Comparison of different equations for estimation of low-density lipoprotein (LDL) – cholesterol

Introduction

Many epidemiological and clinical studies have demonstrated that increased concentration of Low-density lipoprotein cholesterol (LDL-C) is a major risk factor for the development of cardiovascular disease (CVD) [1]. As a result of the strong and positive association between LDL-C and CVD, national and international clinical practice guidelines have focused primarily on LDL-C for the categorization and treatment of dyslipidemia [2], [3], [4], [5], [6]. Thus, accurate measurement of LDL-C is crucial in CVD risk management.

Despite the β-quantification method being the reference method for the determinant for LDL-C in circulation, this method is time-consuming, expensive and not suitable for routine laboratory testing. Furthermore, LDL-C is measured as direct LDL-C (d-LDL-C) using automated homogenous assays, which are expensive and require significant time for analysis [7], [8]. In routine practice, the LDL-C concentration is estimated using the Friedewald equation as an accurate and cost-effective alternative to measuring direct LDL-C. However, the fasting sample is necessary for estimated LDL-C with the Friedewald equation. In addition, the utility of Friedewald this formula is not recommended for diabetes mellitus, renal failure or chronic alcoholic patients [9]. The National Cholesterol Education Program (NCEP) adult treatment Panel III (ATPIII) guideline recommended the estimation of LDL-C by this formula for the determination of LDL-C treatment goals for prevention of CVD [3]. Recently, there have been studies showing the efficiency of different formulas of several researchers in specific populations. The study of Wadhwa et al. has shown the best correlation with the direct method of Vujovic’s formula within the Indian population [10].

Further, in their study, De Cordova et al. showed that their formula yielded better results in terms of the estimation of LDL in the German population [11]. As can be seen, performance differences in the formulas applied in the calculation of LDL may occur owing to metabolic differences in different regions across varied populations. There is no any research on the efficacy of both Friedewald’s formula or other formulas for the Turkish population.

Accurately determining LDL-C values is important in clinical laboratory practice because LDL-C is employed to manage patients having a high risk of coronary heart disease. Therefore, most alternative formulas have been developed to estimate LDL-C to be appropriate for ethnic-specific as well as other populations. The aim of this study was to compare various formulas for estimating LDL-C and directly measure LDL-C among the Turkish population.

Material and methods

Results

A total of 1478 subjects were evaluated in this study. The gender split was 63.8% female and 36.3% male. We were able to examine the use of 10 equations for estimating LDL-C in a Turkish population featuring 1458 patients. There were 292, 262, 304, 254, and 366 patients in Groups 1, 2, 3, 4, and 5, respectively.

The general characteristics of the participants are presented in Table 2. Tables 3–7 compared estimated LDL-C using the 10 formulas to directly determine d-LDL-C, according to TG groups. These tables were shown as mean ± standard deviation (SD) values of the estimated LDL-C according to the formulas, the mean differences of the estimated LDL-C against d-LDL-C and the correlation coefficient between estimated LDL-C and d-LDL-C. There was a statistically significant difference in comparison to the estimated LDL-C results obtained with all formulas and d-LDL-C (p < 0.05). The results obtained by all formulas were statistically significantly correlated with d-LDL-C concentrations for all groups. In Groups 1, 2, 3, and 4, the Teerakanchana formula had the best correlation with d-LDL-C (r=0.955, r=0.961, r=0.961, and r=0.950, respectively). In Group 5, the Anandaraja formula best correlated with d-LDL-C (r=0.792).

Table 2:

Demographics and characteristics values of patients (n=1478).

