Comparison of Equations for the Calculation of Low‑Density

© 2021 Journal of Natural Science, Biology and Medicine | Published by Wolters Kluwer - Medknow224

ABSTRACT

Original Article

IntroductIon

Cardiovascular diseases (CVDs) are the leading cause of morbidity and mortality worldwide. In 2015, it was estimated that around 422 million peoples worldwide suffered from CVDs and 18 million deaths were due to CVDs.[1] A population‑based survey found that CVDs were also a major health burden in Southeast Asian countries, with a high CVD mortality rate of 321/100,000 population. Low‑density lipoprotein cholesterol (LDL‑C) has been considered the risk pathogenesis of arteriosclerotic plaques and their consequences of CVDs.[2] The two recent commonly used clinical practice guidelines for managing dyslipidemia to reduce cardiovascular risk have advised monitoring LDL‑C as the major parameter for cardiovascular risk assessment and the main therapeutic target.[3,4]

The ul t racentr i fugat ion precipi ta t ion, known as beta‑quantification, has been widely accepted as a reference method of LDL‑C measurement because it is unaffected by the presence of chylomicrons or other triglyceride (TG)‑rich

lipoproteins. However, it is not suitable for routine laboratory testing due to its expensive, labor‑intensive, laborious, and time‑consuming technique that requires large blood volume.[5] At present, the direct homogenous enzymatic measurement of LDL‑C is the most used technique due to its acceptable degree of accuracy and precision compared to the ultracentrifugation method.[6] However, the estimation of LDL‑C from various equations is widely used as an alternate assessment for directly measured LDL‑C mainly due to economic reasons, especially in developing countries. Friedewald equation is most commonly used for estimating LDL‑C; however, it has limited accuracy in estimating high TG levels.[7] Therefore, several

Background: Low‑density lipoprotein cholesterol (LDL‑C) has been established as a major risk factor for cardiovascular diseases. Various equations have been proposed for LDL‑C calculation; however, the accuracy of these equations varies among different ethnicities. This study aimed to assess the accuracy and concordance of LDL‑C equations for dyslipidemia classifications in Thai adults. Materials and Methods: The lipid profiles of 1091 healthy Thai adults were measured using a homogenous enzymatic assay. The estimated LDL‑C equations by Friedewald, Ahmadi, Anandaraja, Chen, Cordova, Densethakul, Hattori, Martin, Puavillai, Sampson, and Vujovic were compared to directly measured LDL‑C using Pearson’s correlation test. Cohen’s kappa statistic was also used to test the concordance of the LDL‑C equations with directly measured LDL‑C levels, according to the standard guidelines for blood cholesterol management. Results: The LDL‑C values calculated by Friedewald, Sampson, and Chen equations showed a high degree of correlation and values close to directly measured LDL‑C levels with mean differences ranging from − 0.04 to 0.07 mmol/L. All these three equations had a high degree of concordances with directly measured LDL‑C levels for classifying the degree of dyslipidemia. Conclusion: Friedewald, Sampson, and Chen equations showed better estimations of LDL‑C levels and had higher accuracy in classifying the degree of LDL‑C strata than other equations in the Thai population.

Keywords: Cardiovascular disease, hypercholesterolemia, hyperlipidemias, low‑density lipoprotein cholesterol

Address for correspondence: Dr. Sanguansak Rerksuppaphol, Department of Pediatrics, Faculty of Medicine, Srinakhariwirot University, 62

Mo 7, Rangsit‑Nakorn Nayok Road, Bangkok 26120, Nakorn Nayok, Thailand.

E‑mail: [email protected]

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DOI: 10.4103/jnsbm.jnsbm_53_21

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How to cite this article: Rerksuppaphol L, Rerksuppaphol S. Comparison of equations for the calculation of low‑density lipoprotein cholesterol in Thai population. J Nat Sc Biol Med 2021;12:224‑9.

