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 Table of Contents  
Year : 2022  |  Volume : 13  |  Issue : 4  |  Page : 213-221

A Comparison between Eight Formulas for the Estimation of Plasma Low-Density Lipoprotein Cholesterol in the Saudi Arabian Population

1 Department of Clinical Biochemistry, Faculty of Medicine, King Abdulaziz University; Department of Clinical Biochemistry, Faculty of Medicine, University of Jeddah, Jeddah, Saudi Arabia
2 Department of Clinical Biochemistry, Faculty of Medicine, University of Jeddah, Jeddah, Saudi Arabia

Date of Submission19-May-2022
Date of Decision28-May-2022
Date of Acceptance03-Jun-2022
Date of Web Publication18-Oct-2022

Correspondence Address:
Dr. Dena Abdulbadea Nuwaylati
Department of Clinical Biochemistry, Faculty of Medicine, University of Jeddah, Jeddah 21959
Saudi Arabia
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/joah.joah_48_22

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CONTEXT: Low-density lipoprotein cholesterol (LDL-C) is the classical target in cardiovascular (CV) disease management and is usually estimated by Friedewald's formula. However, this formula may over- or underestimate LDL-C levels.
AIMS: Our aim is to compare eight LDL-C-estimating formulas to the direct LDL-C measurement and validate their use in the Saudi population.
SETTINGS AND DESIGN: This was a retrospective study.
SUBJECTS AND METHODS: A blood sample of fasting 669 Saudi subjects was tested for lipid profiles in King Abdulaziz University Hospital Laboratory, from which directly measured LDL-C was obtained. LDL-C was then estimated from eight different formulas: Friedewald's, Cordova's, Hata's, Puavilai's, Chen's, Ahmadi's, Hattori's, and Vujovic's, which were all compared to direct LDL-C.
STATISTICAL ANALYSIS USED: Mean and standard deviation, paired t-test, and Pearson's correlation were used for statistical analysis.
RESULTS: The mean differences between the direct LDL-C and Hattori and Chen's LDL-C were 0.03 and 0.08 mmol/L, respectively; P < 0.001, while the mean difference observed with Hata, Friedewald, Puavilai, and Vujovic's formulas were higher in comparison: 0.15, 0.24, 0.29, and 0.33 mmol/L, respectively, P < 0.001. Ahmadi and Cordova's LDL-C were estimated to be 0.60 and 0.64 mmol/L more than direct LDL-C levels, respectively, which showed the highest discordance with direct LDL-C, P < 0.001. At a triglyceride (TG) level of <4.5 mmol/L, Hattori also had the best agreement with direct LDL-C, with a mean difference of 0.04 mmol/L, and with TG >4.5 mmol/L, their mean difference was 0.21 mmol/L. All estimated LDL-C strongly correlated with direct LDL-C, except for Ahmadi's.
CONCLUSIONS: Hattori's LDL-C had the best agreement with the direct LDL-C, and across all TG levels. However, we recommend directly measuring LDL-C in those with high CV risk.

Keywords: Beta-quantification, Friedewald formula, low-density lipoprotein-cholesterol, triglycerides, ultracentrifugation

How to cite this article:
Awan ZA, Nuwaylati DA. A Comparison between Eight Formulas for the Estimation of Plasma Low-Density Lipoprotein Cholesterol in the Saudi Arabian Population. J Appl Hematol 2022;13:213-21

How to cite this URL:
Awan ZA, Nuwaylati DA. A Comparison between Eight Formulas for the Estimation of Plasma Low-Density Lipoprotein Cholesterol in the Saudi Arabian Population. J Appl Hematol [serial online] 2022 [cited 2023 Sep 30];13:213-21. Available from: https://www.jahjournal.org/text.asp?2022/13/4/213/358711

  Introduction Top

Cardiovascular diseases (CVDs) remain a major element of mortality in the world, and atherosclerotic cardiovascular diseases (ASCVDs) are the most common of all CVDs; its prevalence in Saudi Arabia is estimated to be 5.5%.[1],[2] CVD is a severe health and economic burden; therefore, its prevention is important to reduce the risk of its detrimental consequences on general and CV health.[2],[3] Atherosclerosis, the leading cause of CVD and the most serious consequence of dyslipidemia, begins early in life, which makes early primary prevention necessary to minimize the impact of CVD and its associated disability.[4],[5] The proper treatment of cardiovascular (CV) risk factors, especially dyslipidemia, is a well-recognized approach for CVD prevention,[3],[4] and elevated low-density lipoprotein cholesterol (LDL-C) is the key controllable CV risk factor; therefore, LDL-C level maintenance within healthy ranges is crucial for CV risk reduction.[5] Moreover, screening for dyslipidemia is recommended for CVD prevention in those with clinically evident CVD and in conditions with increased CV risk, such as diabetes mellitus (DM), hypertension, genetic susceptibility to lipid disorders, chronic kidney diseases, peripheral arterial diseases, and autoimmune disorders,[4] as well as to monitor responses to therapy.[6]