	Group1 (n=292)	Group2 (n=262)	Group3 (n=304)	Group4 (n=254)	Group5 (n=366)
Male/Female, (%)	74.7/25.3	68.5/31.5	68.8/31.2	54.2/45.8	53.4/46.6
Age	50.1 ± 15.4	55.1 ± 15.01	55.5 ± 14.4	54.3 ± 13.9	50.9 ± 13.5
Glu, mg/dL	102.2 ± 13.3	93.8 ± 19.2	97.7 ± 21.8	91.9.8 ± 18.5	97.4 ± 18.7
TC, mg/dL	190.3 ± 43.9	212.4 ± 44.9	227.7 ± 43.8	223.3 ± 43	239.7 ± 56.7
TG, mg/dL	80.2 ± 14.6	144.8 ± 31.6	241.6 ± 43.8	336.5 ± 39.4	532.6 ± 133.5
HDL-C, mg/dL	62.62 ± 15.5	53.8 ± 15.06	46.2 ± 11.6	41.2 ± 14.5	36.1 ± 10.1
HbA1C, %	5.3 ± 0.56	5.41 ± 0.46	5.67 ± 0.59	5.62 ± 0.52	5.56 ± 0.41
d-LDL-c, mg/dL	129.5 ± 38.9	148.5 ± 38.2	157.9 ± 41.7	145.6 ± 38.8	133.7 ± 47.95

Table 3:

Estimated Low-density lipoprotein (LDL) results, performances of correlation and means differences of estimated LDL to direct LDL-C (d-LDL) for all formulas at triglycerides (TG) < 100 mg/dL concentrations.

Group 1	LDL-C, mg/dL	Correlation coefficient (r)		Mean Difference
n=292	X ± SD	R	95%CI	X ± SD	95%CI
Friedewald	111.7 ± 38.8	0.951	0.986–0.988	17.8 ± 12.1	15.1–20.6
Cordova	95.84 ± 30.1	0.949	0.893–0.985	33.7 ± 14.1	30.5–36.9
Ahmadi	107.27 ± 37.8	0.915	0.856–0.0956	22.3 ± 15.9	18.6–25.9
Anandaraja	128.9 ± 38.6	0.917	0.863–0.958	0.67 ± 15.8	−2.9–4.2
Teerakanchana	117.9 ± 36.8	0.955	0.908–0.986	11.7 ± 11.6	9.0–14.4
Chen	106.9 ± 35.5	0.951	0.895–0.987	22.6 ± 12.1	19.8–25.4
Hattori	119.9 ± 37.7	0.949	0.893–0.985	9.7 ± 12.3	6.8–12.5
Vujovic	116.1 ± 39.2	0.951	0.893–0.985	13.5 ± 12.2	10.70–16.3
Puavillai	114.4 ± 39.4	0.949	0.895–0.988	15.2 ± 12.2	12.3–17.9
Hatta	107.8 ± 38.6	0.951	0.895–0.988	21.8 ± 12.1	19.1–24.6

1. X, Mean; SD, Standard deviation; r, Correlation coefficient. Mean difference=d-LDL-C – estimated LDL-C by ten formulas.

Table 4:

Estimated LDL results, performances of correlation and means differences of estimated LDL to d-LDL for all formulas at TG 100–199 mg/dL concentrations.

Group 2	LDL-C, mg/dL	Correlation coefficient (r)		Mean Difference
n=262	X ± SD	r	95%CI	X ± SD	95%CI
Friedewald	129.8 ± 37.8	0.958	0.926–979	19.3 ± 11.3	17.8–21.1
Cordova	118.9 ± 29.5	0.950	0.917–0.971	30.2 ± 14.6	28.5–32.7
Ahmadi	166.9 ± 40.9	0.835	0.770–0.879	−17.8 ± 23.3	−21.1–(−14.3)
Anandaraja	137.5 ± 39.8	0.927	0.892–0.952	11.7 ± 15.1	9.5–14.0
Teerakanchana	136.5 ± 36.1	0.961	0.932–0.982	12.6 ± 11.0	11.2–14.4
Chen	128.4 ± 34.5	0.957	0.925–0.978	20.8 ± 11.9	19.3–22.7
Hattori	148.8 ± 36.9	0.958	0.917–0.971	0.3 ± 12.3	−1.4–2.3
Vujovic	137.6 ± 38.1	0.950	0.926–0.979	11.5 ± 11.3	9.9–13.3
Puavillai	134.6 ± 38.1	0.958	0.926–0.979	14.5 ± 11.3	12.9–16.2
Hatta	122.7 ± 37.6	0.957	0.924–0.978	26.4 ± 11.4	24.0–28.2

1. X, Mean; SD, Standard deviation; r, Correlation coefficient. Mean difference=d-LDL-C – estimated LDL-C by ten formulas.

