Comparison of Novel Equations for Estimating Low-Density Lipoprotein Cholesterol in Patients Undergoing Coronary Angiography

A novel equation for the estimation of low-density lipoprotein cholesterol in the Saudi Arabian population: a derivation and validation study

Low-density lipoprotein cholesterol (LDL-C) is typically estimated by the Friedewald equation to guide atherosclerotic cardiovascular disease (ASCVD) management despite its flaws. Martin-Hopkins and Sampson-NIH equations were shown to outperform Friedewald's in various populations. Our aim was to derive a novel equation for accurate LDL-C estimation in Saudi Arabians and to compare it to Friedewald, Martin-Hopkins and Sampson-NIH equations. This is a cross-sectional study on 2245 subjects who were allocated to 2 cohorts; a derivation (1) and a validation cohort (2). Cohort 1 was analyzed in a multiple regression model to derive an equation (equationD) for estimating LDL-C. The agreement between the measured (LDL-CDM) and calculated levels was tested by Bland-Altman analysis, and the biases by absolute error values. Validation of the derived equation was carried out across LDL-C and triglyceride (TG)-stratified groups. The mean LDL-CDM was 3.10 ± 1.07 and 3.09 ± 1.06 mmol/L in cohorts 1 and 2, respectively. The derived equation is: LDL-CD = 0.224 + (TC × 0.919) - (HDL-C × 0.904) - (TG × 0.236) - (age × 0.001) - 0.024. In cohort 2, the mean LDL-C (mmol/L) was estimated as 3.09 ± 1.06 by equationD, 2.85 ± 1.12 by Friedewald, 2.95 ± 1.09 by Martin-Hopkins, and 2.93 ± 1.11 by Sampson-NIH equations; statistically significant differences between direct and calculated LDL-C was observed with the later three equations (P < 0.001). Bland-Altman analysis showed the lowest bias (0.001 mmol/L) with equationD as compared to 0.24, 0.15, and 0.17 mmol/L with Friedewald, Martin-Hopkins, and Sampson-NIH equations, respectively. The absolute errors in all guideline-stratified LDL-C categories was the lowest with equationD, which also showed the best classifier of LDL-C according to guidelines. Moreover, equationD predicted LDL-C levels with the lowest error with TG levels up to 5.63 mmol/L. EquationD topped the other equations in estimating LDL-C in Saudi Arabians as it could permit better estimation when LDL-C is < 2.4 mmol/L, in familial hyperlipidemia, and in hypertriglyceridemia, which improves cardiovascular outcomes in high-risk patients. We recommend further research to validate equationD in a larger dataset and in other populations.

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.

Comparison of Three Methods for LDLC Calculation for Cardiovascular Disease Risk Categorisation in Three Distinct Patient Populations

BACKGROUND

Limitations of the Friedewald equation for low-density-lipoprotein cholesterol (F-LDLC) calculation led to the Martin-Hopkins (M-LDLC) and Sampson-National Institutes of Health (S-LDLC) equations. We studied these newer calculations of LDLC for correlation and discordance for stratification into the Canadian Cardiovascular Society (CCS) 2021 Dyslipidemia Guidelines' cardiovascular disease (CVD) risk categories.

METHODS

We performed analyses on lipid profiles from 3 populations: records of a hospital biochemistry laboratory (population 1), lipid clinic patients without select monogenic dyslipidemias (population 2A), and lipid clinic patients with familial hypercholesterolemia (FH; population 2B).

RESULTS

There was very strong correlation among the 3 calculated LDLC. In populations 1 and 2A, M-LDLC and S-LDLC were progressively higher than F-LDLC as triglyceride (TG) levels increased from normal to ∼ 5 mmol/L. In population 2B, M-LDLC was higher than F-LDLC, but S-LDLC was progressively lower than F-LDLC. Using the CCS 2021 guidelines' 4 CVD risk categories, 7.0% (population 2A) to 7.2% (population 1) of cases for M-LDLC vs F-LDLC and 3.9% (population 2A) to 4.4% (population 1) of cases for S-LDLC vs F-LDLC were reclassified to an adjacent CVD risk category, mostly from a lower to a higher risk category.

