Cardiovascular disease (CVD) is the leading cause of death globally [1]. Approximately 17.9 million people died from CVD in 2019, accounting for 32% of global mortality. Low-density lipoprotein (LDL)-cholesterol (LDL-C) has been the subject of long-standing clinical interest and is the primary focus for cardiovascular risk assessment and treatment according to international clinical practice guidelines [2-5]. Therefore, clinical decisions depend on accurate and reproducible laboratory measurements [6-8].

The gold standard for LDL-C measurement is β-quantification or ultracentrifugation. However, because of the intensive manual sample preparation methods and lengthy analysis time, these techniques are most commonly used by specialty lipid laboratories and are inconvenient for use in routine clinical practice [1]. Conventionally, the Friedewald equation is considered cost-effective and is a widely used method for LDL-C calculations [9]. However, the Friedewald equation loses accuracy in cases of mild-tomoderate hypertriglyceridemia (TG level ≥150 mg/dL) and low LDL-C levels (<100 mg/dL) [6].

Two approaches have been developed to overcome these limitations: the Martin/Hopkins and Sampson/National Institutes of Health (NIH) equations. The Martin/Hopkins equation is a modified version of the Friedewald method, using the median ratio of the TG level to the very low density lipoprotein–cholesterol (VLDL-C) level by non-HDL cholesterol (HDL-C) and TG strata for TG levels <400 mg/dL. It is now available as an LDL calculator online (https://ldlcalculator.com/) [10]. The Martin/Hopkins equation is now recognized as a useful method, especially with LDL-C levels <70 mg/dL [2] and TG levels of 150–399 mg/dL [10-13]. The Sampson/NIH equation uses a multiple least-squares regression approach to estimate the VLDL-C level with a TG term divided by a fixed factor for TG levels up to 800 mg/dL [14, 15]. This equation was derived using clinical lipid values (TG, total cholesterol [TC], and HDL-C levels) as independent variables and the LDL-C level determined using the beta-quantification reference method as the dependent variable.

More recently, Sajja et al. [16] introduced an extended Martin/Hopkins equation with an expansion of TG levels of 400–799 mg/dL and concluded that this method provided a more accurate estimation than the Friedewald and Sampson/NIH equations. Several studies have compared the extended Martin/Hopkins and Sampson/NIH equations with direct measurement assays [13, 14, 17-20]. However, the results have varied depending on the study population and the analyzer used.

In a previous study of a Korean population with TG levels ranging from 200 to 799 mg/dL, both the original and extended Martin/Hopkins equations demonstrated superior performance among various equations tested, when compared with the results of a direct homogeneous assay using an Abbott analyzer [13]. As assay variability is likely to affect the performance of various LDL-C equations, the optimal method should be chosen by validation in the local population for each clinical laboratory [17]. Hence, in this study, we aimed to compare LDL-C levels estimated using various equations with those obtained using a Roche analyzer, which is another direct homogeneous assay widely used in Korea.

1. Study population

A total of 52,981 patients who underwent examinations for TC, TG, LDL-C, and HDL-C levels at Seoul Medical Center between January 2020 and December 2022 were included in this study. This study was approved by the Institutional Review Board (IRB) of the Seoul Medical Center (IRB No. 2023-07-012) and was exempted from the requirement for obtaining informed consent. After excluding individuals with clinical manifestations of obstructive jaundice, which may have affected the HDL-C test results [21] (Supplementary Table 1), or with TG levels ≥800 mg/dL, 52,589 participants were enrolled.

2. Demographic characteristics and laboratory findings

To reflect real-world practice, we did not exclude non-fasting participants. Serum samples were collected in tubes containing a clot activator and serum gel separator. Centrifugation was performed at 3,000 rpm for 10 min within 30 min of blood withdrawal to prevent glycolysis. All analyses were performed immediately after centrifugation. The levels of TC, TG, LDL-C (DLDL), and HDL-C were measured using a Cobas 8000 c702 analyzer (Roche Diagnostics, Mannheim, Germany).