Table 5:

Estimated LDL results, performances of correlation and means differences of estimated LDL to d-LDL for all formulas at TG 200–299 mg/dL concentrations.

Group 3	LDL-C, mg/dL	Correlation coefficient (r)		Mean Difference
n=304	X ± SD	r	95%CI	X ± SD	95%CI
Friedewald	132.4 ± 41.5	0.952	0.904–0.981	25.4 ± 12.7	23.9–26.8
Cordova	135.7 ± 31.7	0.949	0.906–0.977	22.4 ± 15.9	20.5–24.1
Ahmadi	237.8 ± 45.0	0.778	0.703–0.839	−79.8 ± 27.8	−82.9–(−76.7)
Anandaraja	132.65 ± 39.5	0.945	0.917–0.964	24.9 ± 13.7	23.4–26.2
Teerakanchana	143.6 ± 37.47	0.961	0.923–0.986	14.1 ± 11.8	12.8–15.5
Chen	138.4 ± 36.5	0.955	0.910–0.983	19.4 ± 12.8	17.9–20.8
Hattori	169.5 ± 38.5	0.949	0.906–0.977	−11.8 ± 13.2	−13.3–(−10.3)
Vujovic	145.4 ± 41.6	0.955	0.908–0.983	12.4 ± 12.4	10.9–13.7
Puavillai	140.4 ± 41.6	0.954	0.907–0.983	17.4 ± 12.5	15.9–18.7
Hatta	120.4 ± 41.6	0.948	0.898–0.978	37.4 ± 13.3	35.9–38.9

1. X, Mean; SD, Standard deviation; r, Correlation coefficient. Mean difference=d-LDL-C – estimated LDL-C by ten formulas.

Table 6:

Estimated LDL results, performances of correlation and means differences of estimated LDL to d-LDL for all formulas at TG 300–399 mg/dL concentrations.

Group 4	LDL-C, mg/dL	Correlation coefficient (r)		Mean Difference
n=254	X ± SD	r	95%CI	X ± SD	95%CI
Friedewald	114.6 ± 39.9	0.940	0.917–0.958	30.6 ± 13.7	28.9–32.3
Cordova	136.46 ± 30.1	0.930	0.908–0.948	8.7 ± 15.41	6.87–10.7
Ahmadi	289.2 ± 42.1	0.738	0.682–0.796	−143.9 ± 29.4	−147.5–(−140.3)
Anandaraja	112.3 ± 38.5	0.924	0.890–0.949	32.9 ± 15.1	31.2–34.8
Teerakanchana	132.8 ± 35.6	0.949	0.929–0.964	12.4 ± 12.3	10.9–13.9
Chen	130.1 ± 35.8	0.940	0.918–0.957	15.1 ± 13.2	13.5–16.8
Hattori	170.8 ± 37.8	0.931	0.908–0.948	−25.57 ± 14.3	−27.3–(23.8)
Vujovic	132.8 ± 39.8	0.941	0.919–0.958	12.5 ± 13.5	10.7–14.1
Puavillai	125.8 ± 39.8	0.941	0.918–0.958	19.4 ± 13.6	17.7–21.1
Hatta	97.8 ± 40.5	0.936	0.912–0.955	47.24 ± 14.1	45.6–49.1

1. X, Mean; SD, Standard deviation; r, Correlation coefficient. Mean difference=d-LDL-C – estimated LDL-C by ten formulas.

Table 7:

Estimated LDL results, performances of correlation and means differences of estimated LDL to d-LDL for all formulas at TG 400–1000 mg/dL concentrations.