CONCLUSIONS

Switching from F-LDLC to S-LDLC or M-LDLC can reclassify up to ∼ 4.4% or 7.2% of patients, respectively, to another CCS CVD risk category. The difference between F-LDLC and M-LDLC or S-LDLC is greater with higher TG, and with lower LDLC. We recommend that clinical laboratories switch to reporting results from either M-LDLC or S-LDLC, but S-LDLC should not be used in FH patients, pending further studies.

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.

Comparação das Novas Equações de Martin/Hopkins e Sampson para o Cálculo do Colesterol de Lipoproteína de Baixa Densidade em Pacientes Diabéticos

Fundamentos

Objetivos

Método

Resultados

Conclusão

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.

A Tale of Two Approaches

OBJECTIVES

To summarize and assess the literature on the performances of methods beyond the Friedewald formula (FF) used in routine practice to determine low-density lipoprotein cholesterol (LDL-C).

METHODS

A literature review was performed by searching the PubMed database. Many peer-reviewed articles were assessed.

RESULTS

The examined methods included direct homogeneous LDL-C assays, the FF, mathematical equations derived from the FF, the Martin-Hopkins equation (MHE), and the Sampson equation. Direct homogeneous assays perform inconsistently across manufacturers and disease status, whereas most FF-derived methods exhibit variable levels of performance across populations. The MHE consistently outperforms the FF but cannot be applied in the setting of severe hypertriglyceridemia. The Sampson equation shows promise against both the FF and MHE, especially in severe hypertriglyceridemia, but data are still limited on its validation in various settings, including disease and therapeutic states.

CONCLUSIONS

There is still no consensus on a universal best method to estimate LDL-C in routine practice. Further studies are needed to assess the performance of the Sampson equation.

Application of the Sampson equation to estimate LDL-C in children: Comparison with LDL direct measurement and Friedewald equation in the BLIP study

BACKGROUND AND AIMS

In epidemiological trials and in clinical practices, it is relevant to have affordable and reliable methods to measure the main lipid cardiovascular risk factors, and in particular low-density lipoprotein cholesterol (LDL-C) plasma level. In this context, we aimed to compare the reliability of the Friedewald's (LDL-Cf) and Sampson's (LDL-Cs) equations with the LDL-value dosed by a validated dosage method (LDL-Cd) in a large cohort of children.

METHODS AND RESULTS

We considered the lipid values of 145 infants, 278 preschoolers, 810 scholar children, and 1372 adolescents (Total N. 2605, 1291 males, 1314 females), with mean total cholesterol (TC) = 169.8 ± 39.7 mg/dL, HDL-Cholesterol = 50.8 ± 12.7 mg/dL, non HDL-Cholesterol = 118.9 ± 35.9 mg/dL, Triglycerides (TG) = 90.3 ± 77.9 mg/dL, LDL-Cd = 106.2 ± 29.9 mg/dL, LDL-Cf = 100.9 ± 33.8 mg/dL, and LDL-Cs = 102.2 ± 33.4 mg/dL. Comparing the distance to the LDL-Cd, Friedewald's equation mildly but significantly underestimated in infants (3.4 ± 5.3 mg/dL), preschoolers (1.5 ± 7.1 mg/dL). Children (1.2 ± 2.2 mg/dL) and adolescents (1.1 ± 5.9 mg/dL) compared to Sampson's equation (all comparisons, p < 0.001).

CONCLUSIONS

Our analysis, being carried out on a large population sample, shows that Sampson's equation is more reliable than Friedewald's one at each considered age class and even for extreme TG values.

Usefulness of novel Martin/Hopkins and Sampson equations over Friedewald equation in cardiology outpatients: A CVSCORE-TR substudy

BACKGROUND AND AIMS

The Friedewald equation (LDL-Cf) is known to produce inaccurate estimations of low-density lipoprotein cholesterol (LDL-C) when triglycerides are high (>400 mg/dL) or LDL-C is low (<70 mg/dL). The Martin/Hopkins (LDL-Cmh) and Sampson (LDL-Cs) equations were developed to overcome these limitations, but few data are available to assess whether these equations offer incremental usefulness over LDL-Cf. Our aim was to understand whether there was any incremental usefulness of novel equations on decisions regarding patient management.

METHODS

Four thousand one hundred and ninety-six cardiology patients who were included in a multicentre registry database were analysed. Each patient was assigned to a cardiovascular risk class using the SCORE (Systematic COronary Risk Evaluation) algorithm, and relevant European guidelines were used to assess LDL-C targets.

