Comparison of the effectiveness of Martin's equation, Friedewald's equation, and a Novel equation in low-density lipoprotein cholesterol estimation

The clinical impact of estimating low-density lipoprotein cholesterol (LDL-C) using different equations in the general population

BACKGROUND

Low-density lipoprotein cholesterol (LDL-C) is associated with atherosclerotic cardiovascular disease (ASCVD). Friedewald, Sampson, and Martin-Hopkins equations are used to calculate LDL-C. This study compares the impact of switching between these equations in a large geographically defined population.

MATERIALS AND METHODS

Data for individuals who had a lipid panel ordered clinically between 2010 and 2019 were included. Comparisons were made across groups using the two-sample t-test or chi-square test as appropriate. Discordances between LDL measures based on clinically actionable thresholds were summarized using contingency tables.

RESULTS

The cohort included 198,166 patients (mean age 54 years, 54% female). The equations perform similarly at the lower range of triglycerides but began to diverge at a triglyceride level of 125 mg/dL. However, at triglycerides of 175 mg/dL and higher, the Martin-Hopkins equation estimated higher LDL-C values than the Samson equation. This discordance was further exasperated at triglyceride values of 400 to 800 mg/dL. When comparing the Sampson and Friedewald equations, at triglycerides are below 175 mg/dL, 9% of patients were discordant at the 70 mg/dL cutpoint, whereas 42.4% were discordant when triglycerides are between 175 and 400 mg/dL. Discordance was observed at the clinically actionable LDL-C cutpoint of 190 mg/dL with the Friedewald equation estimating lower LDL-C than the other equations. In a high-risk subgroup (ASCVD risk score > 20%), 16.3% of patients were discordant at the clinical cutpoint of LDL-C < 70 mg/dL between the Sampson and Friedewald equations.

CONCLUSIONS

Discordance at clinically significant LDL-C cutpoints in both the general population and high-risk subgroups were observed across the three equations. These results show that using different methods of LDL-C calculation or switching between different methods could have clinical implications for many patients.

Evaluation of low-density lipoprotein cholesterol equations by cross-platform assessment of accuracy-based EQA data against SI-traceable reference value

OBJECTIVES

Low-density lipoprotein cholesterol (LDLC) is the primary cholesterol target for the diagnosis and treatment of cardiovascular disease (CVD). Although beta-quantitation (BQ) is the gold standard to determine LDLC levels accurately, many clinical laboratories apply the Friedewald equation to calculate LDLC. As LDLC is an important risk factor for CVD, we evaluated the accuracy of Friedewald and alternative equations (Martin/Hopkins and Sampson) for LDLC.

METHODS

We calculated LDLC based on three equations (Friedewald, Martin/Hopkins and Sampson) using the total cholesterol (TC), triglycerides (TG), and high-density lipoprotein cholesterol (HDLC) in commutable serum samples measured by clinical laboratories participating in the Health Sciences Authority (HSA) external quality assessment (EQA) programme over a 5 years period (number of datasets, n=345). LDLC calculated from the equations were comparatively evaluated against the reference values, determined from BQ-isotope dilution mass spectrometry (IDMS) with traceability to the International System of Units (SI).

RESULTS

Among the three equations, Martin/Hopkins equation derived LDLC had the best linearity against direct measured (y=1.141x - 14.403; R2=0.8626) and traceable LDLC (y=1.1692x - 22.137; R2=0.9638). Martin/Hopkins equation (R2=0.9638) had the strongest R2 in association with traceable LDLC compared with the Friedewald (R2=0.9262) and Sampson (R2=0.9447) equation. The discordance with traceable LDLC was the lowest in Martin/Hopkins (median=-0.725%, IQR=6.914%) as compared to Friedewald (median=-4.094%, IQR=10.305%) and Sampson equation (median=-1.389%, IQR=9.972%). Martin/Hopkins was found to result in the lowest number of misclassifications, whereas Friedewald had the most numbers of misclassification. Samples with high TG, low HDLC and high LDLC had no misclassification by Martin/Hopkins equation, but Friedewald equation resulted in ∼50% misclassification in these samples.

