Accurate low-density lipoprotein cholesterol (LDL-C) measurement is crucial for cardiovascular risk assessment. Calculated LDL-C values are often preferred over direct enzymatic measurements because of their lower cost and wider accessibility, particularly in resource-constrained laboratory settings. While the Friedewald equation is widely used to calculate LDL-C, its limitations have led to the development of alternative equations such as the Sampson and Martin–Hopkins equations.
Aim
Therefore, this study aimed to assess the performance of three LDL-C equations in hypertriglyceridaemia samples.
Setting
An academic hospital in the Gauteng province.
Methods
A retrospective analysis was conducted on 9337 lipid profile patient results, with 2758 (29.5%) exhibiting hypertriglyceridaemia, defined as triglycerides ≥ 1.7 mmol/L. Low-density lipoprotein cholesterol was determined using a direct enzymatic assay and was calculated using the three equations: Martin–Hopkins, Sampson and Friedewald. Regression analysis between the direct LDL method and the equations was done using Passing-Bablok. Bias and agreement between the different LDL-C measurement methods were evaluated using the Bland-Altman plot, and where agreement between methods was present at clinically relevant concentrations, it was assessed using weighted Cohen’s Kappa statistics. Differences between LDL-C methods were evaluated using the Kruskal–Wallis test.
Results
In hypertriglyceridaemic samples, the Martin–Hopkins equation demonstrated the strongest correlation and the least bias compared to direct LDL measurement. All equations underestimated LDL-C, resulting in patient misclassification. However, Martin–Hopkins had the least misclassified LDL results, particularly in the < 1.8 mmol/L concentration range.
Conclusion
The findings suggest that LDL-C equations exhibit satisfactory agreement with direct methods, with the Martin-Hopkins equation being the best-performing calculated method, while the Friedewald and Sampson equations exhibited considerable underestimation of LDL-C levels.
Contribution
The underestimation of LDL-C equations shows potential of patient misclassification with regards to treatment intervention limits which may lead to erroneous clinical decisions, emphasising the need for careful consideration in clinical implementation.
hypertriglyceridaemiaLDL cholesterolMartin–HopkinsSampsonFriedewaldFunding information This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.Introduction
Accurate low-density lipoprotein cholesterol (LDL-C) measurement is crucial for the assessment of risk and clinical management of cardiovascular disease (CVD).1 The gold standard for the measurement of LDL-C is β-quantification, which is costly and laborious.2 Consequently, the direct enzymatic assays have been the method of choice in quantifying LDL-C.3 However, the direct methods are also limited by high costs, questionable accuracy compared to modern LDL-C equations and a lack of standardisation.4,5 Alternative methods have been developed where LDL-C is estimated using other lipid parameters such as triglyceride, total cholesterol (TC) and high-density cholesterol.6 The Friedewald equation has been extensively used since the 1970s.7 This equation is of limited use, however, when LDL-C levels are very low or when triglyceride concentrations are elevated.6 Hypertriglyceridaemia is a common lipid abnormality, characterised by high triglyceride levels in the blood. It is often seen in metabolic syndrome and type 2 diabetes. Triglyceride levels are considered high if > 2 mmol/L (non-fasting) or > 1.7 mmol/L (fasting).8 It is also worth noting that this patient population experiences an increased risk for CVD.9 This is in part because of the increased triglyceride levels serving as a reflection of the concentration of apolipoprotein B-containing lipoproteins that are rich in triglyceride content.10
Traditionally, direct methods have been preferred over indirect methods because of their perceived accuracy. However, new equations, such as the ones developed by Sampson et al. and Martin–Hopkins, are not subject to the same limitations as the Friedewald equation.11 Although these methods have been shown to provide results that are comparable to direct methods, they are not widely used in clinical laboratories.11 Moreover, even though direct methods are the preferred method, the cost associated with their use is a limitation, especially in resource-constrained settings. Considering this, in conjunction with the limited information regarding the validity of these equations in populations that are not predominantly Caucasian, this study sought to address the gap by investigating the validity of alternative LDL-C equations, such as the Martin–Hopkins and Sampson equations, in non-Caucasian populations.