Estimations of LDL-C levels using the Friedewald equation (FLDL), Martin/Hopkins equation (MLDL), extended Martin/Hopkins equation (EMLDL), and Sampson equation (SLDL) were performed as previously described [9, 10, 15, 16]. The FLDL levels were calculated using a fixed TG/VLDL-C ratio of 5. Therefore, the FLDL level was calculated as (TC– HDL-C)–TG /5 (mg/dL). The MLDL level was calculated using the median ratio of the TG level to the VLDL-C level using non-HDL-C and TG level strata acquired from 900,605 individuals [10]. The MLDL level was calculated as

TC– HDL-C– TG /(strata-specific median TG/VLDL-C ratio). The original Martin/Hopkins equation was developed for patients with a TG level <400 mg/dL. Therefore, the strata-specific median TG/VLDL-C ratio for TG levels between 400 and 13,975 mg/dL was defined only based on the non-HDL-C levels (non-HDL-C level <100 mg/dL, 11.9; non-HDL-C 100–129 mg/dL, 10.0; non-HDL-C 130–159 mg/dL, 8.8; non-HDL-C 160–189 mg/dL, 8.1; non-HDL-C 190–219 mg/dL, 7.5; and non-HDL-C ≥220 mg/dL, 6.7) [10]. In contrast, the extended Martin/Hopkins equation was developed for use with TG levels 400–799 mg/dL. Therefore, EMLDL levels were calculated using the strata-specific median TG/VLDL-C ratio derived from an extensive database of lipid measurements in individuals with TG levels 400–799 mg/dL using 240-cell methods. The SLDL level was calculated as follows:

TC/0.948–HDL-C/0.971–(TG /8.56+[TG*non-HDL-C]/2,140–TG2/16,100)–9.44 (mg/dL) [15].

3. Statistical analysis

All statistical analyses were performed using SPSS Statistics 27.0 for Windows (IBM Corp., Armonk, NY, USA), MedCalc version 20.211 (MedCalc Software, Mariakerke, Belgium), and R statistical software version 4.3.2 (R Foundation for Statistical Computing, Vienna, Austria). All statistical outcomes were based on two-sided tests, and P<0.05 was considered significant.

For continuous variables, data are expressed as the median and interquartile ranges when their distribution was not normal based on the results of the Kolmogorov–Smirnov test (P<0.05) and are otherwise expressed as the mean±standard deviation (SD). Categorical variables are expressed as percentages. Bland–Altman plots were created to compare the DLDL, FLDL, MLDL, EMLDL, and SLDL values. The difference between the DLDL and LDL-C estimates was evaluated using scatter plots of the mean absolute differences (MADs) according to TG levels. Cochran’s Q test was used to compare the overall concordance between the LDL-C estimates and to evaluate whether their concordance differed from the DLDL category or TG group.

The demographic characteristics, lipid profiles, and overall concordance of the FLDL, MLDL, EMLDL, and SLDL levels with the DLDL level of the participants in our study are shown in Table 1. A total of 52,589 participants were included in this study. The median (interquartile range) value of the TG/VLDL-C level ratio calculated using the original and extended Martin/Hopkins equations for TG levels 400–799 mg/dL were 8.3 (7.4–9.3) and 8.8 (8.1–10.0), respectively. The median and interquartile ranges were as follows: DLDL, 84 (63–113) mg/dL; FLDL, 71 (51–99) mg/dL; MLDL, 76 (56–103) mg/dL; EMLDL, 76 (56–103) mg/dL; and SLDL, 75 (54–102) mg/dL.

Table 1 Baseline patient characteristics (N=52,589)

Variables	Values
Age (years)	62.2±15.5
Male, N (%)	28,613 (54.4)
Total cholesterol (mg/dL)	154 (128–185)
HDL cholesterol (mg/dL)	52 (43–63)
Non-HDL cholesterol (mg/dL)	99 (76–128)
TG (mg/dL)	116 (83–166)
Cases by TG level bins, N (%)
0–99 mg/dL	20,024 (38.1)
100–149 mg/dL	15,929 (30.3)
150–199 mg/dL	8,187 (15.6)
200–399 mg/dL	7,438 (14.1)
400–799 mg/dL	1,011 (1.9)
Cases by DLDL level bins, N (%)
<40 mg/dL	2,124 (4.0)
40–69 mg/dL	15,195 (28.9)
70–99 mg/dL	16,670 (31.7)
100–129 mg/dL	10,565 (20.1)
130–159 mg/dL	5,367 (10.2)
160–189 mg/dL	2,010 (3.8)
≥190 mg/dL	658 (1.3)
TG/VLDL-C ratio by Martin/Hopkins equation
For all TG levels	5.5 (4.8–6.3)
For TG levels 400–799 mg/dL	8.3 (7.4–9.3)
TG/VLDL-C ratio by extended Martin/Hopkins equation
For all TG levels	5.5 (4.8–6.3)
For TG levels 400–799 mg/dL	8.8 (8.1–10.0)
DLDL (mg/dL)	84 (63–113)
FLDL (mg/dL)	71 (51–99)
MLDL (mg/dL)	76 (56–103)
EMLDL (mg/dL)	76 (56–103)
SLDL (mg/dL)	75 (54–102)