CONCLUSIONS

The Martin/Hopkins equation was found to achieve better agreement with the LDLC reference values as compared to Friedewald and Sampson equations, especially in samples with high TG and low HDLC. Martin/Hopkins derived LDLC also enabled a more accurate classification of LDLC levels.

Friedewald formula may be used to calculate non-HDL-C from LDL-C and TG

Background

The Friedewald formula (FF) was originally designed 50 years ago and has been in use to this day despite better methods for estimating LDL cholesterol (LDL-C). Its success was mainly due to its simplicity. Nowadays most laboratories determine or can determine LDL-C by the direct method. The SCORE2 tables, recommended by the European Society of Cardiology, are based on non-HDL cholesterol (non-HDL-C). To calculate its value, one needs to know the values of total cholesterol (TC) and HDL-C. The presented idea is to use the FF to calculate non-HDL-C based on the values of LDL-C and TG instead of TC and HDL-C.

Methods and findings

Based on database of 26,914 laboratory results, covering the complete lipid panel, the error regarding non-HDL-C values calculated in both ways (recommended and proposed) was determined. The average error in the LDL-C value calculated with the FF compared to the LDL-C value measured in the laboratory is 9.77%, while for non-HDL-C the error between the calculated and laboratory-determined value amounts to 8.88%. The proposed transformation of the FF also yields a much lower percentage of error calculations. Both LDL-C and non-HDL-C (calculated) in our material are strongly correlated with LDL-C and non-HDL-C (measured) values of r = 0.965 (p < 0.000) and r = 0.962 (p < 0.000), respectively.

Conclusion

Non-HDL-C may be calculated based on the values of LDL-C and TG (without the need to determine the levels of TC and HDL-C). The proposed calculation may greatly reduce the cost of testing, given the price of a complete lipid profile.

Correlation of extended Martin/Hopkins equation with a direct homogeneous assay in assessing low-density lipoprotein cholesterol in patients with hypertriglyceridemia

BACKGROUND

The Friedewald or Martin/Hopkins equation is widely used to estimate low-density lipoprotein cholesterol (LDL-C) at triglyceride (TG) levels <400 mg/dL. In this study, we aimed to validate the recently developed Sampson and extended Martin/Hopkins equations intended for use in patients with TG levels up to 800 mg/dL by comparing them to a direct homogenous assay.

METHODS

In total, 8676 participants with serum TG levels <800 mg/dL were enrolled in this study. LDL-C was directly measured using Abbott homogeneous assay (DLDL) and estimated using the Friedewald (FLDL), Martin/Hopkins (MLDL), extended Martin/Hopkins (EMLDL), and Sampson equations (SLDL). The overall concordance between the DLDL and LDL-C estimates was calculated. The performance of the four equations was also compared using Bland-Altman plots and mean absolute difference (MAD).

RESULTS

The EMLDL was more accurate than other LDL-C equations particularly for patients with TG≥400 mg/dL (MAD = 10.43; vs. FLDL: MAD = 21.1; vs. SLDL: MAD 11.62). The overall concordance of FLDL, MLDL, EMLDL, and SLDL with DLDL in TG values ranging from 200 to 799 mg/dL were 52.2, 70.5, 71.6, and 65.7%, respectively (p < 0.001), demonstrating the EMLDL as the most optimal estimation method, particularly for high TG levels (≥200 mg/dL).

CONCLUSION

Both the original and extended Martin/Hopkins method are optimal in estimating LDL-C levels in clinical laboratories using the Abbott analyzer in patients with TG levels of 200-399 and 400-799 mg/dL, respectively. Meanwhile, caution is need that considerable underestimation of Friedewald and Sampson equation could lead to undertreatment in hypertriglyceridemia.

