Background

Low-density lipoprotein-cholesterol (LDL-C) remains of utmost clinical importance; it is positioned in clinical trials as a treatment target and is emphasized in worldwide guidelines as the primary cholesterol target. The gold standard of LDL-C measurement has been preparative ultracentrifugation, but given its time requirements and expenses, other methods have been developed as alternatives to estimate LDL-C.

The Friedewald equation was developed in 1972 and estimates LDL-C as: total cholesterol (TC) minus high-density lipoprotein-cholesterol (HDL-C) minus triglycerides (TG)/5, with the latter term serving as an estimate for very low-density lipoprotein-cholesterol (VLDL-C).¹ Originally developed for research purposes from a sample of just 448 individuals, the Friedewald equation has been widely adopted in clinical practice for several decades.

However, the equation is prone to inaccuracy at low LDL-C and/or high TG levels, where errors in estimating VLDL-C are magnified given its use of a fixed factor of 5 to describe the relationship between TG and VLDL-C. This results in marked underestimation of LDL-C.

In the era when the Friedewald equation was introduced, inaccuracies were tolerated because the VLDL-C estimate was a relatively small proportion of the equation. Lower LDL-C levels were not achievable or strongly recommended as statins and other modern pharmacotherapies were not available. In fact, only 35 individuals in Friedewald's derivation sample had an LDL-C <100 mg/dL.¹

Recently, with epidemics of obesity and diabetes resulting in hypertriglyceridemic states, and with novel therapeutics achieving historically low LDL-C levels, underestimation of LDL-C levels with Friedewald's equation may lead to deferral or withdrawal of lipid-lowering therapies, potentially resulting in undertreated high-risk patients.

Martin/Hopkins Equation to Estimate LDL-C

There was little attention to this clinically relevant issue in the Cardiology community until a 2013 JACC paper from the Very Large Database of Lipids.² To address the Friedewald equation inaccuracy, the Martin/Hopkins equation was developed and published in JAMA that same year to estimate LDL-C when TG were <400 mg/dL.³ The fixed factor of 5 used to estimate VLDL-C is instead replaced by an adjustable factor based on a patient's non-HDL-C and TG values. LDL-C is therefore estimated as: TC minus HDL-C minus TG/adjustable factor.

The Martin/Hopkins LDL-C estimation improves LDL-C accuracy compared to the Friedewald estimation across guideline LDL-C and TG strata, but especially where accuracy matters the most in 2020  ̶  at low LDL-C and high TG. Worldwide, various large laboratories have adopted the use of this equation, and the recent AHA/ACC/Multi-society Cholesterol Guideline provided a Class IIa recommendation for using the equation in patients with LDL-C <70 mg/dL.⁴

Both the Friedewald and Martin/Hopkins equations were developed and validated for patients with serum TG levels <400 mg/dL. At higher TG levels, chylomicrons accumulate and may alter the relationship between TG and VLDL-C; therefore, direct chemical assays are typically used to measure LDL-C. Several commercial direct assays have been developed for this purpose, but there remain substantial concerns regarding their standardization and accuracy, especially at high TGs and in those with known coronary disease.

A Novel Proposed NIH Equation

In this context, Sampson and colleagues developed a new equation (henceforth referred as Equation 2 in their JAMA Cardiology paper) using 18,715 lipid samples from 8656 patients from the National Institutes of Health (NIH) Clinical Center.⁵ Using β-quantification LDL-C values as the gold standard and multiple least squares regressions, the authors propose an LDL-C estimation as: TC/0.948 minus HDL-C/0.971 minus (TG/8.56 plus [TG x non-HDL-C]/2140 minus TG²/16100) minus 9.44.

The authors compared Equation 2 to Friedewald and Martin/Hopkins across a variety of clinical scenarios, but largely focused on high TGs ≥400 mg/dL. With respect to LDL-C accuracy across the spectrum of TGs (0 to >2880 mg/dL) and LDL-C values (0-800 mg/dL), the authors found aggregate root mean square errors (RMSE) with Equation 2 (15.2) were significantly lower compared to Friedewald estimation (RMSE 32) or Martin/Hopkins estimation (RMSE 25.7).

