Low-density Lipoprotein Cholesterol Estimation Research Articles

Low-Density Lipoprotein Cholesterol Gymnastics: Exploring the Advantages and Limitations of the Friedewald, Martin–Hopkins, and Sampson Equations for Personalized Lipid Management

Background: The most commonly used method for low-density lipoprotein cholesterol (LDL-C) estimation is the Friedewald equation, which has notable limitations. However, more accurate methods have been proposed. This study investigates the advantages and limitations of these methods and identifies the contexts in which each equation is the most or least applicable. Methods: A cohort of 222 individuals underwent a standard lipid profile assessment, including directly measuring their LDL-C (dLDL-C). LDL-C was also estimated using the Friedewald, Martin–Hopkins, and Sampson equations. The differences (%Delta) between the estimated and measured LDL-C were analyzed in relation to dLDL-C, high-density lipoprotein cholesterol (HDL-C), and triglyceride levels. Results: The %Delta was significantly lower (p < 0.0001) for the Martin–Hopkins (−8.8 ± 9.8) and Sampson (−9.5 ± 9.2) equations compared to Friedewald (−12.2 ± 9.2). All equations increasingly underestimated LDL-C as the dLDL-C levels decreased. The %Delta of the Martin–Hopkins equation showed significant positive correlations with dLDL-C (≤130 mg/dL) and triglycerides and a significant negative correlation with HDL-C. In a subgroup of 30 individuals with extreme %Delta values, patterns of gross underestimation were observed, particularly when low LDL-C, low triglycerides, and high HDL-C coincided. Conclusions: The Martin–Hopkins equation is a superior method for LDL-C estimation and a valuable tool in precision medicine. However, clinicians and laboratory professionals must be aware of its limitations and recognize patterns that could lead to significant LDL-C underestimation. We propose an algorithm for clinical laboratories to provide personalized LDL-C assessments.

More precise method of low-density lipoprotein cholesterol estimation for tobacco and electronic cigarette smokers: A cross-sectional study

More precise method of low-density lipoprotein cholesterol estimation for tobacco and electronic cigarette smokers: A cross-sectional study

Choosing the right equation for calculating indirect LDL-Cholesterol (LDL-C) in adult Pakistani population: Evaluation of seven equations using big data analytics

ObjectiveCardiovascular diseases (CVDs) are a leading cause of mortality worldwide. Low density lipoprotein cholesterol (LDL-C) contributes to the atherogenic process. However, direct LDL-C (d-LDL) has rarely been estimated by the gold standard method because it is cumbersome and expensive. We aim to evaluate calculated low density lipoprotein (LDL-c) by various equations with reference to directly measured LDL-C in the Pakistani adult population as a cost-effective alternative. MethodsWe retrospectively evaluated the validity of seven equations for estimating calculated LDL-C by computing correlation coefficients (r) and Bland Altman plots to assess agreement (mean %) for (d-LDL) and calculated (LDL-c) on all seven equations. Statistical analysis was performed in Stata Statistical Software: Release 17, College Station, TX: StataCorp LLC. ResultsWe analyzed 247082 direct assays of lipid profiles of adults aged ≥18 years. The mean LDL-C levels computed on Friedewald, de Cordova, Chen, Hattori, Vujovic, Teerakanchana, Sampson equations were 106.8 ± 31.4, 103.7 ± 25.0, 108.6 ± 28.2, 100.1 ± 29.5, 115.2 ± 31.2, 113.1 ± 28.3 and 110.3 ± 30.6 respectively. Friedewald and Hattori equations correlated strongly with direct LDL-C (r = 0.937) for each followed by Sampson (r = 0.935) and Vujovic (r = 0.931). However, the median bias was least for the Friedwald equation (−1.6) compared to the other equations. ConclusionIn contrast to the global literature advocating for the use of newer equations, although the conventional and widely utilized Friedewald equation remains the best alternative for calculated LDL-C estimation in adult Pakistani population.