Novel Biomarkers for Atherosclerotic Disease: Advances in Cardiovascular Risk Assessment

Atherosclerosis is a significant health concern with a growing incidence worldwide. It is directly linked to an increased cardiovascular risk and to major adverse cardiovascular events, such as acute coronary syndromes. In this review, we try to assess the potential diagnostic role of biomarkers in the early identification of patients susceptible to the development of atherosclerosis and other adverse cardiovascular events. We have collected publications concerning already established parameters, such as low-density lipoprotein cholesterol (LDL-C), as well as newer markers, e.g., apolipoprotein B (apoB) and the ratio between apoB and apoA. Additionally, given the inflammatory nature of the development of atherosclerosis, high-sensitivity c-reactive protein (hs-CRP) or interleukin-6 (IL-6) are also discussed. Additionally, newer publications on other emerging components linked to atherosclerosis were considered in the context of patient evaluation. Apart from the already in-use markers (e.g., LDL-C), emerging research highlights the potential of newer molecules in optimizing the diagnosis of atherosclerotic disease in earlier stages. After further studies, they might be fully implemented in the screening protocols.

Comparative performance of equations to estimate low-density lipoprotein cholesterol levels and cardiovascular disease incidence: The ATTICA study (2002-2022)

Accurate estimation of low-density lipoprotein cholesterol (LDL-C) is important for monitoring cardiovascular disease (CVD) risk and guiding lipid-lowering therapy. This study aimed to evaluate the magnitude of discordance of LDL-C levels calculated by different equations and its effect on CVD incidence. The study sample consisted of 2354 CVD-free individuals (49% males, mean age 45 ± 14 years); 1600 were re-evaluated at 10 years and 1570 at 20 years. LDL-C was estimated using the Friedewald, Martin/Hopkins, and Sampson equations. Participants were categorized as discordant if estimated LDL-C was below the CVD-risk specific cut-off for one equation and equal/above for its comparator. The Friedewald and Martin/Hopkins equations presented a similar performance in estimating LDL-C; however, both yielded lower values compared to the Sampson. In all pairwise comparisons, differences were more pronounced at lower LDL-C levels, while the Friedewald equation significantly underestimated LDL-C in hypertriglyceridemic participants. Discordance was evident in 11% of the study population, and more specifically 6%, 22%, and 20% for Friedewald versus Martin/Hopkins, Friedewald versus Sampson and Martin/Hopkins versus Sampson equations, respectively. Among discordant participants, median (1st, 3rd quartile) difference in LDL-C was -4.35 (-10.1, 1.95), -10.6 (-12.3, -9.53) and -11.3 (-11.9, -10.6) mg/dL for Friedewald versus Martin/Hopkins, Friedewald versus Sampson and Martin/Hopkins versus Sampson equations, respectively. The 10- and 20-year CVD survival model that included LDL-C values of the Martin-Hopkins equation outperformed the predictive ability of those based on the Friedewald or Sampson equations. Significant differences in estimated LDL-C exist among equations, which may result in LDL-C underestimation and undertreatment.

Comparison of existing methods of low-density lipoprotein cholesterol estimation in patients with type 2 diabetes mellitus

Introduction

Elevated low-density lipoprotein cholesterol (LDL-C) is an important risk factor for atherosclerotic cardiovascular disease (ASCVD). Direct LDL-C measurement is not widely performed. LDL-C is routinely calculated using the Friedewald equation (FLDL), which is inaccurate at high triglyceride (TG) or low LDL-C levels. We aimed to compare this routine method with other estimation methods in patients with type 2 diabetes mellitus (T2DM), who typically have elevated TG levels and ASCVD risk.

Method

We performed a retrospective cohort study on T2DM patients from a multi-institutional diabetes registry in Singapore from 2013 to 2020. LDL-C values estimated by the equations: FLDL, Martin/Hopkins (MLDL) and Sampson (SLDL) were compared using measures of agreement and correlation. Subgroup analysis comparing estimated LDL-C with directly measured LDL-C (DLDL) was conducted in patients from a single institution. Estimated LDL-C was considered discordant if LDL-C was <1.8mmol/L for the index equation and ≥1.8mmol/L for the comparator.