Comparison of Equations for the Calculation of Low‑Density Lipoprotein Cholesterol in Thai Population

Lakkana Rerksuppaphol, Sanguansak Rerksuppaphol1

Departments of Preventive Medicine and 1Pediatrics, Faculty of Medicine, Srinakharinwirot University, Bangkok, Nakorn Nayok, Thailand

Submitted: 16‑May‑2021Accepted: 04‑Jun‑2021

Revised: 01‑Jun‑2021Published: 15‑Jul‑2021

Rerksuppaphol and Rerksuppaphol: Comparison of equations for calculation of LDL‑C

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other equations were proposed for calculating LDL‑D, such as Ahmadi et al.,[8] Anandaraja et al.,[9] Chen et al.,[10] de Cordova and de Cordova,[11] Dansethakul et al.,[12] Friedewald et al.,[13] Hattori et al.,[14] Martin et al.,[15] Puavilai and Laoragpongse,[16] Sampson et al.,[17] and Vujovic.[18] However, these equations’ accuracy varies from one study to another, depending on ethnic population.[19‑22] The present study aimed to determine the accuracy and concordance of 11 LDL‑C equations for dyslipidemia classifications in Thai adults.

MaterIals and Methods

A cross‑sectional study was conducted on healthy Thai adults who had a routine checkup at the MSMC Srinakharinwirot University Hospital checkup center between November 2019 and October 2020. Subjects younger than 18 years or with chronic diseases were excluded. The study was approved by the Ethics Committee of Srinakharinwirot University, and written informed consent was obtained from all participants before enrolment.

After enrolment, demographic characteristics and anthropometric data were collected. Blood samples were taken after 12‑h fasting by venipuncture to assess the participants’ lipid profiles, including total cholesterol (TC), LDL‑C, high‑density lipoprotein cholesterol (HDL‑C), and TG. Lipid profiles were directly determined by the standard homogenous enzymatic method using an automatic chemistry analyzer (Cobas® 8000, Roche Diagnostics). LDL‑C was calculated using the following 11 equations: Friedewald et al.,[13] Ahmadi et al.,[8] Anandaraja et al.,[9] Chen et al.,[10] de Cordova and de Cordova,[11] Dansethakul et al.,[12] Hattori et al.,[14] Martin et al.,[15] Puavilai and Laoragpongse,[16] Sampson et al.,[17] and Vujovic et al.[18]

Statistical analysisContinuous data were presented as mean and standard deviation, whereas discrete data were presented as number and percent. Paired Student’s t‑test was used to compare the difference between directly measured LDL‑C levels and estimated LDL‑C from each equation. Differences were considered statistically significant when P < 0.05. Pearson’s correlation test was used to analyze the correlations between directly measured LDL‑C levels and each estimated LDL‑C level. The degree of correlation was expressed by the Pearson correlation coefficient, and the correlation was considered statistically significant when P < 0.05.

Cohen’s kappa statistic was used to assess the concordance of estimated LDL‑C in relation to directly measured LDL‑C levels according to the blood cholesterol management guidelines. LDL‑C strata were classified as per the two recent clinical practice guidelines; the European (EU) guideline[3] (<1.42, 1.42–<1.81, 1.81–<2.59, 2.59–<3.0, 3.0–<4.92 and ≥ 4.92 mmol/L) and the US guideline[4] (<1.81, 1.81–<2.59, 2.59–<4.14, 4.14–<4.92 and ≥4.92 mmol/L). The Kappa coefficient was interpreted as follows: [23] 0–0.2 no concordance, 0.21–0.39 minimal, 0.40–0.49 weak, 0.60–0.79 moderate, 0.80–0.90

strong, and above 0.90 almost perfect degree of concordance. P <0.05 was considered statistically significant. Statistical analysis was performed using SPSS version 23.0 statistical package (SPSS, Chicago, IL, USA).

results

The present study involved 1091 participants, including 690 females (63%), with a mean age of 51.6 years (range, 18–84 years). Demographic characteristics and serum lipid profiles are summarized in Table 1. The mean serum TC was 5.59 mmol/L (range, 2.67–11.66 mmol/L), whereas the mean serum TG was 1.37 mmol/L (range, 0.16–6.06 mmol/L). Of the 1091 participants, only six had serum TG levels higher than 0.16 mmol/L.

The estimated LDL‑C levels by all equations and directly measured LDL‑C are shown in Table 2, and the correlation graphs between directly measured LDL‑C levels and each estimated LDL‑C level are presented in Figure 1. The estimated LDL‑C levels from all equations except Ahmadi and Anandaraja showed an excellent correlation with directly measured LDL‑C levels, presenting a correlation coefficient of >0.90. Overall, the estimated LDL‑C levels from Friedewald, Vujovic, Puavillai, Sampson, Dansethakul, Martin, and Ahmadi equations were higher than directly measured LDL‑C levels. In contrast, the estimated LDL‑C levels from Cordova, Hattori, and Chen equations were lower than directly measured LDL‑C levels. The mean difference between directly measured LDL‑C and each equation was generally lower than 0.26 mmol/L, except for Cordova (mean difference 0.39 mmol/L; 95% confidence interval [CI] 0.36, 0.41 mmol/L) and Ahmadi (mean difference − 0.55 mmol/L; 95% CI − 0.62, −0.49 mmol/L) equations. Friedewald, Sampson, and Chen’s equations had the least mean differences from directly measured LDL‑C levels, ranging from − 0.04 to 0.07 mmol/L, compared to other equations.