Mean absolute differences (MAD) were calculated between estimated LDL-C and β-quantification LDL-C values at various TG and non-HDL-C cutpoints, and the authors found overall lower MAD with Equation 2 (MAD 24.9 mg/dL) in patients with TG > 400 mg/dL compared to Friedewald (MAD 56.4 mg/dL) or Martin/Hopkins estimation (MAD 44.8 mg/dL). MADs were also smaller overall across the range of TGs (0 to 3000 mg/dL) when compared to the Roche direct LDL-C assay.

Next, reclassification of LDL-C based on guideline LDL-C cutpoints was examined across the entire sample stratified by TG (<400 mg/dL and 400-800 mg/dL). Based on their accuracy definition, the authors found a misclassification rate of 29% with Equation 2 with TGs in the 600-800 mg/dL range, and overall, 30% fewer misclassifications compared to the Martin/Hopkins equation. At the lower TG range (<400 mg/dL), they state similar levels of accuracy when comparing Equation 2 to Martin/Hopkins.

Overall, the authors conclude that Equation 2 allows for a somewhat more accurate estimation of LDL-C at low LDL-C and/or high TG and suggest implementation of the equation can be readily achieved in most laboratories at no added costs. We applaud the efforts of Sampson et al in improving LDL-C accuracy, as for decades the Friedewald equation served as the de facto method for LDL-C estimation without rigorous scrutiny.

With modern medicine emphasizing precision care using the most contemporary tools available, continuing to highlight the issue of accurate LDL-C estimation helps drive momentum in improving LDL-C accuracy. This ultimately benefits patients and allows clinicians to use the most accurate information available when deciding titration of lipid-lowering medications. However, we note several concerns with Equation 2 and suggested conclusions put forth by the authors.

Calculated LDL-C Accuracy at Low LDL-C Levels and Limitations of Equation 2

One of the main conclusions of Sampson et al's analysis is that Equation 2 performs similarly to the Martin/Hopkins equation at low LDL-C with respect to reclassification, but that the latter demonstrated negative bias for low LDL-C values. We first caution that Equation 2 was derived in a population that is much smaller (<20,000 total samples) and more skewed than representative of clinical practice.

Very-high LDL-C values (200-800 mg/dL) and TGs (up to 3000 mg/dL) were included in the derivation set, which sit at the very opposite end of the spectrum where clinical accuracy is most important. If data is fitted and therefore skewed as a result of these very high LDL-C values, then the ability to fit lower LDL-C values may be jeopardized.

In contrast, Martin/Hopkins was derived in a nationally representative cohort containing over 1 million lipid samples with normally distributed lipid samples like those in the National Health and Nutrition Examination Survey (NHANES). Although concerns were raised by Sampson and colleagues about the accuracy of the Vertical Auto Profile ultracentrifugation method used to obtain lipid values in the Very Large Database of Lipids study, yearly random split-sample verification was performed with comparison to β-quantification ultracentrifugation LDL-C values from the Washington University in St. Louis laboratory.

In particular, the data examining low LDL-C in Figure 4 appears to be misleading. The authors defined concordance or accuracy as the percentage of estimated LDL-C falling within the same category of β-quantification LDL-C. This approach is problematic for several reasons: one, this does not mimic clinical practice where a clinician receives an estimated LDL-C value from a standard lipid profile (through Friedewald, Martin/Hopkins, or Equation 2) and the clinical question then becomes: how likely is this estimation correct?

By presenting data in the opposite manner, the issue of LDL-C underestimation is masked at the lowest LDL-C group. This is a large concern and one of the main pitfalls of the Friedewald equation, whereby patients may have calculated LDL-C levels less than 70 mg/dL but have direct LDL-C values above this threshold. In this scenario, a clinician may opt to withhold further intensification of lipid-lowering therapies by falsely believing the LDL-C value is already at goal, potentially leading to adverse patient outcomes.

In Figure 4, even with accuracy defined the way the authors propose, Equation 2 exhibits more underestimation at low LDL-C (<70 mg/dL) compared to Martin/Hopkins estimation. In fact, when using Table 1 below to assess Equation 2, calculated LDL-C values fall in-between Friedewald estimated LDL-C, where underestimation is the most severe, and Martin/Hopkins estimated LDL-C, where underestimation is a minor concern.