Group 5	LDL-C, mg/dL	Correlation coefficient (r)		Mean Difference
n=366	X ± SD	r	95%CI	X ± SD	95%CI
Friedewald	96.98 ± 53.8	0.745	0.527–0.899	36.8 ± 36.7	32.8–45.6
Cordova	152.63 ± 41.8	0.618	0.368–0.813	−18.9 ± 39.5	−0.22.2–(14.8)
Ahmadi	410.7 ± 94.8	0.125	0.23–0.265	−277.1 ± 100.4	−287.3–(−266.7)
Anandaraja	91.9 ± 51.4	0.792	0.593–0.917	41.8 ± 32.2	38.5–45.1
Teerakanchana	129.3 ± 48.5	0.709	0.496–0.903	4.5 ± 35.1	0.8–8.05
Chen	129.8 ± 47.5	0.709	0.464–0.887	3.8 ± 36.3	0.1–7.6
Hattori	191.1 ± 51.6	0.618	0.368–0.813	−57.3 ± 43.7	−61.8–52.8
Vujovic	125.7 ± 51.6	0.728	0.488–0.897	8.1 ± 34.5	4.2–11.8
Puavillai	114.7 ± 53.1	0.736	0.502–0.899	19.1 ± 37.0	15.2–22.8
Hatta	70.4 ± 55.6	0.749	0.542–0.886	63.4 ± 37.4	59.5–67.4

1. X, Mean; SD, Standard deviation; r, Correlation coefficient. Mean difference=d-LDL-C – estimated LDL-C by Ten formulas.

The difference between d-LDL-C and LDL-C estimated by all formulas in patients with TG 0-400 mg/dL is indicated by the Bland-Altman plot in Figure 1 (mean bias ± 1.96*SD). The negative bias was well-evaluated in all graphs. The comparison of the formulas plot [estimated LDL-C(x) and d-LDL-C(y)] in patients with TG 0–400 mg/dL (n=1112) showed a regression equation of y=0.95x + 30.9 (r=0.945) for the Friedewald, y=1.13x + 3.54 (r=0.907) for the Cordova, y=0.29x + 83.6 (r=0.507) for the Ahmadi, y=0.91x + 33.6 (r=0.903) for the Anandaraja, y=1.04x + 7 (r=0.958) for the Teerakanchana, y=1.06 + 11.5 (r=0.950) for the Chen, y=0.91x + 3.7 (r=0.907) for the Hattori, y=0.96x + 17.8 (r=0.953) for the Vujovic, y=0.96x + 22.4 (r=0.951) for the Puavillai, and y=0.92x + 45.7 (r=0.925) for the Hatta Scatter plots are indicated with the Bland-Altman plot in Figure 2.

Figure 1:

Bland-atman plot (mean ± 1.96*SD) for direct LDL-C (D-LDL-C) and Low-density lipoprotein cholesterol (LDL-C) calculated by all Formulas; A. Friedewald, B: De Cordova, C: Ahmadi, D: Anandaraja, E: Teerakanchana, F: Chen, G: Hattori, H: Vujovic, I: Puavillai, J: Hatta.

Figure 2:

Scatter plots are indicated with the Bland-Altman plot for D-LDL-C and LDL-C calculated by all Formulas; A. Friedewald, B: De Cordova, C: Ahmadi, D: Anandaraja, E: Teerakanchana, F: Chen, G: Hattori, H: Vujovic, I: Puavillai, J: Hatta.

The rate of the risk classification based on d-LDL-C measurement using a cut-off LDL-C >100 mg/dL, or minimal risk concentrations according to the recommendation of NCEP ATP III, was 90.0%. The rate of the risk classification based on estimated LDL-C results were 73.9, 83.1, 95.3, 76.2, 84.9, 81.8, 93.9, 83.5, 80.3, and 62.2% for the Friedewald, Cordova, Ahmadi, Anandaraja, Teerakanchana, Chen, Hattori, Vujovic, Puavillai, and Hatta equations, respectively.