Research methods and designStudy design
This was a retrospective cross-sectional observational study to assess the performance of three LDL-C equations in hypertriglyceridaemic samples.
Data analysis
Demographic data and patient results were requested and retrieved from the National Health Laboratory Service (NHLS) laboratory information system, TrakCare®, via the NHLS Corporate Data Warehouse (CDW). Low-density lipoprotein cholesterol levels were categorised based on the South African dyslipidaemia guidelines for treatment intervention limits, that is, LDL-C < 1.8 mmol/L (Optimal); 1.8 mmol/L – 2.5 mmol/L (Near Optimal); 2.5 mmol/L – 4.9 mmol/L (High); and > 4.9 mmol/L (Very High).12 Agreement between the different measurement methods, at the clinically relevant LDL-C categories, was assessed using a weighted Cohen’s Kappa statistic and expressed as a Kappa value (k). Agreement was considered excellent if k ≥ 0.81; good if k was between 0.41 and 0.80; fair if k was between 0.21 and 0.40; and poor if k ≤ 0.20. Bias and agreement between the different LDL-C measurement methods were evaluated using the Bland-Altman plot, and Passing-Bablok regression analysis was performed to determine the relationship between the different methods. The difference between LDL-C levels measured by the different methods was assessed using the Kruskal–Wallis test and the Benjamini–Hochberg test. The McNemar test was used to evaluate the difference between the methods in the different LDL-C categories. All analyses were conducted using Statistical Package for Social Sciences (SPSS) version 28 (IBM Corp, New York, United States [US]).
Methods
Serum samples were analysed using the Siemens Atellica automated chemistry system (Siemens Healthineers, Erlangen, Germany). Triglycerides (TG) were measured using an enzymatic colorimetric assay with glycerol phosphate oxidase and peroxidase. The assay for TC uses cholesterol esterase and cholesterol oxidase, in which the hydrolysis and oxidation of cholesterol esters subsequently lead to the generation of a light-absorbing compound. The intensity of the absorbance of the compound at a wavelength of 505 nm out of 694 nm is directly proportional to the concentration of cholesterol. Low-density lipoprotein cholesterol and high-density lipoprotein cholesterol (HDL-C) were measured directly using enzymatic colorimetric assays with cholesterol esterase and cholesterol oxidase. In addition, LDL-C was calculated using the following equations:
Patients were anonymised using unique codes for each patient. The study commenced after receiving approval from the Sefako Makgatho Health Sciences University research committee (SMUREC). The ethics approval number for this study was SMUREC/M/198/2023:PG.
Results
Out of the initial 64 777 result profiles retrieved, only 9337 lipid result profiles were retained for the study, and of these, 2759 exhibited hypertriglyceridaemia. The rest of the result profiles were excluded because of incomplete lipogram profile results. The lipogram results revealed notable differences in lipid profiles between males and females (Table 1). Total cholesterol levels differed between genders, with females having a higher median value (3.95 mmol/L) compared to males (3.70 mmol/L). Females also had higher median LDL cholesterol (2.80 mmol/L) and HDL cholesterol (1.23 mmol/L) values compared to males (2.58 mmol/L and 1.11 mmol/L, respectively). In contrast, males had slightly higher median triglyceride levels (1.63 mmol/L) than females (1.50 mmol/L). Additionally, females had higher median non-HDL cholesterol values (5.88 mmol/L) compared to males (5.61 mmol/L). These findings suggest distinct lipid profiles between males and females, with females having higher levels of LDL, HDL and non-HDL cholesterol, while males have slightly higher triglyceride levels.
The distribution of LDL-C results across age and gender revealed that LDL-C categories were spread across all age ranges (0–106 years) without a clear age-related pattern. Notably, females tended to have higher LDL-C values than males, particularly in the 2.5 mmol/L – 4.9 mmol/L category (Table 2). Most individuals (51.1%) fell into this category, followed by the 1.8 mmol/L – 2.4 mmol/L category (26.4%). In contrast, the < 1.8 mmol/L category had a relatively small number of individuals (10.3%), while the > 4.9 mmol/L category had the smallest number (6.2%).