Table 1

	Friedewald LDL-C	Martin/Hopkins LDL-C	Equation 2 LDL-C
Estimation equation	LDL-C = TC – HDL-C – TG/5	LDL-C = TC – HDL-C – TG/*novel factor * an adjustable factor based on a patient's Non-HDL-C and TG levels derived from a 174-cell 2D table	Using least squares regressions, LDL-C = TC/0.948 – HDL-C/0.971 – (TG/8.56 + [TG x NonHDL-C]/2140 – TG2/16100) – 9.44
Recommended TG range for use	TG <400 mg/dL	TG <400 mg/dL	TG <800 mg/dL
Gold standard direct LDL-C method used in derivation	Direct LDL-C by Beta-quantification	Direct LDL-C by Vertical Auto Profile (VAP) direct ultracentrifugation. These underwent yearly random split-sample verification with comparison to βeta-quantification at the Washington University in St. Louis laboratory.	Direct LDL-C by Beta-quantification
Derivation dataset	Sample of 448 individuals with familial hyperlipoproteinemia or their relatives.	Nationally representative sample of 1.35 million patients with lipid distributions similar to NHANES.	18,715 lipid samples from 8656 patients at the NIH collected between 1970s and 1990s. Derivation sample is moderately hyperlipidemic with higher TG and non-HDL-C levels than the general population.
Validation datasets	External validation in several datasets over decades	External validation in multiple national and international datasets including validation in the FOURIER trial where patients achieved very low LDL-C levels on PCSK9 inhibitors	External validation in multiple US datasets by the authors. No independent validation. No validation at LDL-C <40 mg/dL.
Performance at different TG and NonHDL-C cutpoints compared to gold standard direct measurement (The most accurate equation has the lowest mean absolute deviation (MAD) compared to BQ LDL-C)
TG <400 mg/dL	Lowest accuracy	Similar accuracy to Equation 2 with MAD difference of 0.3	Similar accuracy to Martin/Hopkins with MAD difference of 0.3
TG ≥400 mg/dL	Estimating LDL-C using this equation is not recommended. Direct measurement is the preferred choice.	Estimating LDL-C using this equation is not recommended and has not been validated. Direct measurement is the preferred choice.	Best accuracy at these TG levels but with clinically relevant LDL-C estimation errors up to 30 mg/dL at TG of 800 mg/dL. Therefore, direct LDL-C measurement is still the preferred choice
NonHDL-C <100 mg/dL	Worst accuracy	Best accuracy, especially at very low Non-HDL-C levels <70 mg/dL	Relatively similar accuracy to Martin/Hopkins at Non-HDL-C of 70-99 mg/dL but accuracy decreases and approaches Friedewald's at levels <70 mg/dL
NonHDL-C >100 mg/dL	Accuracy improves as Non-HDL-C levels increase	Similar accuracy to Equation 2. Tends to overestimate LDL-C at high Non-HDL-C levels	Similar accuracy to Martin/Hopkins. Less overestimation at high Non-HDL-C levels
Estimation in the non-fasting state	Low accuracy in non-fasting state, particularly at low LDL-C and high TG levels.	Better accuracy than Friedewald's in the non-fasting state across all LDL-C levels; with significantly higher accuracy at very low LDL-C <70 mg/dL and elevated TG 150-399 mg/dL levels.	Equation 2 had comparable accuracy to Roche direct LDL-C in the non-fasting state. It's performance in the non-fasting state was not compared to Friedewald or Martin/Hopkins equations.
Summary	Worst accuracy at low LDL-C and high TG levels Not recommended for TG ≥400 mg/dL - LDL-C should be directly measured	Best accuracy at low LDL-C levels, particularly <70 mg/dL, and TG levels <400 mg/dL Not recommended for TG ≥400 mg/dL - LDL-C should be directly measured In those with LDL-C <70 mg/dL (high-risk range) and TG <400 mg/dL, this equation is the least likely to underestimate risk by falsely reclassifying patients into a lower risk category. Therefore, it is the least likely to cause undertreatment. Undertreatment of residual CV risk in high-risk patients at these LDL-C levels is arguably more clinically relevant than overtreatment.	Best accuracy at TG ≥400 mg/dL but both Friedewald and Martin/Hopkins equations were not designed to estimate LDL-C at these TG levels   Equation 2 has a clinically relevant margin of error up to 30 mg/dL at TG levels of 800 mg/dL; therefore, direct LDL-C measurement is still highly recommended at TG levels ≥400 mg/dL. Furthermore, the clinical priority is TG lowering to prevent pancreatitis and LDL-C can be better assessed after TG lowering. In those with LDL-C <100 mg/dL, this equation is the least likely to overestimate risk by falsely reclassifying patients into a higher risk category. Therefore, it is the least likely to cause overtreatment, is less clinically relevant compared to undertreatment at this high-risk LDL-C range.