Explainable artificial intelligence for LDL cholesterol prediction and classification

IntroductionMonitoring LDL-C levels is essential in clinical practice because there is a direct relation between low-density lipoprotein cholesterol (LDL-C) levels and atherosclerotic heart disease risk. Therefore, measurement or estimate of LDL-C is critical. The present study aims to evaluate Artificial Intelligence (AI) and Explainable AI (XAI) methodologies in predicting LDL-C levels while emphasizing the interpretability of these predictions. Materials and methodsWe retrospectively reviewed data from the Laboratory Information System (LIS) of Ankara Etlik City Hospital (AECH). We included 60.217 patients with standard lipid profiles (total cholesterol [TC], high-density lipoprotein cholesterol, and triglycerides) paired with same-day direct LDL-C results. AI methodologies, such as Gradient Boosting (GB), Random Forests (RF), Support Vector Machines (SVM), and Decision Trees (DT), were used to predict LDL-C and compared directly measured and calculated LDL-C with formulas. XAI techniques such as Shapley additive annotation (SHAP) and locally interpretable model-agnostic explanation (LIME) were used to interpret AI models and improve their explainability. ResultsPredicted LDL-C values using AI, especially RF or GB, showed a stronger correlation with direct measurement LDL-C values than calculated LDL-C values with formulas. TC was shown to be the most influential factor in LDL-C prediction using SHAP and LIME. The agreement between the treatment groups based on NCEP ATPIII guidelines according to measured LDL-C and the LDL-C groups obtained with AI was higher than that obtained with formulas. ConclusionsIt can be concluded that AI is not only a reliable method but also an explainable method for LDL-C estimation and classification.

Comparison of Performance of Various Calculated Low-Density Lipoprotein (LDL) Methods in the Indian Population: A Hospital-Based Study.

In recent times, there has been a surge in proposed alternative approaches to computing low-density lipoprotein cholesterol (LDL-C), with a focus on enhancing precision, particularly within diverse demographic and clinical groups. Our aim is to assess the agreement, precision, and practicality of these methods compared to direct LDL-C measurements, with the goal of identifying the most effective approach for estimating LDL-C in the Indian context. It is a retrospective analytical study. Lipid profile data were gathered from the laboratory and organized in Microsoft Excel for analysis. LDL-C was computed using three different methods: the Friedwald formula, the Martin-Hopkins formula, and Sampson's formula. These calculations were then compared with the direct method of LDL-C estimation in two distinct groups: when triglyceride (TG) levels were less than 400 mg/dL and when TG levels exceeded 400 mg/dL. Bland-Altman plots were generated, and concordance correlation coefficients (CCCs) were computed to determine the most suitable calculated method. Data from 1,776 participants were analysed and divided into two groups. In both Group 1 (TG < 400 mg/dL) and Group 2 (TG > 400 mg/dL) considering bias, limits of agreements, and correlation coefficient, as seen on the Bland-Altman and CCC, Martin-Hopkins equation was found to be performing better than Friedwald and Sampson's equation. In this study, the Martin-Hopkins formula appears to be the most appropriate choice for precise LDL-C level measurements and indicated improved accuracy and consistency in LDL-C measurements, especially in individuals with elevated TG levels. This underscores its importance in ensuring precise assessment and suitable clinical management.

A comparative evaluation of low-density lipoprotein cholesterol estimation: Machine learning algorithms versus various equations

BackgroundGiven the critical importance of Low-density lipoprotein cholesterol (LDL-C) levels in determining cardiovascular risk, it is essential to measure LDL-C accurately. Since the Friedewald formula generates incorrect predictions in many circumstances, new equations have been developed to overcome the Friedewald equations' shortcomings. This study aimed to compare estimated LDL-C with directly measured LDL-C (dLDL-C), as well as their performance in predicting LDL-C, utilizing Friedewald, extended Martin–Hopkins, Sampson, de Cordova, and Vujovic formulas and five machine learning (ML) algorithms. MethodsA total of 29,504 samples from the ISLAB-2 Core Laboratory were included in the study. All statistical analysis was performed using R version 4.1.2. Statistical Language. ResultsBayesian-Regularized Neural Network (BRNN) (r = 0.957) and Random Forest (RF) (r = 0.957) algorithms showed a higher correlation with dLDL-C than the other equations in all-testing dataset. All ML algorithms demonstrated less bias than pre-existing LDL-C equations with dLDL-C and outperformed the LDL-C estimation equations in terms of concordance in all-testing dataset. ConclusionsThe results of our research indicate that when compared to conventional equations, ML algorithms are much more effective in predicting LDL-C. ML algorithms, aided by a vast dataset, could have the capability to predict LDL-C levels even in cases where triglyceride levels are high, unlike the limited usage of Friedewald formula.