Therapeutic interventions favorably modify CV outcomes in those with elevated LDL-C,[6] and based on accumulated evidence, guidelines have been formulated with screening and treatment strategies that focus on LDL-C as the primary target for cholesterol-lowering therapy.[6],[7],[8] Considering that, several international guidelines, such as the American College of Cardiology/American Heart Association, recommend LDL-C as a primary treatment target for dyslipidemia and CVD prevention.[7],[8]

Therefore, an accurate and reliable LDL-C estimation is the cornerstone of proper dyslipidemia management and fundamental to formulate an effective treatment approach, and decisions based on inaccurate LDL-C levels can have unfavorable effects on CV health,[3],[4],[6] since obtaining a false lower LDL-C level may postpone a necessary treatment and leads to the loss of LDL-C target attainment, and an incorrectly high level may lead to therapeutic adverse effects that can be preventable.[9]

The gold standard LDL-C measurement method is the direct beta-quantification, but it is a costly and a slow process that is not always available in all laboratories;[6] hence, different formulas for LDL-C estimation have been formulated. However, when calculated, it relies on three parameters: total cholesterol (TC), triglyceride (TG), and high-density lipoprotein cholesterol (HDL-C), instead of a single direct independent measurement, which decreases its accuracy.[10],[11]

The Friedewald formula, developed in 1972,[13] is the most utilized in the medical laboratory, yet it has some limitations. First, it is based on a presumption that TG-to-very low-density lipoprotein (VLDL) ratio is constantly 5:1, which is not always accurate; the Lipid Research Clinics Prevalence Study reported a mean TG: VLDL-C ratio that ranges from 5.2 to 8.9;[12] therefore, in cases with altered relationship between TG and VLDL, such as in hypertriglyceridemia (TG > 4.5 mmol/L),[13],[14],[15] a false misleading LDL-C level will be obtained.[10],[11] Similarly, Friedewald formula underestimated LDL-C even with TG <4.5 mmol/L.[16],[17],[18] Moreover, in other studies, discordance was seen between calculated and directly measured LDL-C in lower TG states (0.79 mmol/L); calculated LDL-C levels were underestimated.[10] This is particularly significant in conditions with metabolic disturbances associated with hypertriglyceridemia predisposing to high CV risk, such as metabolic syndrome, insulin resistance, and obesity.[10],[11],[19] Moreover, Friedewald formula overestimated LDL-C in patients with type III hyperlipoproteinemia with elevated VLDL,[14] and underestimated LDL-C by around 8% in diabetics[20] and by 15% in those with alcoholic liver cirrhosis.[21]

Second, LDL-C estimated by Friedewald formula requires a fasting state, because chylomicrons in a nonfasting sample reflect VLDL that is overestimated, which therefore underestimates LDL-C.[14],[22] Third, in some cases, it gives an inaccurate LDL-C estimation when LDL-C levels are low (<2.4 mmol/L);[9],[10],[11] however, LDL-C levels of that range were not tested when Friedewald formula was derived.[3],[13] While the inaccuracy of Friedewald formula has been acceptable for years, the increasing prevalence of DM and obesity with the associated hypertriglyceridemia, and the emerging novel lipid-lowering drugs, such as PCSK9 inhibitors attaining even lower levels of LDL-C (<2 mmol/L), necessitates improving the accuracy of LDL-C-estimating methods.[23]

In view of that, using a formula that can mostly predict accurate LDL-C levels is of ultimate importance.[9],[10],[11] Intending to overcome the setbacks of Friedewald's formula, other formulas have been formulated, such as those by Cordova, Hata, Puavilai, Chen, Ahmadi, Hattori, and Vujovic [Table 1].[13],[24],[25],[26],[27],[28],[29],[30]
Table 1: Eight formulas for low-density lipoprotein cholesterol estimation