Results

A total of 154,877 patients were included in the final analysis, and 11,475 patients in the subgroup analysis. All 3 equations demonstrated strong overall correlation and goodness-of-fit. Discordance was 4.21% for FLDL-SLDL and 6.55% for FLDL-MLDL. In the subgroup analysis, discordance was 21.57% for DLDL-FLDL, 17.31% for DLDL-SLDL and 14.44% for DLDL-MLDL. All discordance rates increased at TG levels >4.5mmol/L.

Conclusion

We demonstrated strong correlations between newer methods of LDL-C estimation, FLDL, and DLDL. At higher TG concentrations, no equation performed well. The Martin/Hopkins equation had the least discordance with DLDL, and may minimise misclassification compared with the FLDL and SLDL.

Accuracy of 23 Equations for Estimating LDL Cholesterol in a Clinical Laboratory Database of 5,051,467 Patients

Background

Alternatives to the Friedewald low-density lipoprotein cholesterol (LDL-C) equation have been proposed.

Objective

To compare the accuracy of available LDL-C equations with ultracentrifugation measurement.

Methods

We used the second harvest of the Very Large Database of Lipids (VLDbL), which is a population-representative convenience sample of adult and pediatric patients (N = 5,051,467) with clinical lipid measurements obtained via the vertical auto profile (VAP) ultracentrifugation method between October 1, 2015 and June 30, 2019. We performed a systematic literature review to identify available LDL-C equations and compared their accuracy according to guideline-based classification. We also compared the equations by their median error versus ultracentrifugation. We evaluated LDL-C equations overall and stratified by age, sex, fasting status, and triglyceride levels, as well as in patients with atherosclerotic cardiovascular disease, hypertension, diabetes, kidney disease, inflammation, and thyroid dysfunction.

Results

Analyzing 23 identified LDL-C equations in 5,051,467 patients (mean±SD age, 56±16 years; 53.3% women), the Martin/Hopkins equation most accurately classified LDL-C to the correct category (89.6%), followed by the Sampson (86.3%), Chen (84.4%), Puavilai (84.1%), Delong (83.3%), and Friedewald (83.2%) equations. The other 17 equations were less accurate than Friedewald, with accuracy as low as 35.1%. The median error of equations ranged from -10.8 to 18.7 mg/dL, and was best optimized using the Martin/Hopkins equation (0.3, IQR-1.6 to 2.4 mg/dL). The Martin/Hopkins equation had the highest accuracy after stratifying by age, sex, fasting status, triglyceride levels, and clinical subgroups. In addition, one in five patients who had Friedewald LDL-C <70 mg/dL, and almost half of the patients with Friedewald LDL-C <70 mg/dL and triglyceride levels 150-399 mg/dL, had LDL-C correctly reclassified to >70 mg/dL by the Martin/Hopkins equation.

Conclusions

Most proposed alternatives to the Friedewald equation worsen LDL-C accuracy, and their use could introduce unintended disparities in clinical care. The Martin/Hopkins equation demonstrated the highest LDL-C accuracy overall and across subgroups.

Comparison of Newly Proposed LDL-Cholesterol Estimation Equations

BACKGROUND

Low-density lipoprotein cholesterol is an important marker highly associated with cardiovascular disease. Since the direct measurement of it is inefficient in terms of cost and time, it is common to estimate through the Friedewald equation developed about 50 years ago. However, various limitations exist since the Friedewald equation was not designed for Koreans. This study proposes a new low-density lipoprotein cholesterol estimation equation for South Koreans using nationally approved statistical data.

METHODS

This study used data from the Korean National Health and Nutrition Examination Survey from 2009 to 2019. The 18,837 subjects were used to develop the equation for estimating low-density lipoprotein cholesterol. The subjects included individuals with low-density lipoprotein cholesterol levels directly measured among those with high-density lipoprotein cholesterol, triglycerides, and total cholesterol measured. We compared twelve equations developed in the previous studies and the newly proposed equation (model 1) developed in this study with the actual low-density lipoprotein cholesterol value in various ways.