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.

An improved method for estimating low LDL-C based on the enhanced Sampson-NIH equation

BackgroundThe accurate measurement of Low-density lipoprotein cholesterol (LDL-C) is critical in the decision to utilize the new lipid-lowering therapies like PCSK9-inhibitors (PCSK9i) for high-risk cardiovascular disease patients that do not achieve sufficiently low LDL-C on statin therapy.ObjectiveTo improve the estimation of low LDL-C by developing a new equation that includes apolipoprotein B (apoB) as an independent variable, along with the standard lipid panel test results.MethodsUsing β-quantification (BQ) as the reference method, which was performed on a large dyslipidemic population (N = 24,406), the following enhanced Sampson-NIH equation (eS LDL-C) was developed by least-square regression analysis:eSLDL-C=TC1.15-HDL-C1.25-TG6.99-TG×NonHDL-C1120+TG28910+TG×ApoB1240+ApoB4.54-4.73\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$eS\\,LDL-C= \\frac{TC}{1.15}-\\frac{HDL-C}{1.25}-\\frac{TG}{6.99}-\\frac{\\left(TG\ imes NonHDL-C\\right)}{1120}+\\frac{{TG}^{2}}{8910}+\\frac{\\left(TG\ imes ApoB\\right)}{1240}+\\frac{ApoB}{4.54}-4.73$$\\end{document}ResultsThe eS LDL-C equation was the most accurate equation for a broad range of LDL-C values based on regression related parameters and the mean absolute difference (mg/dL) from the BQ reference method (eS LDL-C: 4.51, Sampson-NIH equation [S LDL-C]: 6.07; extended Martin equation [eM LDL-C]: 6.64; Friedewald equation [F LDL-C]: 8.3). It also had the best area-under-the-curve accuracy score by Regression Error Characteristic plots for LDL-C < 100 mg/dL (eS LDL-C: 0.953; S LDL-C: 0.920; eM LDL-C: 0.915; F LDL-C: 0.874) and was the best equation for categorizing patients as being below or above the 70 mg/dL LDL-C treatment threshold for adding new lipid-lowering drugs by kappa score analysis when compared to BQ LDL-C for TG < 800 mg/dL (eS LDL-C: 0.870 (0.853–0.887); S LDL-C:0.763 (0.749–0.776); eM LDL-C:0.706 (0.690–0.722); F LDL-C:0.687 (0.672–0.701). Approximately a third of patients with an F LDL-C < 70 mg/dL had falsely low test results, but about 80% were correctly reclassified as higher (≥ 70 mg/dL) by the eS LDL-C equation, making them potentially eligible for PCSK9i treatment. The M LDL-C and S LDL-C equations had less false low results below 70 mg/dL than the F LDL-C equation but reclassification by the eS LDL-C equation still also increased the net number of patients correctly classified.ConclusionsThe use of the eS LDL-C equation as a confirmatory test improves the identification of high-risk cardiovascular disease patients, who could benefit from new lipid-lowering therapies but have falsely low LDL-C, as determined by the standard LDL-C equations used in current practice.

Applicability of Artificial Intelligence in the Field of Clinical Lipidology: A Narrative Review.

The development of advanced technologies in artificial intelligence (AI) has expanded its applications across various fields. Machine learning (ML), a subcategory of AI, enables computers to recognize patterns within extensive datasets. Furthermore, deep learning, a specialized form of ML, processes inputs through neural network architectures inspired by biological processes. The field of clinical lipidology has experienced significant growth over the past few years, and recently, it has begun to intersect with AI. Consequently, the purpose of this narrative review is to examine the applications of AI in clinical lipidology. This review evaluates various publications concerning the diagnosis of familial hypercholesterolemia, estimation of low-density lipoprotein cholesterol (LDL-C) levels, prediction of lipid goal attainment, challenges associated with statin use, and the influence of cardiometabolic and dietary factors on the discordance between apolipoprotein B and LDL-C. Given the concerns surrounding AI techniques, such as ethical dilemmas, opacity, limited reproducibility, and methodological constraints, it is prudent to establish a framework that enables the medical community to accurately interpret and utilize these emerging technological tools.