Click here to view

Cordova's formula was shown to outperform various other LDL-C-estimating formulas in the Brazilian population.[24] While Hata's provided a better option than Friedewald's for Japanese individuals with an assumption of TG: VLDL is 4 instead of 5.[25] Puavilai formula did not surpass Friedewald's in those with TG <2.2 mmol/L, but it correlated with direct LDL-C better than Friedewald with TG >2.2 mmol/L in Thai individuals; however, it was not investigated among dyslipidemics.[26] Furthermore, among Chinese subjects, Chen formula significantly reduced the limitations of Friedewald's in cases of hypertriglyceridemia.[27] The Iranian population-based Ahmadi formula overestimated LDL-C in those with low TG while slightly overestimated LDL-C as TG levels increased in their studied population.[28] Interestingly, Hattori proposed that excluding intermediate-density lipoproteins from their formula would provide a better estimation for LDL-C, which gave them promising results.[29] Similarly, Vujovic formula accurately estimated LDL-C in Serbian population.[30]

Given that genetic backgrounds have largely affected the success of these formulas in populations where they were tested, we sought to assess whether any of them would outperform Friedewald's in Saudis. Our aim is to validate the use of these eight formulas for LDL-C calculation by comparing their performance in predicting LDL-C among the Saudi Arabian population.

  Subjects and Methods Top

Study design and subjects' selection

This is a retrospective study using data from medical records of King Abdulaziz University Hospital (KAUH) in Jeddah. Eight thousand seven hundred and twenty-three medical records of Saudi Arabian patients were screened for complete lipid profiles tested between 2009 and 2021. The inclusion criteria were as follows: subjects of both genders, aged 18–75, with available complete fasting lipid profiles, and TC, TG, and LDL-C obtained on the same day. The exclusion criteria were as follows: those with nonfasting samples, and those with missing lipid parameters. Six hundred and sixty-nine subjects were included. Less than 10% of screened records were included; as lipid parameters are performed in the laboratory based on separate orders rather than a bundle of complete lipid profile, the majority of subjects had their outpatient follow-ups with incomplete lipid parameters performed in the same visit, and in a large portion of subjects, HDL-C was not tested.

Since this study was done retrospectively on preexisting data, informed consent was not taken. The Ethics Committee of Human Research at KAUH, Jeddah, approved this study (Reference No. 644-19, October 2019).

Data collection and biochemical measurements

The following data were recruited: demographics and complete fasting lipid parameters: TC, TG, LDL-C, and HDL-C. All parameters were directly and quantitatively measured in the central hospital laboratory using the SIEMENS autoanalyzer Dimension Vista® System, including LDL-C. LDL-C values were then calculated by the tested formulas, as shown in [Table 1].

Statistical analysis

Normality of the tested variables was analyzed [Appendix 1]. All tested variables were described as mean and standard deviation, and the differences between the direct LDL-C and those calculated were compared by paired t-test. The strength of association between direct and calculated LDL-C was analyzed by Pearson's correlation. The differences between all LDL-C levels were then reassessed and compared across two groups according to TG levels: Group 1 of TG <4.5 mmol/L, and Group 2 of TG >4.5 mmol/L. Calculated LDL-C is ranked from smallest to largest absolute values of the mean differences regardless of their direction of over/underestimating LDL-C. Statistical significances were set at P < 0.05 for all tests. All statistical analysis was implemented by IBM® SPSS® Statistics software, version 20.0.0, developed by IBM® in Chicago, The United States of America.

  Results Top

Of the 669 subjects enrolled, 445 (63.6%) were females and 224 (36.4%) were males. The characteristics of the study subjects are outlined in [Table 2]. The mean age of the study subjects was 51 ± 14 years. The mean of all eight calculated LDL-C levels significantly differed from the direct LDL-C, with Friedewald, Hata, Puavilai, Ahmadi, and Vujovic formulas overestimating LDL-C; the mean difference between direct and Hata's LDL-C was the lowest (0.15 ± 0.35 mmol/L) among the five overestimating formulas, while the remaining formulas underestimated LDL-C; the lowest difference in the means among the underestimating formulas was observed with Hattori's (0.03 ± 0.33 mmol/L) [Table 2].
Table 2: Characteristics of the study subjects with the mean differences between direct and calculated low-density lipoprotein cholesterol by the eight formulas ranked from smallest to largest absolute values

Click here to view

The strength of association between the direct and calculated LDL-C was analyzed by Pearson's correlation [Table 1] and [Figure 1]. All calculated LDL-C levels showed a strong significant positive association with direct LDL-C (r = 0.924–0.945, P < 0.001), apart from Ahmadi's LDL-C which appeared to moderately associate with direct LDL-C (r = 0.764, P < 0.001).
Figure 1: Pearson's correlation between direct and calculated LDL-C by the eight formulas. LDL-C = Low-density lipoprotein cholesterol