Values are presented as the mean±SD, median (interquartile range), or number

(percentage) unless otherwise indicated.

Abbreviations: DLDL, directly measured LDL-cholesterol; EMLDL, LDL-cholesterol estimated using the extended Martin/Hopkins equation; FLDL, LDL-cholesterol estimated using the Friedewald equation; MLDL, LDL-cholesterol estimated using the Martin/Hopkins equation; SLDL, LDL-cholesterol estimated using the Sampson equation; TG, triglyceride; VLDL-C, very low-density lipoprotein cholesterol.

Most FLDL, MLDL, EMLDL, and SLDL estimates were within 2 SDs of the DLDL values, for TG levels 400–799 mg/dL and <400 mg/dL, as depicted using Bland–Altman plots (Fig. 1 and Supplementary Fig. 1). Interestingly, the mean difference was smallest between the DLDL and EMLDL levels (-1.3), followed by the difference between the DLDL and MLDL levels (-3.2) for TG levels 400–799 mg/dL. Meanwhile, the mean differences between the DLDL and FLDL levels (+40.4) and between the DLDL and SLDL levels (+17.7) were large for TG levels 400–799 mg/dL, indicating an underestimation of the LDL-C level by the Friedewald and Sampson/Hopkins equations in patients with hyperglyceridemia. Scatter plots for the differences between the DLDL levels and the levels estimated using various equations are depicted in Fig. 2. The MAD values indicated the overall superiority of the MLDL and EMLDL estimates over the FLDL and SLDL estimates, especially for TG levels 400–799 mg/dL (MLDL: MAD=12.63; EMLDL: MAD=13.05; FLDL: MAD=41.46; and SLDL: MAD=20.61; P<0.001).

Figure 1. Bland–Altman plot for the comparison of directly measured LDL-C (DLDL) levels and those estimated using the Friedewald equation (A), Martin/Hopkins equation (B), extended Martin/Hopkins equation (C), or Sampson equation (D) for TG levels 400–799 mg/dL.
Abbreviations: DLDL, directly measured low-density lipoprotein–cholesterol (LDL-C) level; EMLDL, LDL-C level estimated using the extended Martin/Hopkins equation; FLDL, LDL-C level estimated using the Friedewald equation; MLDL, LDL-C level estimated using the Martin/Hopkins equation; SLDL, LDL-C level estimated using the Sampson equation.

Figure 2. Scatter plots for LDL-C levels estimated using the Friedewald equation (A), Martin/Hopkins equation (B), extended Martin/Hopkins equation (C), and Sampson equation (D) against the TG level.
Abbreviations: DLDL, directly measured low-density lipoprotein–cholesterol (LDL-Ch); EMLDL, LDL-C level estimated using the extended Martin/Hopkins equation; FLDL, LDL-C level estimated using the Friedewald equation; MAD, mean absolute difference; MLDL, LDL-C level estimated using the Martin/Hopkins equation; SLDL, LDL-C level estimated using the Sampson equation; TG, triglyceride.

Overall, the concordance between the DLDL and LDL-C estimates, in agreement with LDL-C treatment classes, showed that the MLDL, EMLDL, and SLDL estimates had better agreement than the FLDL estimate with the DLDL classification (MLDL, 69.0%; EMLDL, 69.0%; SLDL, 67.0%; and FLDL, 57.7%; P<0.001).