Concordance between low density lipoprotein cholesterol concentration measurement by enzymatic method and calculation by Friedewald formula in cardiovascular risk classification

Accurate estimation of low-density lipoprotein cholesterol (LDL-C) is important for cardiovascular risk assessment and guiding cholesterol-lowering therapy. Due to the high cost of β-quantification (Gold standard) and time-consuming, direct measurement of LDL-C is an alternative method. However, unlike the calculation of LDL-C by Friedewald formula, there is an additional cost in terms of reagents for performing a direct LDL-C test. The current study aimed to compare direct LDL-C concentration determination to data calculated by Friedewald formula. 752 lipid profiles of 710 people with LDL-C estimated by direct LDL assay, in the Biochemistry laboratory of university hospital center of Angré, were included in the study. In the same group, LDL-C was calculated using Friedewald formula. Lin’s concordance correlation coefficient (ccc) and Passing-Bablok regression analysis using, MedCal software, were performed to assess the strength of concordance between the 2 methods, and identify any possible bias. The concordance between the two methods was moderate (ρc = 0.9466). Passing-Bablok regression analysis revealed a systematic bias between the two methods. The total error observed (TEobs) between the two methods was higher than allowable total error recommended by the NCEP-ATPIII when LDL-C values was less than 159 mg/dL (4.112 mmol/L). The Friedewald formula resulted in lower LDL-C concentration values. Despite its cost-effectiveness in the estimation of LDL-C, an underestimation of LDL-C levels could result in inaccurate cardiovascular diseases (CVD) risk assessments and potentially significant future societal costs due to inadequate prevention and treatment of CVD.

Assessing the Practical Differences in LDL-C Estimates Calculated by Friedewald, Martin/Hopkins, or NIH Equation 2: An Observation Cross-Sectional Study.

Low-density lipoprotein-cholesterol (LDL-C) remains a clinically important cholesterol target in primary prevention of atherosclerotic cardiovascular disease. The present study aimed to assess the practical differences among three equations utilized for the estimation of LDL-C: the Friedewald, the Martin/Hopkins, and the NIH equation 2. Blood lipid measurements from 4,556 noninstitutionalized participants, aged 12 to 80, were obtained from the 2017-2020 National Health and Nutrition Examination Survey study. We 1) assessed the differences between three calculated LDL-C estimates, 2) examined the correlations between LDL-C estimates using correlation coefficients and regression, and 3) investigated the degree of agreement in classifying individuals into the LDL-C category using weighted Kappa and percentage of agreement. The differences in LDL-C estimates between equations varied by sex and triglyceride levels (p<0.001). Overall, the mean of absolute differences between Friedewald and Martin/Hopkins was 3.17 mg/dL (median=2.0, 95% confidence interval [CI] [3.07-3.27]). The mean of absolute differences between Friedewald and NIH Equation 2 was 2.08 mg/dL (median=2.0, 95% CI [2.03-2.14]). Friedewald correlated highly with Martin/Hopkins (r=0.991, rho=0.989) and NIH Equation 2 (r=0.998, rho=0.997). Cohen's weighted Kappa=0.92 between Friedewald and Martin/Hopkins, and 0.95 between Friedewald and NIH equation 2. The percentage of agreement in classifying individuals into the same LDL-C category was 93.0% between Friedewald and Martin/Hopkins, and 95.4% between Friedewald and NIH equation 2. Understanding the practical differences in LDL-C calculations can be helpful in facilitating decision-making during a paradigm shift.

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

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. 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). 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). 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.

Development of a Modified Friedewald's Formula to Calculate Low-Density Lipoprotein in an Iranian Population.

Elevated low-density lipoprotein cholesterol (LDL-C) is a significant risk factor for cardiovascular diseases. LDL-C can be directly measured using various methods, but this requires expensive equipment. Currently, clinical laboratories estimate LDL-C based on Friedewald's formula (FF). We aimed to develop a modified formula based on directly measured LDL-C (D-LDL-C) values in a large population in Southern Iran and compare the results with various other estimation formulas. The participants of this cross-sectional study were adults aged >18 years living in Southern Iran. Blood samples from 15,200 individuals were collected, and the measured lipid parameters were randomly divided into training (n=10,184) and validation (n=5,016) datasets. A new formula was developed using a linear regression model, and its accuracy was validated. Pearson's correlation and Cohen's kappa were used to determin the relationship between D-LDL-C and calculated LDL-C (C-LDL-C). The developed formula for the estimation of LDL-C was 0.857 total cholesterol (TC)-0.915 high-density lipoprotein cholesterol (HDL-C)-0.115 triglycerides (TG). Based on our proposed formula, for TG<150 and TG≥150 mg/dL, there was a significant correlation between mean values of D-LDL-C and C-LDL-C (r=0.985 and r=0.974, respectively). Compared to other formulas, C-LDL-C obtained from the proposed formula had the highest correlation with D-LDL-C. The agreement between D-LDL-C and C-LDL-C for TC<200, 200-239, and ≥240 mg/dL was 80.8%, 63.2%, and 67.4%, respectively, indicating a higher level of agreement than other formulas. The new formula appears to be more accurate than FF when applied to the population of Southern Iran.