According to the clinical classification of EU and American (US) guidelines for managing dyslipidemia, the degree of concordances between the directly measured LDL‑C and the estimated LDL‑C of each formula was assessed; the results are

Table 1: Baseline characteristics of study population

Parameter Mean (SD)Age (years) 51.6 (11.4)Male, n (%) 401 (36.8)Weight (kg) 63.4 (11.4)Height (cm) 159.8 (7.5)BMI (kg/m2) 24.82 (4.03)Lipid profiles (mmol/L)

Total cholesterol 5.59 (1.08)HDL‑C 1.38 (0.34)LDL‑C, direct 3.55 (0.94)Triglycerides 1.37 (0.73)

HDL‑C: High‑density lipoprotein cholesterol, LDL‑C: Low‑density lipoprotein cholesterol, BMI: Body mass index, SD: Standard deviation


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shown in Table 2. Regarding the EU guidelines, Chen, Sampson, Friedewald, Martin, and Puavillai’s equations showed a high degree of concordance with directly measured LDL‑C (Kappa coefficient range: 0.626–0.663, P < 0.001), whereas Vujovic, Hattori, Dansethakul, and Anandaraja’s equations showed a low degree of concordance (Kappa coefficient range: 0.483–0.598, P < 0.001). Chen’s equation had the highest degree of concordance with the direct measured (Kappa coefficient: 0.663, P < 0.001) followed by Sampson (Kappa coefficient: 0.636, P < 0.001) and Friedewald’s equation (Kappa coefficient: 0.635, P < 0.001), respectively. Ahmadi and Cordova’s equations had the lowest concordance level with the directly measured LDL‑C (Kappa coefficient ranges: 0.323–0.381, P < 0.001). Regarding the US guidelines, Sampson’s equation showed the highest degree of concordance with the directly measured LDL‑C (Kappa coefficient: 0.708, P < 0.001) followed by Friedewald and Chen’s equations (Kappa coefficient: 0.706 and 0.700, respectively, P < 0.001). Puavilai, Hattori, and Vujovic’s equations showed a moderate degree of concordance, while Ahmadi and Cordova’s equations had the lowest concordance with the direct LDL‑C level (Kappa coefficient range: 0.319–0.393, P < 0.001).

dIscussIon

The present study demonstrated that Friedewald, Sampson, and Chen’s equations strongly correlated with a minimal difference from directly measured LDL‑C in Thai people. Chen equation provided marginal underestimated level, while Friedewald and Sampson’s equations had marginal overestimated levels, compared to the directly measured LDL‑C. These three equations showed a higher degree of concordance than the rest, according to the international practice guidelines for the management of blood cholesterol.

Previous studies have reported different accuracy results of the various estimated LDL‑C formulas in different ethnicities

and disease entities.[19,21] Regarding a retrospective study in the Indian population, Wadhwa and Krishnaswamy[21] reported that Vujovic’s equation was the most accurate. Simultaneously, a national survey study[19] carried out in the Korean population found that Martin’s equation was more accurate than other commonly used equations. In addition, a study among Iranian participants with metabolic health issues found that Hattori and Cordova’s equations were the best alternatives for LDL‑C measurement in the Iranian population, especially for healthy participants.[20] A study including 164 participants recruited from the National Institute of Health (Bethesda, MD) found that Friedewald’s equation was the best equation for estimating LDL‑C, which was similar to our findings.[22]

Friedewald equation is the equation of choice for estimation LDL‑C in most laboratories worldwide. However, many studies reported that the accuracy of Friedewald’s equation was prone to decrease in some conditions, such as in low LDL‑C and/or high TG levels.[8,15,24‑26] Friedewald’s equation was originally developed in 1972 for research purposes of a sample size of just 448 participants, and it used a fixed factor of 5 to describe the relationship between TG and very‑LDL‑C (VLDL‑C).[13] However, it is a simplified equation compared to the more recent equations. The present study found that Friedewald’s equation is the best formula for LDL‑C estimation in Thai participants. A potential explanation of its high accuracy in this study could be due to the small number of participants with high TG levels. Further studies with various ranges of TG and LDL‑C are needed to generalize the results for all Thai people.