RESULTS

The low-density lipoprotein cholesterol value estimated using the estimation formula and the actual low-density lipoprotein cholesterol value were compared using the root mean squared error. When the triglyceride level was less than 400 mg/dL, the root mean squared of the model 1 was 7.96, the lowest compared to other equations, and the model 2 was 7.82. The degree of misclassification was checked according to the NECP ATP III 6 categories. As a result, the misclassification rate of the model 1 was the lowest at 18.9%, and Weighted Kappa was the highest at 0.919 (0.003), which means it significantly reduced the underestimation rate shown in other existing estimation equations. Root mean square error was also compared according to the change in triglycerides level. As the triglycerides level increased, the root mean square error showed an increasing trend in all equations, but it was confirmed that the model 1 was the lowest compared to other equations.

CONCLUSION

The newly proposed low-density lipoprotein cholesterol estimation equation showed significantly improved performance compared to the 12 existing estimation equations. The use of representative samples and external verification is required for more sophisticated estimates in the future.

Comparison of Estimated LDL Cholesterol Equations with Direct Measurement in Patients with Angiographically Confirmed Coronary Artery Disease

Background and aims: Our goals in the study were to (1) quantify the discordance in LDL-C levels between equations (the Friedewald, Sampson, and Martin/Hopkins equations) and compare them with direct LDL-C (dLDL-C); and (2) explore the proportion of misclassified patients by calculated LDL-C using these three different equations. Methods: A total of 30,349 consecutive patients with angiographically confirmed coronary artery disease (CAD) were prospectively enrolled. Concordance was defined as if the LDL-C was <1.8 mmol/L with each pairwise comparison of LDL-C equations. Estimated LDL-C that fell into the same category as dLDL-C at the following levels: <1.4, 1.4 to 1.7, 1.8 to 2.5, 2.6 to 2.9, and ≥3.0 mmol/L was considered to have been correctly categorized. Results: The concordance was 96.3% (Sampson vs. Martin/Hopkins), 95.0% (Friedewald vs. Sampson), and 91.4% (Friedewald vs. Martin/Hopkins), respectively. This proportion fell to 82.4% in those with hypertriglyceridemia (TG ≥ 1.7 mmol/L). With an accurate classification rate of 73.6%, the Martin/Hopkins equation outperformed the Sampson equation (69.5%) and the Friedewald equation (59.3%) by a wide margin. Conclusions: Comparing it to the validated Martin/Hopkins equation, the Friedewald equation produced the lowest levels of LDL-C, followed by the Sampson equation. In the classification of LDL-C, the Martin/Hopkins equation has also been shown to be more accurate. There is a significant difference between the equations and the direct measurement method, which may lead to overtreatment or undertreatment.

How should low-density lipoprotein cholesterol be calculated in 2022?

PURPOSE OF REVIEW

The reference method for low-density lipoprotein-cholesterol (LDL-C) quantitation is β-quantification, a technically demanding method that is not convenient for routine use. Indirect calculation methods to estimate LDL-C, including the Friedewald equation, have been used since 1972. This calculation has several recognized limitations, especially inaccurate results for triglycerides (TG) >4.5 mmol/l (>400 mg/dl). In view of this, several other equations were developed across the world in different datasets.The purpose of this review was to analyze the best method to calculate LDL-C in clinical practice by reviewing studies that compared equations with measured LDL-C.

RECENT FINDINGS

We identified 45 studies that compared these formulae. The Martin/Hopkins equation uses an adjustable factor for TG:very low-density lipoprotein-cholesterol ratios, validated in a large dataset and demonstrated to provide more accurate LDL-C calculation, especially when LDL <1.81 mmol/l (<70 mg/dl) and with elevated TG. However, it is not in widespread international use because of the need for further validation and the use of the adjustable factor. The Sampson equation was developed for patients with TG up to 9 mmol/l (800 mg/dl) and was based on β-quantification and performs well on high TG, postprandial and low LDL-C samples similar to direct LDL-C.

SUMMARY

The choice of equation should take into the level of triglycerides. Further validation of different equations is required in different populations.