The concordance rate of estimated cholesterol levels using each calculation method across directly measured LDL cholesterol and TG level bins is demonstrated in Supplementary Table 2. The concordance between the DLDL level and LDL-C classes estimated using each calculation method was stratified according to TG levels <150 mg/dL and 150–799 mg/dL (Table 2). For TG levels <150 mg/dL, the FLDL and MLDL levels showed similar concordance with the DLDL level, whereas the SLDL level showed superior concordance. For TG levels 150–799 mg/dL, the concordance between the DLDL and MLDL/EMLDL levels was superior to that between the FLDL and SLDL levels, except for DLDL levels <40 mg/dL. Similar results were observed for TG levels 150–399 mg/dL (Supplementary Table 3).

Table 2 Concordance rates of estimated cholesterol using the Friedewald, Martin/Hopkins, extended Martin/Hopkins, and Sampson equations, according to directly measured LDL-cholesterol level bins and TG levels

DLDL (mg/dL)	TG <150 mg/dL					TG 150–799 mg/dL
	N	FLDL	MLDL	SLDL	P value*	N	FLDL	MLDL	EMLDL	SLDL	P value*
All ranges	35,953	23,948 (66.6)	24,677 (68.6)	25,580 (71.2)	<0.001†	16,636	6,371 (38.3)	11,620 (69.9)	11,613 (69.8)	9,661 (58.1)	<0.001II
<40	1,540	1,491 (96.8)	1,471 (95.5)	1,480 (96.1)	<0.001‡	584	560 (95.9)	418 (71.6)	409 (70.0)	520 (89.0)	<0.001II
40–69	11,182	8,969 (80.2)	9,272 (82.9)	9,235 (82.6)	<0.001‡	4,013	1,981 (49.4)	3,381 (84.3)	3,396 (84.6)	3,038 (75.7)	<0.001II
70–99	11,521	7,164 (62.2)	7,692 (66.8)	7,726 (67.1)	<0.001‡	5,149	1,742 (33.8)	3,890 (75.6)	3,890 (75.6)	2,950 (57.3)	<0.001II
100–129	6,906	3,862 (55.9)	3,899 (56.5)	4,281 (62.0)	<0.001†	3,659	1,088 (29.7)	2,269 (62.0)	2,271 (62.1)	1,780 (48.7)	<0.001II
130–159	3,320	1,739 (52.4)	1,681 (50.6)	2,002 (60.3)	<0.001†	2,047	577 (28.2)	1,091 (53.3)	1,083 (52.9)	866 (42.3)	<0.001II
160–189	1,154	518 (44.9)	475 (41.2)	629 (54.5)	<0.001†	856	251 (29.3)	385 (45.0)	378 (44.2)	327 (38.2)	<0.001II
≥190	330	205 (62.1)	187 (56.7)	227 (68.8)	<0.001†	328	172 (52.4)	186 (56.7)	186 (56.7)	180 (54.9)	<0.001¶

Values shown are n/N in group (%).

*P values are calculated with Cochran’s Q test.; ^†FLDL vs. MLDL, FLDL vs. SLDL, MLDL vs. SLDL <0.05; ^‡FLDL vs. MLDL, FLDL vs. SLDL <0.05; ^†FLDL vs. SLDL, MLDL vs. SLDL <0.05; ^IIFLDL vs. MLDL, FLDL vs. EMLDL, FLDL vs. SLDL, MLDL vs. SLDL, EMLDL vs. SLDL <0.05; ^¶FLDL vs. MLDL, FLDL vs. EMLDL <0.05.

Abbreviations: DLDL, directly measured LDL-cholesterol; EMLDL, LDL-C cholesterol estimated using the extended Martin/Hopkins equation; FLDL, LDL-cholesterol estimated using the Friedewald equation; MLDL, LDL-cholesterol estimated using the Martin/Hopkins equation; SLDL, LDL-cholesterol estimated using the Sampson equation; TG, triglyceride.