Distribution of low-density lipoprotein cholesterol results across gender.
Gender
LDL-C category
< 1.8 mmol/L (N)
1.8 mmol/L – 2.4 mmol/L (N)
2.5 mmol/L – 4.9 mmol/L (N)
> 4.9 mmol/L (N)
Male
775
850
1534
69
Female
924
1372
3172
183
LDL-C, low-density lipoprotein cholesterol.
Agreement between the equations: Friedewald, Martin–Hopkins and Sampson
The agreement between the three equations was excellent in hypertriglyceridaemic samples, indicating consistent classification of LDL-C levels into the same categories. While there were some minor discrepancies, particularly between Friedewald and Martin-Hopkins, the overall agreement was remarkable, with Martin showing the most consistency with Friedewald (see Table 3).
Kappa value between low-density lipoprotein cholesterol equations in hypertriglyceridaemic patients.
Correlation between the direct low-density lipoprotein cholesterol and the equations: Friedewald, Martin–Hopkins and Sampson in hypertriglyceridaemic patients
In patients with hypertriglyceridaemia, the correlations between direct LDL-C and calculated LDL-C values from Friedewald, Martin–Hopkins and Sampson equations demonstrated a positive linear association (Figure 1). As evidenced by the exceptional r value (0.94), the Martin–Hopkins equation demonstrated the strongest correlation, while the Sampson equation demonstrated the least correlation with direct LDL-C (Table 4).
(a) Direct low-density lipoprotein cholesterol (LDL-C) versus Friedewald LDL-C, (b) Direct LDL-C versus Martin–Hopkins LDL-C and (c) Direct LDL-C versus Sampson LDL-C for the hypertriglyceridaemic patients.
Correlations between direct low-density lipoprotein cholesterol (LDL-C) versus Friedewald LDL-C, Martin–Hopkins LDL-C, and Sampson LDL-C.
Bias and agreement between the direct low-density lipoprotein cholesterol and the equations: Friedewald, Martin–Hopkins and Sampson in hypertriglyceridaemic patients
Analysis of the Bland-Altman plots indicated good agreement between direct LDL-C measurement and calculated LDL-C methods (Figure 2a–c). The Martin–Hopkins demonstrated the lowest mean difference, while the Sampson equation demonstrated the highest mean difference (Table 5).
(a) Bland-Altman plot for direct low-density lipoprotein cholesterol (LDL-C) versus Friedewald LDL-C in hypertriglyceridaemic patients. (b) Bland-Altman plot for Direct LDL-C versus Martin–Hopkins LDL-C in hypertriglyceridaemic patients. (c) Bland-Altman plot for Direct LDL-C versus Sampson LDL-C in hypertriglyceridaemic patients.
Mean difference observed between direct low-density lipoprotein cholesterol and the equations.
It was observed that the Friedewald equation tends to underestimate LDL-C values by an average of 0.86799 mmol/L (95% CI: 0.8461 to 0.8899) compared to the direct LDL-C method (Figure 2a).
Further analysis between the direct method with the other two equations (Martin–Hopkins and Sampson) investigated in the study showed a systematic difference, whereby a mean difference of 0.57199 mmol/L (95% CI: 0.5518 to 0.5922) was observed between the direct method (Figure 2b) and the Martin–Hopkins equation, whereas a mean difference of 0.92780 mmol/L (95% CI: 0.8879 to 0.9577) was seen between the direct method and the Sampson equation (Figure 2c).