Some limitations of Friedewald’s equation are its inaccuracy in certain situations, which led to the development of new equations for LDL‑C calculation. Among them, Chen et al.[10] proposed an equation that measured LDL‑C from the blood samples of 2180 Chinese participants (1220 had TG <2.26 mmol/L; 480 had TG 2.26–4.52 mmol/L; and 480 had TG 4.52–11.3 mmol/L). Chen’s equation estimated

Table 2: Mean differences, correlation coefficient, and degree of concordance between the estimated low‑density lipoprotein cholesterol and directly measured low‑density lipoprotein cholesterol according to the European and American guidelines for the management of dyslipidemia

Mean (SD) (mmol/L)

Correlation coefficient

P Mean difference (95% CI)

EU guideline US guideline

Kappa coefficient P Kappa coefficient PDirect LDL‑C 3.55 (0.94)Friedewald 3.59 (0.97) 0.950 0.001 −0.04 (−0.05–−0.002) 0.635 0.001 0.706 0.001Ahmadi 4.11 (1.46) 0.618 0.001 −0.55 (−0.62–−0.49) 0.323 0.001 0.319 0.001Anandaraja 3.74 (0.95) 0.895 0.001 −0.19 (−0.22–−0.17) 0.483 0.001 0.539 0.001Chen 3.48 (0.89) 0.948 0.001 0.07 (0.05–0.09) 0.663 0.001 0.700 0.001Cordova 3.17 (0.79) 0.919 0.001 0.39 (0.36–0.41) 0.381 0.001 0.393 0.001Dansethakul 3.77 (0.97) 0.949 0.001 −0.21 (−0.23–−0.20) 0.559 0.001 0.595 0.001Hattori 3.37 (0.92) 0.949 0.001 0.19 (0.17–0.20) 0.580 0.001 0.631 0.001Martin 3.68 (0.98) 0.940 0.001 −0.13 (−0.15–−0.11) 0.627 0.001 0.673 0.001Puavillai 3.69 (0.98) 0.951 0.001 −0.14 (−0.22–−0.17) 0.626 0.001 0.662 0.001Sampson 3.59 (0.98) 0.947 0.001 −0.04 (−0.05–−0.02) 0.636 0.001 0.708 0.001Vujovic 3.76 (0.98) 0.951 0.001 −0.20 (−0.22–−0.19) 0.598 0.001 0.621 0.001LDL‑C: Low‑density lipoprotein cholesterol, SD: Standard deviation, CI: Confidence interval



LDL‑C using a fixed factor of 0.9 and 0.1 for non‑HDL‑C and TG, respectively. The accuracy of Chen’s equation was proven superior to Friedewald’s in the Chinese and Korean populations.[10,19] The good correlation and concordance of Chen’s equation with the directly measured LDL‑C were also demonstrated in Thai people, which could be explained by the similarity of Asian ethnicities. However, estimated LDL‑C levels from Chen’s equation should be interpreted with caution. The present study found that LDL‑C levels from

Chen’s equation were underestimated compared to the direct measurement, which may lead to deferral or undertreatment of lipid‑lowering therapies in high‑risk patients.

Martin et al.[15] proposed a novel equation to estimate LDL‑C using an adjustable factor for the ratio of TG to VLDL‑C instead of a fixed factor of 5, which is used in Friedewald’s equation. The adjustable factor in Martin’s equation is based on individual non‑HDL‑C and TG levels derived

Figure 1: Correlations between directly measured low‑density lipoprotein cholesterol and each estimated low‑density lipoprotein cholesterol level by (a) Friedewald, (b) Ahmadi, (c) Anandaraja, (d) Chen, (e) Cordova, (f) Dansethakul, (g) Hattori, (h) Martin, (i) Puavillai, (j) Sampson, and (k) Vujovic presented separately for gender and all participants combined

j

f

i

e

b h

a g

d

c

k


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from a 174‑cell 2D table, which is more complicated than Friedewald’s equation. Martin’s equation was developed using blood samples of 1.35 million patients, including children, adolescents, and adults in the United States. However, both Friedewald and Martin’s equations were initially developed and validated for patients with TG lower than 4.52 mmol/L. Some studies showed that Martin’s equation provided high fidelity estimates than Friedewald’s equation.[15,19,27] However, these findings require external validation at an international level before applying them to other populations. Even though Martin’s equation showed a moderate agreement in the classification of LDL‑C, same as Friedewald, Chen, and Sampson’s equations, the mean difference between directly measured LDL‑C and estimated levels from Martin’s equation was higher than other equations. Therefore, Martin’s equation was inferior when applied to the Thai population compared to Friedewald, Chen, and Sampson’s equations.