The reclassification rates based on the FLDL, MLDL, EMLDL, and SLDL levels in the TG group are shown in Table 3. The maximal underestimation and overestimation rates of the FLDL, MLDL, EMLDL, and SLDL levels across the TG groups were as follows: FLDL: 84.5% and 1.1%, MLDL: 32.2% and 23.1%, EMLDL: 32.2% and 20.1%, and SLDL: 57.2% and 4.2%, respectively. Even for TG levels 150–199 mg/L and 200–399 mg/dL, the FLDL levels were significantly underestimated by 51.1% and 69.3%, respectively. Similarly, for TG levels 150–199 mg/L and 200–399 mg/dL, the SLDL levels were underestimated by 35.3% and 44.2%, respectively. In contrast, the underestimation and overestimation rates of the MLDL levels when the TG levels were 150–399 mg/dL did not exceed 27.3% and 4.2%, respectively. Conversely, the underestimation rates of the FLDL and SLDL levels when the TG levels were 400–799 mg/dL were 84.5% and 57.2%, respectively, whereas the underestimation and overestimation rates of the MLDL levels were only 16.1% and 23.1%, respectively. These rates were similar to those of the EMLDL level, which showed 19.9% and 20.1% underestimation and overestimation rates, respectively.

Table 3 Overall discordance rate (%) of estimated LDL-cholesterol using the Friedewald, Martin/Hopkins, extended Martin/Hopkins, and Sampson equations compared to directly measured LDL-Cholesterol levels, classified by NCEP-ATP III guideline according to TG level bins

Triglyceride (mg/dL)	FLDL		MLDL		EMLDL		SLDL
	Underestimation	Overestimation	Underestimation	Overestimation	Underestimation	Overestimation	Underestimation	Overestimation
<100	29.0	0.5	32.2	0.3	32.2	0.3	27.1	0.6
100–149	37.9	0.5	29.0	1.0	29.0	1.0	29.4	0.9
150–199	51.1	0.4	27.3	1.6	27.3	1.6	35.3	0.9
200–399	69.3	0.4	26.0	4.2	26.0	4.2	44.2	1.4
400–799	84.5	1.1	16.1	23.1	19.9	20.1	57.2	4.2

Abbreviations: EMLDL, LDL-C cholesterol estimated using the extended Martin/Hopkins equation; FLDL, LDL-cholesterol estimated using the Friedewald equation; MLDL, LDLcholesterol estimated using the Martin/Hopkins equation; NCEP-ATP III, National Cholesterol Education Program Adult Treatment Panel-III; SLDL, LDL-cholesterol estimated using the Sampson equation; TG, triglyceride.

The proportion of misclassified patients per treatment class based on the DLDL levels for each calculation method in the TG 400–799 mg/dL group is shown in Fig. 3. When classifying for LDL-C levels <40 mg/dL, the FLDL level demonstrated the highest concordance rate (97%), followed by the SLDL (84%), MLDL (38%), and EMLDL (25%) levels. There was no underestimation among the four equations. However, overestimation was the main cause of the low concordance rate for the MLDL or EMLDL levels. When classifying for LDL-C levels 40–69 mg/dL, the EMLDL level demonstrated the highest concordance rate (65%), followed by the MLDL (59%), SLDL (54%), and FLDL (7%) levels. Only 3% of patients showed one guideline class underestimation with the MLDL and EMLDL levels, whereas 93% and 40% showed one guideline class underestimation with the FLDL and SLDL levels, respectively. For LDL-C levels ≥70 mg/dL, two or three as well as one guideline class underestimation occurred with all equations. Notably, the underestimation rates of the FLDL and SLDL levels reached 95% and 87%, respectively, depending on the LDL-C levels. The proportion of misclassified participants per estimation method in each estimated LDL-C category, with TG levels <400 mg/dL also demonstrated underestimation rates of FLDL reaching 61% (Supplementary Fig. 2).

Figure 3. Proportion of misclassified participants for each estimation method by estimated LDL-C level category for TG levels 400–799 mg/dL. Graphs represent the total percentage of patients who were underclassified and overclassified within each LDL-C level category.
Abbreviations: LDL-C, low-density lipoprotein–cholesterol; ≥3.under, underclassified by three bins or more; 2.under, underclassified by two bins; 1.under, underclassified by one bin; 1.over, overclassified by one bin; 2.over, overclassified by two bins; 3.over, overclassified by three bins or more.