Click here to view

These formulas performed differently when the subjects were split into two groups of high and low TG levels as: Group 1 of TG < 4.5 mmol/L and Group 2 of TG > 4.5 mmol/L [Table 3]. Friedewald, Hata, Puavilai, Ahmadi, and Vujovic formulas overestimated LDL-C levels in both the groups, while the remaining formulas underestimated LDL-C only in Group 2 [Table 3].
Table 3: The mean differences between direct and calculated low-density lipoprotein cholesterol in Group 1 (triglycerides <4.5 mmol/L) and Group 2 (triglycerides >4.5 mmol/L) ranked from smallest to largest absolute values

Click here to view

Hattori's formula displayed the best concordance with direct LDL-C in Group 1 followed by Chen's with the lowest differences between their means (0.04 ± 0.31 mmol/L, P < 0.001, and 0.09 ± 0.31, P < 0.001, respectively). However, the mean differences between direct LDL-C and estimated LDL-C by all the eight formulas in Group 2 were all >0.21 mmol/L, and they all strongly correlated with direct LDL-C (r = 0.815–0.855, P < 0.001), except for Ahmadi's LDL-C which appeared to moderately correlate with direct LDL-C.

  Discussion Top

CVDs are a major health problem with a huge health and economic burden worldwide that can be minimized by proper primary CVD prevention. The key element of ASCVD prevention is blood lipid control, which can be achieved by early screening for dyslipidemia and frequent monitoring of blood lipids, especially in those with high CV risk. According to all international dyslipidemia management guidelines, LDL-C is the primary target for screening and prevention of ASCVD, and attaining LDL-C below certain levels based on specific CV risk categories ensures the reduction of primary and secondary CV events. Furthermore, individuals with metabolically compromised conditions, such as DM and MetS, are at a higher risk of ASCVD, which necessitates a higher degree of care and a strict management plan. In addition, subjects with familial hypercholesterolemia, defined by an LDL-C of > 4.9 mmol/L, are at high CV risk and premature myocardial infarctions if treatment was delayed; hence, the early screening of those subjects with accurate LDL-C is mandatory.[31]

Given that, obtaining accurate LDL-C levels is important to construct a personalized management approach for dyslipidemics and high CV risk patients, and an inaccurate LDL-C estimation may have undesirable effects. LDL-C underestimation might mask those with dyslipidemia, miss their diagnosis, delay their management, or predispose them to ineffective low-intensity treatments, all of which worsen CVD burden by increasing the prevalence of ASCVD and its associated mortality, in addition to the economic burden of more laboratory testing, hospitalizations, and revascularization procedures. On the other hand, LDL-C overestimation places patients on unnecessary treatments, facilitates unneeded follow-ups, and leads to extra cost for surplus medications and blood testing.

Accurate LDL-C estimation is a very familiar challenge in the medical laboratory. Despite the accuracy of the widely employed Friedewald's formula in most individuals, its application is still hindered in those with the ultimate need for an accurate LDL C test; those with hyperlipidemia in general, and those with metabolically compromised states accompanied by hypertriglyceridemia in specific.[9],[24],[29] In addition, in those following unusual diets, Friedewald's formula has also been shown to poorly predict LDL-C.[32] With the expanding prevalence of CVD and its associated health and economic burden, aggressive lipid-lowering approaches have been adopted to achieve the recommended LDL-C reduction in guidelines. Monitoring LDL-C in those with low LDL-C requires an accurate method since Friedewald's formula is incapable of accurately estimating low LDL-C levels.

To bypass these problems, other investigators came up with other formulas for LDL-C estimation, which were all compared in this study to evaluate the properness of their use among Saudis. Our results demonstrated that Friedewald, Hata, Puavilai, Ahmadi, and Vujovic formulas all overestimated LDL-C, while the remaining formulas underestimated LDL-C [Table 2]. The absolute values of the mean difference between the direct and calculated LDL-C were the lowest with Hattori's formula (0.03 mmol/L), followed by Chen's (0.08 mmol/L), Hata's (0.15 mmol/L), Friedewald's (0.24 mmol/L), Puavilai's (0.29 mmol/L), Vujovic's (0.33 mmol/L), Ahmadi's (0.60 mmol/L), and finally Cordova's formula, which showed the largest mean difference (0.64 mmol/L), P < 0.005 among all of the eight formulas [Table 2]. Hence, the best predictors of LDL-C levels were Hattori's, followed by Chen's formula. This is in line with another study on an Iranian population where Hattori's formula was the best LDL-C's predictor.[9]

Direct LDL-C had a strong positive association with all estimated levels, except for Ahmadi's LDL-C which moderately correlated with direct LDL-C [Figure 1]. This is also concordant with other studies that showed a strong association between direct and calculated LDL-C by various formulas,[9],[11],[30],[32] and a weaker association of direct LDL-C with LDL-C estimated by Ahmadi's.[9]