This raises the concern that Equation 2 continues to perpetuate this issue of underestimation at lower LDL-C values possibly leading to under-treatment and adverse outcomes. Part of this underestimation issue may be related to the derivation dataset used and the inherent skewness of the data as mentioned earlier, but regardless of the upstream cause, this issue is concerning for clinical use.

The Era of Targeting Ultra-low LDL-C Values

This issue is likely more exacerbated at progressively lower LDL-C values below 70 mg/dL. In an era of PCSK9 inhibitors, bempedoic acid, ezetimibe, and other novel lipid-lowering agents, the accuracy at even lower LDL-C levels increasingly becomes important. European cholesterol guidelines recommend LDL-C goals of <55 mg/dL in very high-risk patients, and median treated LDL-C levels in patients on PCSK9 inhibitors from clinical trials are routinely <40 mg/dL and closer to 30 mg/dL.

If the authors claim Equation 2 can be used in patients treated with these novel agents, then data on accuracy at these lower LDL-C values should be presented. It is concerning that the authors exclude data on LDL-C <40 mg/dL in their presentation of accuracy results. We previously showed the robustness of Martin/Hopkins equation when applied at such levels, including to patients from the FOURIER trial.⁶ We recommend a similar analysis with Equation 2 to get a better sense of its true clinical utility.

Furthermore, it was previously demonstrated that the issue of hypertriglyceridemia with low LDL-C Friedewald estimation is an issue at TG levels above 150 mg/dL, without much of a difference at lower TG values. Figure 4 lumps all low TG into one bin at <400 mg/dL. Without further granularity by assessing various combined LDL-C and TG strata together, the performance of Equation 2 remains unclear at low LDL-C.

As calculated LDL-C relies on non-HDL-C and TG values, which are common terms in all three equations examined in the paper, taking an integrative approach in evaluating the performance of these equations at different LDL-C and TG categories at the low LDL-C needs to be undertaken for validation. Simply binning together all patients with "low" TG <400 mg/dL will effectively hide nuanced differences in performance at low LDL-C. However, it is for these patients in particular where nuances truly matter in order to implement effective treatment and reduce residual cardiovascular risk. In order for implementation into clinical practice, rigorous and thorough investigation of Equation 2 needs to be undertaken.

Finally, the authors also only perform reclassification analysis and investigated accuracy of Equation 2 at low LDL-C values using one cohort from LabCorp. The Martin/Hopkins equation underwent vigorous external validation in several external cohorts prior to adoption by clinical laboratories worldwide. In addition to validity in the FOURIER trial, the equation showed significant improvement over Friedewald estimation in a variety of cohorts from North America, South America, and Asia.^7-10 Similar rigorous external validation should occur first to ensure Equation 2 performs adequately.

Furthermore, in the supplement, the authors suggest that across LDL-C strata in the LabCorp dataset, the Martin/Hopkins equation did not result in statistically improved accuracy over Friedewald estimation. These results are clearly discordant with the evidence that has already been established in the literature comparing these two estimated methods demonstrating the superior accuracy of Martin/Hopkins. This raises concerns about the validity of the analyses in this JAMA Cardiology paper; it may be an issue of how accuracy was defined as noted earlier and could signal a significant potential problem in the LabCorp dataset.