Discussion

In the present study, we compared the performance of estimated LDL-C using 10 formulas with a homogeneous method for d-LDL-C measurement in a sample of 1478 Turkish adults. The estimated LDL-C results with the Teerakanchana formula had a better correlation than other formulas with direct measurement of various levels of TG. The results of the Ahmadi formula were fairly correlated compared to other formulas with direct measurement across all TG levels groups.

Friedewald’s formula is widely applied in clinical laboratories and is also recommended to be used by the NCEP ATP III [3]. In a number of investigations, many new formulas were developed to provide an alternative to the Friedewald formula [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. Ahmadi et al. found that their formula is better than Friedewald formula [14]. In a study by Vujovic et al. they compared their formulas with the Anandaraja and Friedewald formula in terms of d-LDL-C measurement results, where the Anandaraja and Friedewald formulas were shown to feature a negative bias. This bias has not been established with the Vujovic formula [20]. Krishnavemi et al. further established that the Friedewald formula had a better correlation value than that the Anandaraja formula, but in both, negative bias existed according to the results of d-LDL-C measurement, and negative bias increased depending on TG concentration [9]. In contrast, Anandaraja et al. observed that their formula had more accurate results than Friedewald formula [16]. In a study carried out by de Cordova et al., they assessed seven formulas (Cordova, Friedewald, Chen, Teerakanchana, Hattori, Anandaraja, and Ahmadi) for a large database of German individuals. Their formula estimated the best accuracy compared to both Friedewald and other formulas, as well as a higher hazard ratio of mortality by cardiovascular-related events. [11]. In a study of Razi et al., the Chen, Anandaraja and Friedewald formulas yielded greater results than direct measurement [23]. In a study of Choi et al., between the Friedewald, Chen, Vujovic, Hattori, Cordova, and Anandaraja formulas, d-LDL-C results were demonstrated to have a robust correlation in Korean individuals with CVD risk. In their work, the Friedewald formula exhibited better performance than the other formulas. Another result of their study is that the Vujovic formula was better at determining TG concentrations >300 mg/dL [24]. Onyenekwu et al. compared the Cordova, Friedewald and Ahmadi formulas for estimating LDL in a healthy South African population. The Friedewald and Cordova formulas had a stronger correlation than the Ahmadi formula with respect to determining d-LDL-C concentrations. Meanwhile, the Friedewald exhibited better performance than the Cordova formula [25]. In Wadhwa et al., there was the validation of different formulas (Friedewald, Cordova, Vujovic, Ahmadi, Anandaraja, Puavillai, Hattori) in an Indian population. In their study, it was shown there was the best correlation with the direct method of the Vujovic formula in the Indian population [10]. In another large set of hospitalized patients in South Africa, Martins et al. assessed four formulas (Friedewald, Chen, Cordova, and Hattori). They observed a strong correlation of the Cordova formula with that of Friedewald at low TG values. However, the Hattori formula appears to be best for application in patients, even at extreme lipid concentrations [26]. In a study carried out by Cordova et al., the Friedewald formula had a positive bias at TG < 150 mg/dL, non-bias at TG 150–300 mg/dL, and a negative bias at TG >300 the mg/dL that was seen in a large heterogeneous population with more than 10,000 Brazilian individuals [26]. In the works of Kannan et al., the correlation between direct LDL measurement and the Friedewald formula was found to the highest at 0.90 according to TG concentrations for a large Indian laboratory database [27]. The d-LDL-C measurement was also compared with many formulas in different populations and varied results were obtained in these studies. In our study, this is relevant because it is the first study on the Turkish population.