Agreement and result classification in hypertriglyridemic samples
The agreement between direct LDL-C and calculated LDL-C values from Friedewald and Martin–Hopkins was good (k = 0.73 and k = 0.79, respectively), while that of Sampson was excellent (k = 0.82). However, all equations were shown to underestimate direct LDL-C concentrations, leading to the majority of the calculated results falling under the < 1.8 mmol/L results category. When comparing direct LDL-C to the equations, 1169 (42%) results were in the < 1.8 mmol/L category using the Friedewald equation, while 1187 (43%) results were in this category when using the Sampson equation. The Martin–Hopkins equation was least affected in this regard, with 835 (30%) results falling into this category. This contrasts the corresponding findings in the direct LDL-C measurement results, with only 416 (15%) results falling into the < 1.8 mmol/L category and the majority of results (56%) falling into the 2.5 mmol/L – 4.9 mmol/L category (Table 6 to Table 8).
Crosstab and Kappa value between direct low-density lipoprotein cholesterol and Friedewald low-density lipoprotein cholesterol.
The Kruskal–Wallis test demonstrated a significant difference (p < 0.0001) in mean LDL-C concentrations between the LDL-C measuring techniques. Post hoc analysis using the Benjamini–Hochberg test revealed statistically significant differences (p < 0.05) between the methods; hence, each of the four methods produces distinct results (Table 5).
Discussion
This study evaluated the performance of three LDL-C equations – Martin–Hopkins, Sampson and Friedewald – in hypertriglyceridaemic samples. The results showed that the Martin–Hopkins equation performed best relative to direct LDL-C measurement, demonstrating the strongest correlation and lowest bias. The study’s findings are consistent with previous research, which has also shown the Martin–Hopkins equation to outperform the Friedewald equation in patients with hypertriglyceridaemia.16 The Friedewald equation exhibited a weaker correlation and poorer agreement with LDL-C direct, likely because of its reliance on a fixed ratio of VLDL cholesterol to triglycerides (> 4.5 mmol/L), which may not hold true in all individuals, particularly those with hypertriglyceridaemia.17 The Sampson equation showed intermediate performance, suggesting that it may be effective in certain populations but not others.18
The overall superior performance of the Martin–Hopkins and Sampson equations over the Friedewald equation may be attributed to the analytical techniques used to derive the Martin–Hopkins and Sampson equations. The Martin–Hopkins and Sampson equations were based on vertical auto-profile and beta quantification, respectively, whereby both techniques utilise ultracentrifugation to partition the various lipoproteins, a method considered the gold standard in lipoprotein analysis. Furthermore, the use of a variable factor by the Martin–Hopkins equation and least squares regression by the Sampson equation allows both equations to accurately account for VLDL-C in hypertriglyceridaemic (> 1.7 mmol/L) states.19
This study also investigated the agreement between the direct LDL-C assay and calculated LDL values to classify patients into different categories qualitatively. The results revealed good agreement between calculated LDL-C values and direct LDL-C measurements, as evidenced by the high Kappa values; however, a disparity exists between the methods, indicating a potential for misclassification of LDL-C levels in hypertriglyceridaemic patients. Notably, the calculated LDL-C equations demonstrated exceptionally high agreement amongst themselves, suggesting interchangeability for classification purposes. The significant differences between methods, shown by the Benjamini–Hochberg test and the underestimation of LDL-C by equations versus direct assays, may explain the discordance and potential for patient misclassification and inadequate treatment.
The results of this study align with several other investigations that have evaluated the performance of LDL-C equations in hypertriglyceridaemic samples. However, some studies have yielded differing results, such as Wieczorek et al, which found the Sampson equation to be superior in patients with severe hypertriglyceridaemia (triglyceride levels > 5 mmol/L). Additionally,19 comparable performance was observed between the Friedewald and Martin–Hopkins equations in patients with mild hypertriglyceridaemia (triglyceride levels of 2 mmol/L – 4 mmol/L). These discrepancies may be attributed to variations in study populations, lipid measurement methods and the range and severity of hypertriglyceridaemia.