Estimated LDL-C Accuracy at High TG Levels

Much of Sampson et al's analysis focused on LDL-C accuracy at high TG with values from 400 up to 3000 mg/dL. However, we caution against several of the conclusions suggested by the authors. The authors directly compare Equation 2 to Martin/Hopkins and Friedewald estimation at these higher TG values, although both latter equations were not explicitly validated for TG values above 400 mg/dL.

In fact, Martin et al assigned only one row of adjustable TG/VLDL-C factors (6 total factors) from the 180-cell table to estimate LDL-C at TG values above 400 mg/dL and acknowledged the limited adaptability of their equation at these higher TG levels. It is important to emphasize that the primary intention behind developing the Martin/Hopkins equation was to improve LDL-C estimation accuracy at clinically relevant low LDL-C and moderately elevated TG (150-400 mg/dL) levels, not to replace the need for direct LDL-C measurement at TG ≥400 mg/dL.

This issue helps explain several of the discrepancies between Equation 2 and Martin/Hopkins estimation in the data presented. Figures 1 and 2 in the JAMA Cardiology paper demonstrate differences in VLDL-C and LDL-C estimation between Equation 2 and Martin/Hopkins, but include TGs ranging from 0 to >2880 mg/dL. Only one color, the light purple shade in the figures corresponding to TG values of 0-320 mg/dL, is directly applicable and comparable for Martin/Hopkins and Friedewald equations; however, this represents a minority of the visually presented data.

The color scheme in these two figures can be visually misleading for two reasons. First, the fanning of the scatter plots of Martin/Hopkins equation vs. Equation 2 at higher TG values sways the reader at first glance towards assuming that Equation 2 is more accurate. Second, the superimposing of all other shades over the light purple shade (TG 0-320 mg/dL) doesn't allow for a fair comparison between both equations at TG<400 mg/dL, where performance of Martin/Hopkins is similar as clearly demonstrated by MAD and reclassification analyses in Figures 3 and 4.

The authors also state that errors of up to 30 mg/dL in VLDL-C (and hence in LDL-C) were tolerated in their equation with TGs ranging up to 800 mg/dL, noting similar absolute errors were present with Friedewald estimation at moderately elevated TG values. However, this calls into question whether one should tolerate this level of error, as up to 30 mg/dL in absolute error represents one full strata difference in guideline LDL-C categories.

Most patients will have LDL-C values falling in the middle of a guideline category, and therefore redistribution upwards or downwards by up to 30 mg/dL may easily reclassify a patient. Whether such errors would be acceptable according to the National Cholesterol Education Program thresholds remains to be seen, but certainly such errors may have implications in high and very-high risk patients. Also, using Friedewald errors as the comparator may not be appropriate, as the AHA/ACC/Multi-society Cholesterol Guidelines specifically note direct LDL-C assays should instead be used at higher TG levels.⁴

Concluding Thoughts About the Need for More Rigorous Testing of Equation 2

Equation 2 is an interesting development and brings more attention to the clinically relevant issue of LDL-C accuracy. However, compared with the Martin/Hopkins calculation, it was derived in a much smaller population that is much less reflective of common and contemporary clinical practice. Whereas the Martin/Hopkins calculation has undergone extensive independent validation by other investigators around the world, the results of the JAMA Cardiology paper are yet to be replicated. Given methodologic issues such as exclusion of LDL-C <40 mg/dL along with unusual findings in the LabCorp dataset, Equation 2 will need further testing in patients with low or very low LDL-C and moderately elevated TG before it could be considered ready for prime time.

After all the analyses, it is still unclear how Equation 2 performs in the clinically relevant scenario of low LDL-C and elevated TGs. The waters are muddied by lumping together TG<400 and those with higher TGs in the analyses. At very high triglyceride values, the immediate clinical priority is not LDL-C reduction, but rather reduction of triglycerides first to reduce hypertriglyceridemia-associated morbidity such as pancreatitis as recommended by guidelines.

Moreover, marked hypertriglyceridemia states are relatively rare, with TG values above 400 mg/dL representing the top 97-99th percentile of lipid samples. Therefore, deriving an equation with a focus on hypertriglyceridemia and then applying this equation to low LDL-C samples may be problematic.