This study was conducted to identify the most useful calculation for estimating LDL-C levels, based on the best correlation with the results of a widely used direct homogeneous assay provided by Roche in Korea [22]. Although Sampson et al. [15] asserted that their method provides a more accurate calculation of LDL-C for low LDL-C levels or with TG levels <800 mg/dL, this study demonstrated that the Martin/Hopkins or extended Martin/Hopkins equations calculated LDL-C more accurately than the Friedewald or Sampson/NIH equations for patients with TG levels 150–799 mg/dL. Even for TG levels 150–399 mg/dL, the Martin/Hopkins equation showed a better concordance rate than the Friedewald or Sampson/NIH equations with the direct measurement for LDL-C levels between 40 and 189 mg/dL (Supplementary Table 3). According to Korean National Health Insurance standards, the Friedewald equation must be used when TG levels are below 400 mg/dL. However, we demonstrated better agreement of the Martin/Hopkins equation than the Friedewald equation with LDL-C values measured using a Roche instrument.

Zararsız et al. [20] validated each LDL-C equation across Roche, Beckman, and Siemens analyzers in a Turkish population. They found that the extended Martin/Hopkins equation exhibited the highest level of concordance across all TG levels. The difference in concordance compared to other formulas was more pronounced when TG levels were ≥100 mg/dL, aligning with our observation regarding the superior performance of the original or extended Martin/Hopkins equations among various equations for TG levels ≥150 mg/dL. The use of the Martin/Hopkins equation was associated with 39.2% or fewer misclassifications compared to that of the Sampson/NIH equation (61.4%) and Friedewald equation (85.6%) across all TG levels. For TG levels 150–799 mg/dL, there were considerable underestimations with the Friedewald and Sampson/NIH equations, which may lead to undertreatment. The underestimation increased with hypertriglyceridemia, reaching 84.5% with the Friedewald equation and 57.2% with the Sampson/NIH equation in patients with TG levels 400–799 mg/dL. Therefore, adopting the Sampson/NIH equation to determine LDL-C levels would result in appropriate treatment for less than half of individuals with TG levels 400–799 mg/dL.

In this study, the concordance rate between the LDL-C levels estimated using various calculation methods and the DLDL levels measured using a Roche analyzer was lower than that reported in previous studies where the DLDL level was measured using an Abbott analyzer in a Korean population (MLDL, 76.7%; EMLDL, 76.8%; SLDL, 76.2%; and FLDL, 74.2%) [13]. Even in participants with normal TG levels or mild hypertriglyceridemia, the concordance rates between the estimated LDL-C levels and the directly measured LDL-C levels using the Roche analyzer were lower than the rates between the estimated LDL-C levels and the directly measured LDL-C levels using the Abbott analyzer. In a previous study utilizing an Abbott analyzer as a direct measurement instrument, the concordance rate between the directly measured LDL-C level and the level estimated using various equations was 69.1–100.0% for TG levels <200 mg/dL, depending on the directly measured LDL-C level [13]. In the present study, among individuals with TG levels <150 mg/dL, the concordance rate between directly measured LDL-C using the Roche analyzer and estimates from various equations ranged from 41.2 to 96.8%. Steyn et al. [20] also reported a similar result that both the Sampson/NIH method and the extended Martin/Hopkins equation displayed better correlations with directly measured LDL-C levels using the Abbott analyzer than using the Roche analyzer for TG levels 400–799 mg/dL in a South African population. They concluded that the extended Martin/Hopkins equation exhibits a stronger correlation than the Sampson/NIH equation with both the Abbott and Roche analyzer results for TG levels up to 800 mg/dL. The Sampson/NIH equation demonstrated a negative deviation and tended to underestimate LDL-C when compared with the direct assay method.

The LDL-C overestimation rate for MLDL was lower in our study than in a previous study that utilized an Abbott analyzer (≤23.1 vs.≤42.6%). This is in agreement with the results reported by Steyn et al. in a South African population (Roche≤9.0 vs. Abbott ≤12.1%) [18].