As data collection for our study is still ongoing, our sample did not yield yet a large number of subjects with TG > 4.5 mmol/L, but reevaluation was done in two groups of high and low TG levels [Table 3]. Once again, Hattori's LDL-C agreed with the direct LDL-C in both the groups at all TG levels better than other formulas; the absolute values of the mean differences between direct and Hattori's LDL-C were 0.04 and 0.21 mmol/L in Groups 1 and 2, respectively [Table 3]. In Group 1, Chen's formula was the second-best LDL-C estimator with the lowest mean difference (0.09 mmol/L), yet it did not show the same performance when TG was >4.5 mmol/L; the mean difference was 0.54 mmol/L. Hata's formula also agreeably predicted LDL-C in both the groups [Table 3]; LDL-C was estimated to be 0.15 and 0.21 mmol/L higher than the direct LDL-C in Groups 1 and 2, respectively.

As various studies have established, Friedewald's LDL-C agreed with direct LDL-C in Group 1.[11],[17],[33] This was in line with studies that evaluated Friedewald's formula only in subjects with TG <4.5 mmol/L but excluded subjects with TG >4.5 mmol/L.[11],[17] However, Friedewald's LDL-C was discordant with direct LDL-C in Group 2; LDL-C was estimated as 0.54 mmol/L higher than direct LDL-C, which supports its inaccuracy despite its small variation with direct LDL-C in Group 1 (mean difference is 0.23 mmol/L). This is in agreement with a study that analyzed Friedewald formula on all TG ranges and showed the best agreement with direct LDL-C levels when TG values fell between 1.2 and 1.6 mmol/L, with less accuracy of the Friedewald's with greater TG levels.[33]

In addition, Cordova's formula seemed to underestimate LDL-C in Group 1, which represents the bigger portion of our subjects, with a mean difference of 0.66 mmol/L. This is opposite to what was observed in an Iranian population where Cordova's LDL-C was the best LDL-C estimator among different tested formulas.[9] Furthermore, Puavilai and Vujovic formulas showed a higher mean difference from direct LDL-C in Group 1 of 0.28 and 0.31 mmol/L, respectively, and they both hugely miscalculated LDL-C in Group 2.

Of all tested formulas, Vujovic, Ahmadi, and Cordova's do not seem to be a promising alternative for direct LDL-C in our population, with the highest inaccuracy observed with Cordova formula. Conclusively, our results demonstrate that Hattori's formula is the best estimator of LDL-C in the Saudi population across all TG levels. Hata's formula also gave a closely concordant LDL-C with the directly measured in both the groups of different TG levels but to a lesser extent than Hattori's. Finally, Chen showed a good agreement with direct LDL-C only in Group 1.

This study has limitations. First, medical records prevented the enrollment of a larger portion of patients with TG levels of >4.5 mmol/L; therefore, findings associated with Group 2 may be due to the low statistical power resulting from the sample size of 16 and might not be very accurate, and additional data recruitment is required for a better evaluation of these formulas in this group.

Moreover, in few of the subjects, HDL-C measurements were obtained from samples taken on dates close to those of the remaining lipid parameters due to unavailability of samples taken on the same day; since calculated LDL-C is a biomarker that relies on three parameters (TC, TG, and HDL-C) instead of a single direct independent measurement, obtaining all parameters of the same sample reflects the lipid status at one point of time more accurately; nevertheless, variations within the small reference range of HDL-C were not expected to alter the results significantly. In addition, further judgment on these formulas by specifically analyzing their performance in very low LDL-C levels was not taken into consideration as those are less common among our subjects, which may play a role in the accuracy of the formulas' performance. These limitations will be addressed later in a prospective manner to obtain more accurate results. The strength of our study is in being the first to evaluate different LDL-C-estimating formulas in the Saudi Arabian population to evaluate the possibility of accurately obtaining LDL-C levels at a low cost, and with the slightest limitations.

  Conclusions Top

Our study finds that Hattori and Chen formulas can be used as an alternative for direct LDL-C measurement in the Saudi Arabian population as it showed the highest concordance with direct LDL-C levels, while Ahmadi and Cordova formulas cannot be considered for LDL-C estimation in Saudis. However, these formulas should be used cautiously when TG levels exceed 4.5 mmol/L. Our recommendation is to encourage direct LDL-C measurement for patients of high CV risk and in hypertriglyceridemia, and to formulate a population-specific formula that accurately predicts LDL-C levels in our population to be implemented in laboratories where direct LDL-C measurement cannot be undertaken.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

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  [Figure 1]

  [Table 1], [Table 2], [Table 3]


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