cells table is used in the Martin-Hopkins equation [2]. The 2018 American Heart Association and American College of Cardiology (AHA/ACC) guideline and the 2020 joint European Atherosclerosis Society (EAS) and European Federation of Clinical Chemistry and Laboratory Medicine (EFLM) guideline recommended using the Martin-Hopkins equation to improve accuracy of LDL-C estimates especially at LDL-C <1.8 mmol/L (70 mg/dL) and in non-fasting samples [3], 4]. Since at that time the Martin-Hopkins equation was not yet validated for samples with TG >4.5 mmol/L (400 mg/dL), the Sampson equation has been developed at the US National Institutes of Health (NIH) using TG and non-HDL-C in least squares regression for estimating VLDL-C to extend LDL-C calculation to TG concentrations of 9.0 mmol/L (800 mg/dL) [5].

In recent years many publications have reported divergent cardiovascular risk classifications with Friedewald-calculated LDL-C compared to the newer equations. Only a few of these reports are based on comparison of the equations against the LDL-C ultracentrifugation reference method: beta-quantification (BQ). Rather, direct homogeneous assays were used as references, which vary significantly between the different manufacturers [4].

In this issue of Clin Chem Lab Med, Drobnik et al. reports the performances of Friedewald, Martin-Hopkins, and Sampson-NIH calculations against the BQ reference method using data from three cohorts comprising 5,738 datasets [6]. The study revealed that Friedewald equation provided acceptable estimates of LDL-C in most samples, even for LDL-C below 1.8 mmol/L (70 mg/dL). At TG <1.7 mmol/L (150 mg/dL), no clinically significant divergences from Martin-Hopkins or Sampson equations were observed. As TG concentrations increased, Friedewald equation offered the most accurate estimation, followed by Sampson-NIH, while the Martin-Hopkins equation showed positive bias [6].

From these data, the authors conclude that the Friedewald equation remains reliable for estimating LDL-C in routine use, and its replacement by alternative equations is not justified. Their findings align with a previous analysis by Ginsberg et al. of pooled data in 10 ODYSSEY (alirocumab) trials showing that the discrepancy of Friedewald, Martin-Hopkins, and Sampson-NIH calculations with BQ is small and clinically insignificant, with approximately 50 % or greater of LDL-C values differing by less than 0.13 mmol/L (5 mg/dL) even at very low LDL-C [7]. However, at TG >2.8 mmol/L (250 mg/dL) all equations exhibited noticeable discrepancies, whereby the Sampson equation still provided the most accurate estimation [7].

These results are puzzling because they contradict many other previous studies on how the Friedewald equation becomes inaccurate on hypertriglyceridemic samples. The authors’ conclusions based on the study data should be interpreted with caution. Their findings on the relatively good accuracy of the Friedewald equation on hypertriglyceridemic samples maybe a statistical fluke because of the relatively small number of such samples. The majority (75 %) of samples investigated are normotriglyceridemic: interquartile ranges of TG concentrations in the datasets are <2.3 mmol/L (200 mg/dL) [6]. At these concentrations the Friedewald formula is not expected to show major accuracy problems. To justify their conclusion, the authors’ investigation should have more focused on hypertriglyceridemic samples in the range 2.2–4.5 mmol/L (200–400 mg/dL) wherein the Friedewald formula is expected to be less accurate. It is well known that with increasing number of TG-enriched lipoprotein particles the factor for dividing TG to estimate VLDL-C goes up, consistent with the Martin-Hopkins table [2].

The numbers of samples investigated by Drobnik et al. are substantial. However, it is important to recognize that the original studies by Sampson and Martin were conducted on much larger datasets. The Martin-Hopkins equation has been validated against vertical auto profile ultracentrifugation, which is not the gold standard reference method [2]. The Sampson-NIH equation has been validated against the gold standard BQ in a population with high frequency of hypertriglyceridemia and showed greater accuracy at higher TG concentrations 4.5–9.0 mmol/L (400–800 mg/dL) compared with both Friedewald and the original Martin-Hopkins equations [5]. Also an “extended” Martin-Hopkins equation has been developed to extend its range of applicability to TG 9.0 mmol/L (800 mg/dL) – at these levels the Friedewald equation cannot be used [8]. This has been confirmed by verification studies comparing the three equations against BQ in large datasets [5], 9], 10]. In these comparisons, mean absolute difference (MAD) vs. BQ was less than 0.5 mmol/L (20 mg/dL) for all equations up to TG 5.1 mmol/L (450 mg/dL). At higher TG levels, MAD of LDL-C increased to 1.3 mmol/L (50 mg/dL) and more with the Friedewald equation while MAD remained less than 0.8 mmol/L (30 mg/dL) with “extended” Martin-Hopkins and Sampson equations up to TG 11.3 mmol/L (1,000 mg/dL) [5], 9], 10].