In a prior study utilizing an Abbott analyzer for direct LDL-C measurements, the extended Martin/Hopkins equation showed a 13% increase in concordance rate compared to the original Martin/Hopkins equation for TG levels ranging from 400 to 799 mg/dL (concordance rates: 65.5% for EMLDL vs. 52.5% for MLDL) [13]. However, in the current study, the extended Martin/Hopkins equation did not show any additional improvement in the concordance rate with directly measured LDL-C levels using the Roche analyzer compared to the original Martin/Hopkins equation for TG levels ranging from 400–799 mg/dL. In both the original and extended Martin/Hopkins equation derivation datasets, TG levels were measured using an Abbott analyzer [10, 16]. Hence, the extended Martin/Hopkins equation, derived from the strata-specific TG/VLDL-C ratio for TG levels fractioned by 10 mg/dL, may offer a more accurate prediction of LDL-C levels measured using the Abbott chemistry analyzer than those measured using the Roche analyzer. Specifically, the TG/VLDL-C ratio, based on non-HDL-C and TG levels, ranged from 5.9 to 23.9 in the extended Martin/Hopkins equation derivation dataset [16]. Nonetheless, in our study using a Roche analyzer, the TG/VLDL-C ratio determined using the extended Martin/Hopkins equation ranged from 5.9 to 17.5 (Supplementary Fig. 3). Consequently, it is possible that the extended Martin equation provides a more accurate prediction of LDL-C levels measured using the Abbott chemistry analyzer than those measured using the Roche analyzer.

Another difference between the previous study utilizing the Abbott analyzer and the present study is that only 12-h fasting samples were included in the previous study [13]; however, nonfasting samples were not excluded in the present study. As chylomicronemia in a non-fasting state causes overestimation of VLDL-C levels and may change the association between TG and VLDL-C levels [23-25], the difference in fasting status might have contributed to the difference in the TG/VLDL-C ratio between these studies. Although non-fasting samples typically display TG levels that are approximately 27 mg/dL higher than the levels in fasting samples for most individuals, this increment is not of clinical significance [26, 27]. Thus, in agreement with a number of recent guidelines that highlight the suitability of non-fasting samples for initial screening of atherosclerotic cardiovascular disease (ASCVD) risk, we did not exclude non-fasting samples in this study [2, 26, 28, 29].

Vasse et al. [30] conducted a study that assessed the Friedewald, Sampson/NIH, and Martin/Hopkins equations for estimating LDL-C levels in fasting and non-fasting hypertriglyceridemic patients. The Sampson/NIH equation was shown to be the most accurate method for fasting samples. In contrast, the extended Martin/Hopkins equation was found to be the most accurate method for non-fasting samples. The superiority of the Martin/Hopkins equation in non-fasting samples may be related to the larger study population (n=74,611) that was analyzed to derive the equation and the inclusion of non-fasting samples. Notably, the original studies that derived the Friedewald and Sampson/NIH equations included only fasting samples (n=448; n=8,656, respectively).

As demonstrated in the study by Vasse et al. [30], in approximately 30% of patients with LDL-C estimated using the Friedewald and Sampson equations, missed opportunities for treatment in patients with ASCVD were noted due to LDL-C level underestimation, in both fasting and non-fasting patients with LDL-C levels ≥70 mg/dL, which is similar to the results observed in our study. Therefore, in the era of accepting non-fasting samples for the assessment of lipid profiles, the Martin/Hopkins equation may be a useful alternative to the Friedewald equation.

This study has some limitations in that the reference method and ultracentrifugation were unavailable. The equations were only compared with a widely used direct measurement assay from Roche. Therefore, these results can only be used as a reference by laboratories that use Roche instruments and reagents. Additional research is required to generalize the study results to devices and reagents other than those supplied by Roche. Furthermore, a lack of clinical information, such as fasting status or underlying disease, might have affected the TG/VLDL-C level ratio.

In conclusion, the performance of different equations for LDL-C estimation is influenced by the choice of analyzer and the levels of LDL-C and TG. We found that the original and extended Martin/Hopkins equations exhibited stronger correlations than the Friedewald or Sampson/NIH equations with directly measured LDL-C levels using a Roche analyzer in patients with hypertriglyceridemia (TG levels ranging from 150 to 799 mg/dL). The original or extended Martin/Hopkins equations were less likely to underestimate LDL-C levels than the Sampson/NIH or Friedewald equations in cases of hypertriglyceridemia. While caution is warranted when using LDL-C equations for patients with TG levels of 400–799 mg/dL, the original Martin/Hopkins method, rather than the Friedewald or Sampson/NIH methods, may serve as a clinical alternative to direct LDL-C measurements in laboratories utilizing the Roche analyzer for patients with TG levels of 150–399 mg/dL.

We thank the Medical Research Collaborating Center of Seoul National University Hospital for the statistical analysis.

None declared.