We are concerned that minimal data are actually presented to support the study's conclusion that the greatest benefit of Equation 2 may be in patients with low LDL-C. We therefore recommend more rigorous testing of Equation 2 to assess its overall accuracy at varying TG levels at lower LDL-C to ensure patients are receiving the most accurate LDL-C assessment.

That said, we again congratulate Sampson and colleagues on raising awareness of this important issue of LDL-C accuracy, as we should constantly be vigilant about redefining our estimation methods as our treatment targets evolve and novel therapeutics come to fruition.

References

1. Friedewald WT, Levy RI, Fredrickson DS. Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge. Clin Chem 1972;18:499-502.
2. Martin SS, Blaha MJ, Elshazly MB et al. Friedewald-estimated versus directly measured low-density lipoprotein cholesterol and treatment implications. J Am Coll Cardiol 2013;62:732-39.
3. Martin SS, Blaha MJ, Elshazly MB, et al. Comparison of a novel method vs the Friedewald equation for estimating low-density lipoprotein cholesterol levels from the standard lipid profile. JAMA 2013;310:2061-68.
4. Grundy SM, Stone NJ, Bailey AL et al. 2018 AHA/ACC/AACVPR/AAPA/ABC/ACPM/ADA/AGS/AphA/ASPC/NLA/PCNA Guideline on the Management of Blood Cholesterol: A Report on the American College of Cardiology/American Heart Association Task Force Clinical Practice Guidelines. J Am Coll Cardiol 2019;73:3168-3209.
5. Sampson M, Ling C, Sun Q et al. A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia. JAMA Cardiol Published online Feb 2020.
6. Martin SS, Giugliano RP, Murphy SA, et al. Comparison of low-density lipoprotein cholesterol assessment by Martin/Hopkins estimation, Friedewald estimation, and preparative ultracentrifugation: insights from the FOURIER trial. JAMA Cardiol 2018;3:749-53.
7. Pallazola VA, Sathiyakumar V, Ogunmoroti O et al. Impact of improved low-density lipoprotein cholesterol assessment of guideline classification in the modern treatment era – results from a racially diverse Brazilian cross-sectional study. J Clin Lipidol 2019;13:804-11.e2.
8. Kang M, Kim J, Lee SY, Kim K, Yoon J, Ki H. Martin's equation as the most suitable method for estimation of low-density lipoprotein cholesterol levels in Korean adults. Korean J Fam Med 2017;38:263-69.
9. Lee J, Jang S, Son H. Validation of the Martin method for estimating low-density lipoprotein cholesterol levels in Korean adults: findings from the Korea National Health and Nutrition Examination Survey, 2009-2011. PLoS One 2016;11:e0148147.
10. Schneider EE, Sarkar S, Margolick JB, Martin SS, Post WS, Brown TT. Short communication: comparison of calculated low-density lipoprotein cholesterol (LDL-C) values in HIV-infected and HIV-uninfected men using the traditional Freidewald and the novel Martin-Hopkins LDL-C equations. AIDS Res Hum Retroviruses 2020;36:176-79.

Clinical Topics: Diabetes and Cardiometabolic Disease, Dyslipidemia, Hypertriglyceridemia, Lipid Metabolism, Nonstatins, Novel Agents, Statins

Keywords: Dyslipidemias, Arthropod Proteins, Cardiovascular Diseases, Cholesterol, Cholesterol, VLDL, Cholesterol, LDL, Cholesterol, HDL, Chylomicrons, Cohort Studies, Coronary Disease, Diabetes Mellitus, Dicarboxylic Acids, Epidemics, Fatty Acids, Goals, Hydroxymethylglutaryl-CoA Reductase Inhibitors, Hyperlipidemias, Hyperlipoproteinemias, Hypertriglyceridemia, Hypolipidemic Agents, Least-Squares Analysis, Lipoproteins, HDL2, Longitudinal Studies, National Institutes of Health (U.S.), Nutrition Surveys, Pancreatitis, Obesity, Diet Records, Risk Factors, Serine Endopeptidases, Thiadiazines, Triglycerides, Ultracentrifugation, Universities, Proprotein Convertases

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