Sampson et al. proposed another novel equation using lipid measurement data analyzed by beta quantification method from 8656 patients (18,715 LDL‑C samples) from the National Institutes of Health Clinical Center, USA.[17] In contrast to Friedewald’s equation which is valid for patients with TG lower than 4.52 mmol/L, Sampson’s equation could accurately estimate LDL‑C level in patients with TG up to 9.04 mmol/L. In addition, Sampson’s equation has good accuracy, like Friedewald’s equation, in patients with TG levels <4.52 mmol/L and has fewer misclassification in patients with TG levels 4.52–9.04 mmol/L.[17] Our findings are consistent with previous studies, which showed that Sampson’s equation could estimate LDL‑C as accurately as Friedewald’s equation; however, the equation’s accuracy for hypertriglyceridemia should be confirmed in future studies. Notably, Sampson’s equation is more complicated than the other equations as LDL‑C estimation is calculated through TC/0.948 − HDL‑C/0.971− (TG/8.56 plus (TG × non‑HDL‑C)/2140 − TG2/16,100) −9.44.

The present study investigated the limited accuracy of other equations; this could be explained by the limitations and unclarity of the equation‑derived methods. Cordova’s equation was derived from a wide age range (1–93 years) of the Brazilian population with a wide TG range (0.20–29.09 mmol/L).[11] Anandaraja’s equation did not contain the HDL‑C variable in the equation,[9] while Hattori’s equation theoretically excluded intermediate‑density lipoprotein cholesterol from the equation.[14] Ahmadi’s equation was generated from a small sample size study which included 230 serum samples from Iran.[8] Both Puavilai and Dansethakul’s equations were derived from a small Thai population with a variety of TG levels and used the inferior reference enzymatic method as the standard reference of direct LDL‑C levels.[12,16] In addition, the most vulnerable point of Puavillai’s equation was that the authors postulated the equation by modifying Friedewald’s equation, using 6 instead of 5 as a fixed factor, without supported evidence.[16]

The present study had some limitations. LDL‑C levels were assessed using a homogenous enzymatic method instead

of the ultracentrifugation reference method, which is the gold standard for direct LDL‑C measurement. However, a direct homogeneous assay has been accepted as one of the standard measurements with a satisfactory degree of accuracy and precision compared to the reference method of beta quantification assay.[6] In addition, the present study’s findings cannot be generalized to all hypotriglyceridemic patients since the population size was relatively small, especially in subjects with TG higher than 4.52 mmol/L. However, the subjects included in the present study were healthy adults seeking routine health checkups, representing the general healthy Thai population. Our findings are significant due to the inclusion and analysis of novel equations, such as Martin and Sampson’s equations. In addition, the current standard cutoff levels from both the US and the EU guidelines for the management of blood cholesterol were applied.

conclusIon

The present study investigated and compared the accuracy of Friedewald, Sampson, and Chen’s equations in calculating LDL‑C level. In healthy Thai adults, these three equations were more accurate in estimating LDL‑C and had a higher degree of concordance with the standard guidelines than other formulas. Compared to directly measured LDL‑C levels, the calculated LDL‑C levels by Friedewald and Sampson’s equations appeared to be slightly overestimated, while the calculated level by Chen’s equation was marginally underestimated. Although the three equations have comparable accuracy, Friedewald’s equation might be the most suitable equation for estimating LDL‑C in the Thai population.

AcknowledgmentWe would like to thank the participants and all people who contributed to the study in different ways. The study was supported by Srinakharinwirot University, Thailand (Grant number SWU 077/2563).

Financial support and sponsorshipThe present study was supported by grants from the Faculty of Medicine of Srinakharinwirot University.

Conflicts of interestThere are no conflicts of interest.

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Comparison of Equations for the Calculation of Low‑Density