Directly Measured vs. Calculated Low-Density Lipoprotein Cholesterol Does Not Identify Additional Individuals With Coronary Artery Disease and Diabetes at Higher Risk of Adverse Events: Insight From a Large Percutaneous Coronary Intervention Cohort in Asia

Background

The objective of our study was to assess whether calculated low-density lipoprotein cholesterol (LDL-C) is inferior to direct LDL-C (dLDL-C) in identifying patients at higher risk of all-cause mortality, recurrent acute myocardial infarction (AMI), and major adverse cardiovascular event (MACE).

Methods

A total of 9,751 patients with coronary artery disease (CAD) undergoing percutaneous coronary intervention (PCI) in the Fuwai PCI registry were included. DLDL-C was measured by the selective solubilization method (Kyowa Medex, Tokyo, Japan). Correct classification was defined as the proportion of estimated LDL-C in the same category as dLDL-C based on dLDL-C levels: less than 1.4, 1.4–1.8, 1.8–2.6, 2.6–3.0, and 3.0 mmol/L or greater.

Results

Underestimation of LDL-C was found in 9.7% of patients using the Martin/Hopkins equation, compared with 13.9% using the Sampson equation and 24.6% with the Friedewald equation. Cox regression analysis showed compared the correct estimation group, underestimation of LDL-C by the Martin/Hopkins equation did not reduce all-cause mortality (HR 1.26, 95% CI: 0.72–2.20, P = 0.4), recurrent AMI (HR 1.24, 95% CI: 0.69–2.21, P = 0.5), and MACE (HR 1.02, 95% CI: 0.83–1.26, P = 0.9). Similarly, the overestimated group did not exacerbate all-cause mortality (HR 0.9, 95% CI: 0.45–1.77, P = 0.8), recurrent AMI (HR 0.63, 95% CI: 0.28–1.44, P = 0.3), and MACE (HR 1.07, 95% CI: 0.86–1.32, P = 0.6). The results of the diabetes subgroup analysis were similar to those of the whole population.

Conclusion

Compared with dLDL-C measurement, misclassification by the Martin/Hopkins and Sampson equations was present in approximately 20% of patients. However, directly measured vs. calculated LDL-C did not identify any more individuals in the PCI population with increased risk of all-cause mortality, recurrent AMI, and MACE, even in high-risk patients such as those with diabetes.

Validation of Friedewald, Martin-Hopkins and Sampson low-density lipoprotein cholesterol equations

Background

Low-density lipoprotein cholesterol (LDL-C) is an important biomarker for determining cardiovascular risk and regulating lipid lowering therapy. Therefore, the accurate estimation of LDL-C concentration is essential in cardiovascular disease diagnosis and prognosis. Sampson recently proposed a new formula for the estimation of LDL-C. However, little is known regarding the validation of this formula.

Objectives

This study aimed to validate this new formula with other well-known formulas in Turkish population, composed of adults.

Methods

A total of 88,943 participants above 18 years old at Sivas Cumhuriyet University Hospital (Sivas, Turkey) were included to this study. LDL-C was directly measured by homogeneous assays, i.e., Roche, Beckman and Siemens and estimated by Friedewald’s, Martin-Hopkins’, extended Martin-Hopkins’ and Sampson’s formulas. The concordances between the estimations obtained by the formulas and the direct measurements were evaluated both in general and separately for the LDL-C, TG and non-HDL-C sublevels. Linear regression analysis was applied and residual error plots were generated between each estimation and direct measurement method. Coefficient of determination (R²) and mean absolute deviations were also calculated.

Results

The results showed that the extended Martin-Hopkins approach provided the most concordant results with the direct assays for LDL-C estimation. The results also showed that the highest concordances were obtained between the direct assays with the extended Martin-Hopkins formula calculated with the median statistics obtained from our own population. On the other hand, it was observed that the results of the methods may differ in different assays. The extended Martin-Hopkins approach, calculated from the median statistics of our population, gave the most concordant results in patients with “low LDL-C level (LDL-C levels < 70 mg/dL) or hypertriglyceridemia (TG levels ≥ 400 mg/dL)”.

Conclusions

Although the results of the formulas in different assays may vary, the extended Martin-Hopkins approach was the best one with the highest overall concordances. The validity of the Martin Hopkins’ and Sampson’s formulas has to be further investigated in different populations.