RESULTS

Compared with LDL-Cmh and LDL-Cs, LDL-Cf was able to correctly identify 96.9%-98.08% of patients as within or outside the LDL-C target, respectively, and 1.95%-2.8% of patients were falsely identified as being within the LDL-C target. Kappa coefficients for agreement between LDL-Cf vs LDL-Cmh and LDL-Cf vs LDL-Cs were 0.868 and 0.918 (P < .001). For patients not on cholesterol-lowering drugs, the decision to initiate treatment would be different in 1.2%-1.8% of cases if LDL-Cs or LDL-Cmh were used, respectively. For those already on cholesterol-lowering drugs, decisions regarding treatment intensification would be different in 1.5%-2.4% of cases if LDL-Cs or LDL-Cmh were used.

CONCLUSIONS

In most cardiology outpatients, the Friedewald equation has excellent agreement with the novel Martin/Hopkins and Sampson equations, and treatment decisions should not change in most patients.

Calculated values of serum LDL-cholesterol (LDL-C) - for better or worse?

BACKGROUND AND AIMS

The use of Friedewald's formula to calculate serum low-density lipoprotein cholesterol (LDL-C) is well-known to have limitations. A modification of it, in 2013, has been proposed to be superior. However, it was not known whether LDL-C values (calculated by the modified formula) meet laboratory performance criteria for their estimation. This study aimed to evaluate this.

METHODS AND RESULTS

LDL-C values were calculated for 129,821 lipid profiles, using both Friedewald's formula and its modified version. Kappa statistics and intra-class correlation coefficient (ICC) were used to determine degree of agreement between directly measured and calculated values for LDL-C. Bias and total percentage error of the values were calculated. LDL-C concentrations calculated by the modified formula showed a greater degree of agreement with directly measured values (kappa = 0.713) than those calculated by Friedewald's formula (kappa = 0.595). Both the formulae produced values with negative biases (-3.47 for the modified formula and -7.62 for Friedewald's formula) and total percentage errors above the recommended limit of 12% (15.57% for the modified formula and 21.77% for Friedewald's formula). ICC showed that values calculated by the modified formula showed a greater degree of agreement with directly measured values, across a range of LDL-C values.

CONCLUSION

Calculated LDL-C values, using the modified formula, showed better agreement with directly measured values, and less bias and percentage total error than those obtained by use of Friedewald's formula. However, the percentage total error with use of the modified formula exceeded the recommended limit for LDL-C.

Non-HDL-C/TG ratio indicates significant underestimation of calculated low-density lipoprotein cholesterol (LDL-C) better than TG level: a study on the reliability of mathematical formulas used for LDL-C estimation

OBJECTIVES

Low-density lipoprotein cholesterol (LDL-C) is the main laboratory parameter used for the management of cardiovascular disease. The aim of this study was to compare measured LDL-C with LDL-C as calculated by the Friedewald, Martin/Hopkins, Vujovic, and Sampson formulas with regard to triglyceride (TG), LDL-C and non-high-density lipoprotein cholesterol (non-HDL-C)/TG ratio.

METHODS

The 1,209 calculated LDL-C results were compared with LDL-C measured using ultracentrifugation-precipitation (first study) and direct (second study) methods. The Passing-Bablok regression was applied to compare the methods. The percentage difference between calculated and measured LDL-C (total error) and the number of results exceeding the total error goal of 12% were established.

RESULTS

There was good correlation between the measurement and calculation methods (r 0.962-0.985). The median total error ranged from -2.7%/+1.4% (first/second study) for Vujovic formula to -6.7%/-4.3% for Friedewald formula. The numbers of underestimated results exceeding the total error goal of 12% were 67 (Vujovic), 134 (Martin/Hopkins), 157 (Samspon), and 239 (Friedewald). Less than 7% of those results were obtained for samples with TG >4.5 mmol/L. From 57% (Martin/Hopkins) to 81% (Vujovic) of underestimated results were obtained for samples with a non-HDL-C/TG ratio of <2.4.

CONCLUSIONS

The Martin/Hopkins, Vujovic and Sampson formulas appear to be more accurate than the Friedewald formula. To minimize the number of significantly underestimated LDL-C results, we propose the implementation of risk categories according to non-HDL-C/TG ratio and suggest that for samples with a non-HDL-C/TG ratio of <1.2, the LDL-C level should not be calculated but measured independently from TG level.