Drobnik et al. report that Friedewald equation was not inferior to Sampson and Martin-Hopkins equations in terms of concordance/discordance of risk classification [6]. In the aforementioned previous studies comparing the three LDL-C calculations vs. BQ in larger datasets [5], 9], 10], risk misclassifications were comparable with Martin-Hopkins and Sampson formulas but always better than with Friedewald equation even at TG <4.5 mmol/L (400 mg/dL), which is the range of applicability of the Friedewald equation.

In the study by Drobnik et al., HDL-C was quantified by the ultracentrigation/precipitation method [6]. This is never the case in clinical laboratories where direct HDL-C assays are commonly used and, like direct LDL-C assays, their performance varies across manufacturers’ reagents used [4]. The study data are therefore not representative to real-life routine laboratorv practice. In common practice, HDL-C measured by a direct automated assay is used in the LDL-C equations, and the poor standardization of these assays contributes to bias of the equation vs. ultracentrifugation. Indeed, Rossouw et al. showed that discordant Friedewald, Martin-Hopkins and Sampson calculations are depending on the choice of analytical platform used to measure HDL-C [11].

The Sampson-NIH and Martin-Hopkins formulas are currently not yet in widespread use, probably because of the apparent complexity of implementation in the laboratory information system. Most laboratories continue to use the Friedewald calculation and perform direct LDL-C measurement in patients with TG >4.5 mmol/L (400 mg/dL). Based on the study by Drobnik et al. and its limitations, there is no justification for the authors’ conclusion to consider continuation of this practice. Unlike Friedewald’s equation, the alternative equations can be used in non-fasting samples. Moreover, Sampson and “extended” Martin-Hopkins equations can be used at higher TG up to 9.0 mmol/L (800 mg/dL), obviating the need for direct LDL measurements in these patients [5], 8]. An “enhanced” Sampson-NIH equation developed by including apolipoprotein B (apoB) as independent variable in the equation, yielded nearly perfect agreement of calculated LDL-C with BQ even in Type 3 dysbetalipoproteinemia, and it can be used at TG concentrations up to 17.0 mmol/L (1,500 mg/dL) [10]. These advantages cannot be offered by the Friedewald formula and its replacement by one of the alternative equations is therefore justified in routine laboratory practice.

In science nobody has the last word and the data from Drobnik et al. add importantly to the debate whether the Friedewald equation should be replaced by Martin-Hopkins or Sampson equation and which of the two would then be preferrable. However, this is the wrong debate. The discussion should rather be about which biomarker is best fit for purpose: LDL-C, non-HDL-C, or apoB? LDL-C is the premier and evidence-based marker of the lipoprotein-associated risk of cardiovascular disease, the standard of care test promoted by all prevention guidelines, and the measure accepted by healthcare professionals and patients worldwide. But does LDL-C deserve to remain the preeminent laboratory test for assessing LDL-related risk? In other words: should we continue to rely on (measured or calculated) LDL-C for quantifying atherogenic lipoprotein particles?

Each of the LDL particles contains one molecule of apoB but different amounts of cholesterol and TGs. ApoB can be accurately measured over the full range of concentrations encountered in whatever concentration and lipid composition of the LDL particles is present [12]. This is not the case for LDL-C or non-HDL-C whatever method, direct or indirect, is used to measure or calculate their concentrations [12]. LDL-C and HDL-C (used in calculations of LDL-C and non-HDL-C) are estimates of the cholesterol within density-defined lipoprotein fractions. These density ranges may contain other lipoprotein classes which also carry cholesterol. This non-selectivity is a major analytical problem, particularly in dyslipidemic samples with atypical lipoproteins such as in obesity, diabetes, and chronic kidney disease [4]. In contrast, apoB is selectively and unequivocally measured [12]. The equipment necessary to measure apoB is present in virtually all clinical laboratories and there are automated assays available from all the major diagnostic companies. The measurement of apoB is adequately standardized by the International Federation of Clinical Chemistry (IFCC) since 1994, and further efforts by the IFCC will improve the standardization, but it is the overall clinical performance of an assay that should determine justification of its medical use [12]. Based on evidence from data of prospective observational studies and meta-analyses of clinical trials, multiple consensus groups including AHA/ACC 2018 and the joint statements by the EFLM and EAS have declared that apoB is the preferred accurate marker over LDL-C and non-HDL-C for assessment of cardiovascular risk attributable to atherogenic lipoproteins in hypertriglyceridemia – affecting 25–30 % of the population [3], 4].