Factors to consider with estimated low-density lipoprotein cholesterol using the new Sampson/NIH equation

IntroductionThe most commonly utilized method for determining low-density lipoprotein cholesterol (LDLc) is by Friedewald estimation (FeLDLc). A new approach to better estimate LDLc has been proposed by Sampson et al. 2020, known as the Sampson/National Institutes of Health (NIH) estimation of LDLc (NeLDLc), to overcome the limitations of FeLDLc. Non-high-density lipoprotein-cholesterol (Non-HDLc), has equivalent cut-offs to LDLc, established by the 2021 Canadian Cardiovascular Society (CCS) guideline. We hypothesized that NeLDLc remains an inadequate substitute at high triglyceride levels when compared to Non-HDLc. MethodsA retrospective analysis of 120,959 lipid profiles (47085 patients) spanning five years across a large academic medical center was utilized for comparison of NeLDLc and FeLDLc relative to Non-HDLc as a function of triglyceride content. Regression and concordance between calculated methods were determined at various triglyceride levels to determine optimal utilization of NeLDLc. ResultsNeLDLc is generally more correlated and has greater concordance than FeLDLc with Non-HDLc. NeLDLc with increasing triglycerides can produce negatively erroneous results, even with triglycerides < 4.52 mmol/L (400 mg/dL). The largest variation of NeLDLc results is notable at < 0.5 mmol/L (19 mg/dL). Currently, the 2021 CCS guideline recommends reliance on Non-HDLc when triglycerides are > 1.5 mmol/L (133 mg/dL). With the use of NeLDLc, this triglyceride cut-off can be increased to 1.7 mmol/L(150 mg/dL), making it consistent with the hypertriglyceridemia flagging limit. ConclusionNeLDLc offers increased concordance and correlation to Non-HDLc when compared to FeLDLc. However, caution is warranted when triglycerides are > 4.5 mmol/L and when NeLDLc results are < 0.5 mmol/L. Adopting NeLDLc enables flagging at 1.7 mmol/L (vs. 1.5 mmol/L) of triglycerides to suggest reliance on Non-HDLc while simultaneoulsly indicating hypertriglyceridemia.

Martin's Formula As the Most Suitable Method for Estimation of Low-Density Lipoprotein Cholesterol in Indian Population.

Background Because of cost effectiveness, most of the laboratories in India estimate low-density lipoprotein cholesterol (LDL-C) levels with the Friedewald's formula. There were many shortcomings of the Friedewald's formula. Recently, Martin and colleagues have derived a new formula for calculating LDL-C. The present study was undertaken to calculate LDL-C using various formulae (Friedewald's formula, Anandaraja's formula, and Martin's formula) and to compare directly measured LDL-C (D-LDL-C) with calculated LDL-C at various ranges of triglyceride (TG) concentration. Materials and Methods The present study compared LDL-C measured by Martin's formula, Friedewald's formula, and Anandaraja's formula with D-LDL-C in 280 outpatient fasting samples between the age groups of 18 and 50 years. Depending on the TG values, study samples were divided into four groups. Group 1: less than 200 mg/dL; Group 2: 200 to 300 mg/dL; Group 3: 300 to 400 mg/dL; and Group 4: more than 400 mg/dL. Results Martin's formula shows highest correlation with r -value of 0.9979 compared with Friedewald's (0.9857) and Anandaraja's (0.9683) r -values. The mean difference was least for Martin's formula (0.31 ± 3.53) compared with other formulae. Among all the groups, percentage of error was least for Martin's formula (0.23%). Martin's LDL-C shows highest concordance (90.90%) compared with Friedewald's (79.60%) and Anandaraja's formulae (82.90%). Conclusion Among all the groups, Martin's formula shows highest correlation, least percentage of error, highest concordance, and least mean differences. At all TG levels, Martin's formula is the best formula compared with the Friedewald's formula and Anandaraja's formula.