This study boasts several strengths, including a large sample size, which provides robust results, and the inclusion of patients with hypertriglyceridaemia (≥ 1.7 mmol/L), which allows for a more comprehensive evaluation of three LDL-C equations. However, the study is not without its limitations. The retrospective design and single-centre nature of the study may introduce selection bias, which limits generalisability to other populations. Furthermore, the lack of data on patient outcomes makes it challenging to assess the clinical impact of the findings. Potential measurement errors or variability in lipid measurements may also have influenced the results. Differences in analytical methods, calibration procedures or instrument types used across laboratories can introduce variation in lipid measurements, particularly for triglycerides and calculated LDL-C. Such inter-assay variability could contribute to discrepancies between equations and direct assays, and should be considered a limitation of the study. Incomplete lipid profiles were excluded from the study. However, where non-HDL-C results were available, a discordance may be observed between non-HDL-C and triglyceride levels, particularly in cases of moderate to severe hypertriglyceridaemia, such as in patients with diabetes and metabolic syndrome, because of the contribution of chylomicrons and their remnants to non-HDL-C values.
Conclusion
This study evaluated the agreement between direct LDL-C measurements and calculated LDL-C values from Friedewald, Martin–Hopkins and Sampson equations. The results showed that the Martin–Hopkins equation demonstrated the best performance amongst the calculated methods, with excellent agreement and minimal bias compared to direct LDL-C measurements. Friedewald and Sampson equations exhibited significant underestimation of LDL-C levels, potentially leading to patient misclassification and erroneous clinical decisions. The study’s findings have significant implications for clinical practice, suggesting that in settings where direct assays for LDL-C measurement are not available, the adoption of the Martin–Hopkins equation for LDL-C estimation may be a suitable alternative for hypertriglyceridaemic patients. Although the Martin Hopkins Equation could be a suitable alternative, further validation of this indirect method is needed with various cohorts that include different population groups to account for variability in settings where direct LDL-C measurement is not available.
Acknowledgements
This article is based on research previously presented in abstract form at PathRed Congress 2025, held in Emperors Palace Convention Centre, Johannesburg, on 02–05 October 2025. The abstract has since been developed into a full article, which has been expanded and revised for journal publication. This republication is done with permission from the conference organisers.
This article is based on research originally conducted as part of Valentia Mohononi’s honor’s mini dissertation titled ‘The assessment of the performance of three low-density lipoprotein cholesterol equations in hypertriglyceridemia samples from an academic hospital in Gauteng province’, submitted to the Sefako Makgatho Health Sciences University in 2024. The mini dissertation is currently unpublished and not publicly available. The mini dissertation was supervised by Siphokazi Gwiliza and Luthando Hlati. The mini dissertation was reworked, revised and adapted into a journal article for publication. The author confirms that the content has not been previously published or disseminated and complies with ethical standards for original publication.
During the preparation of this work, the authors used QuillBot to check grammar. The content was reviewed and edited by the authors, who take full responsibility for its accuracy.
Competing interest
The authors, Valentia Mohononi; Siphokazi Gwiliza and Luthando Hlati, declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.
CRediT authorship contribution
Valentia Mohononi: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualisation, Writing – original draft and Writing – review & editing. Siphokazi Gwiliza: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Software, Supervision and Visualisation. Luthando Hlati: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Software, Supervision, Visualisation and Writing – review & editing. All authors reviewed the article, contributed to the discussion of results, approved the final version for submission and publication, and take responsibility for the integrity of its findings.
Data availability
The data that support the findings of this study are not openly available due to ethical and confidentiality restrictions and are available from the corresponding author, Valentia Mohononi, upon reasonable request.
Disclaimer
The views and opinions expressed in this article are those of the authors and are the product of professional research. They do not necessarily reflect the official policy or position of any affiliated institution, funder, agency or that of the publisher. The authors are responsible for this article’s results, findings, and content.
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How to cite this article: Mohononi V, Gwiliza S, Hlati L. The assessment of the performance of three low-density lipoprotein cholesterol equations in hypertriglyceridaemia samples from an academic hospital in Gauteng province. J Med Lab Sci Technol S Afr. 2026;8(1), a125. https://doi.org/10.4102/jmlstsa.v8i1.125