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

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. 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. 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. 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.

Dataset dependency of low-density lipoprotein-cholesterol estimation by machine learning.

We evaluated the applicability of a machine learning-based low-density lipoprotein-cholesterol (LDL-C) estimation method and the influence of the characteristics of the training datasets. Three training datasets were chosen from training datasets: health check-up participants at the Resource Center for Health Science (N = 2664), clinical patients at Gifu University Hospital (N = 7409), and clinical patients at Fujita Health University Hospital (N = 14,842). Nine different machine learning models were constructed through hyperparameter tuning and 10-fold cross-validation. Another test dataset of another 3711 clinical patients at Fujita Health University Hospital was selected as the test set used for comparing and validating the model against the Friedewald formula and the Martin method. The coefficients of determination of the models trained on the health check-up dataset produced coefficients of determination that were equal to or inferior to those of the Martin method. In contrast, the coefficients of determination of several models trained on clinical patients exceeded those of the Martin method. The means of the differences and the convergences to the direct method were higher for the models trained on the clinical patients' dataset than for those trained on the health check-up participants' dataset. The models trained on the latter dataset tended to overestimate the 2019 ESC/EAS Guideline for LDL-cholesterol classification. Although machine learning models provide valuable method for LDL-C estimates, they should be trained on datasets with matched characteristics. The versatility of machine learning methods is another important consideration.

Comparison of low-density lipoprotein cholesterol estimation methods in individuals with insulin resistance: A cross-sectional study

Background and aimsThe Friedewald, Sampson, and Martin equations were developed to estimate low-density lipoprotein cholesterol levels; however, the validation data of these equations with and without insulin resistance are insufficient. Materials and methodsWe collected data on low-density lipoprotein cholesterol and lipid profiles from the Korea National Health and Nutrition Examination Survey. Using the data on insulin requirement, insulin resistance was calculated for 4,351 participants (median age, 48 [36–59] years; 49.9% male) using the homeostatic model assessment for insulin resistance (n = 2,713) and quantitative insulin-sensitivity check index (n = 2,400). ResultsAccording to the mean and median absolute deviation, the Martin equation yielded more accurate estimates than other equations when the triglyceride level was < 400 mg/dL with insulin resistance; the Sampson equation yielded lower estimates when the direct low-density lipoprotein cholesterol level was < 70 mg/dL and triglyceride level was < 400 mg/dL without insulin resistance. However, the three equations yielded similar estimates when the triglyceride level was < 150 mg/dL with and without insulin resistance. ConclusionThe Martin equation yielded more appropriate estimates than the Friedewald and Sampson equations for triglyceride levels < 400 mg/dL with and without insulin resistance. If the triglyceride level was < 150 mg, the Friedewald equation could also be considered.

Concordance of LDL-C Estimating Equations with Direct Enzymatic Measurement in Diabetic and Prediabetic Subjects.

Low-density lipoprotein cholesterol (LDL-C) is a well-established biomarker in the management of dyslipidemia. Therefore, we aimed to evaluate the concordance of LDL-C-estimating equations with direct enzymatic measurement in diabetic and prediabetic populations. The data of 31,031 subjects included in the study were divided into prediabetic, diabetic, and control groups according to HbA1c values. LDL-C was measured by direct homogenous enzymatic assay and calculated by Martin-Hopkins, Martin-Hopkins extended, Friedewald, and Sampson equations. The concordance statistics between the direct measurements and estimations obtained by the equations were evaluated. All equations evaluated in the study had lower concordance with direct enzymatic measurement in diabetic and prediabetic groups compared to the non-diabetic group. Even so, the Martin-Hopkins extended approach demonstrated the highest concordance statistic in diabetic and prediabetic patients. Further, Martin-Hopkins extended was found to have the highest correlation with direct measurement compared with other equations. Over the 190 mg/dL LDL-C concentrations, the equation with the highest concordance was again Martin-Hopkins extended. In most scenarios, the Martin-Hopkins extended performed best in prediabetic and diabetic groups. Additionally, direct assay methods can be used at low values of the non-HDL-C/TG ratio (<2.4), as the performance of the equations in LDL-C estimation decreases as non-HDL-C/TG decreases.

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.