In our study, the Friedewald, Anandaraja, and Hatta formulas all had a negative bias that increased with the rise in TG concentration for all groups. For example, this difference was 17.8 in Group 1 (TG < 100 mg/dL), while this difference rose to 36.8 in high TG concentrations for the Friedewald formula. There is a negative bias for the Ahmadi and Hattori formulas in Group 1, while there is positive bias for Ahmadi and Hattori formulas in other existing groups. This positive bias increased in parallel with the rise in TG concentrations. The negative bias did not change with respect to the mean differences of all groups by association with increased TG concentration for Vujovic, Puavillai, and Teerakanchana formulas. The Teerakanchana formula also exhibited a much better correlation and lower negative bias compared to all formulas. In all groups with TG < 400 mg/dL, there was not a significant change in the mean differences of all groups associated with elevated TG concentrations for this formula. The Anandaraja formula has the best average difference for Group 1. The Teerakanchana and Chen formulas had the lowest negative bias for TG > 400 mg/dL levels. Moreover, the Cordova formula has a positive bias for the first four groups. This positive bias decreased in contrast with the rise in TG concentrations. Moreover, across our study, for all groups between TG < 400 mg/dL, there was a high correlation between all formulas and d-LDL-C measurement concentrations except for the Ahmadi formula (r=0.907–0.958). However, in our study, for patients with TG concentrations between 400 and 1000 mg/dL, the correlation coefficient values for other formulas decreased considerably (r=changed from 0.618 to 0.792). The Ahmadi formula had the worst correlation coefficient value (r=0.125). As a result, for all formulas we investigated, the performance of them was observed to be clearly diminished in patients with TG > 400 mg/dL.

Establishing the concentration of LDL-C helps in the assessment of cardiovascular risk and is confirmed as a target for treatment decisions. In the classification by the NCEP ATP III, LDL-C concentrations of >100, 100–129, 130–159, 160–189, and ≥190 mg/dL are optimal goals for low-risk, moderate risk, high-risk, and very high-risk patients for CVD, respectively [3]. Our study exhibits underestimate according to the results of estimated LDL-C. Besides the ratio of patients with risk according to the d-LDL-C measurement (cut-off >100 mg/dL) was 90%, whereas this ratio in other formulas, except the Ahmadi and Hattori formulas, was <85% in our study. As a result, although there were strong correlations between the examined formulas and direct measurement, the underestimation in our study may lead to placing a patient into a no-risk or low-risk group when they have a high risk for CVD and therefore requires changes to plans surrounding drug therapy. However, the precise and accurate measurement of LDL-C is important for the estimation of CVD and therapeutic decisions. The difference between d-LDL-C and estimated LDL-C results can be substantial in terms of patients’ risk classification for coronary artery disease (CAD).

Beta quantification (BQ) by ultra-centrifugation is the gold standard reference method for measuring the LDL-C. This method is time-consuming, requires costly devices, and experienced trained personal. Therefore, it is not used for routine laboratories. As a result, over the last 15 years, direct homogenous LDL-C measurement offers a practicable and economical alternative, according to BQ and is widely used in routine laboratory tests [7], [8], [9]. Recently, the agreement between LDL-C assays and the BQ method has been evaluated by many researchers [20], [28], [29], [30], [31], [32]. The majority of homogenous LDL-C assays have satisfied total error goals of NCEP for no diseased individuals compared with the BQ method [20], [30], [31], [32]. Our study made use of a direct method (Roche) instead of BQ of LDL-C. When we review the research on the Roche direct LDL-C method in a study of Nauck et al. it was reported that it may be employed in the determination of patients with increased risk of CVD and as a possibly useful tool in the management of patients with hyperlipoproteinemia, particularly when Roche’s d-LDL-C measurement is compared against the BQ method. Roche d-LDL-C measurement is precise and acceptably accurate with BQ by ultra-centrifugation [28]. Rifai et al. described that the N-generous Roche LDL-C assay has established analytical performance goals by NCEP and appears to have a role in the diagnosis and management of hypercholesterolemia patients. In the study of Estaban-Salan et al. it was figured out that the Roche direct LDL-C assay represented a valid alternative to BQ for clinical laboratories. The direct LDL-C measurement assay was presented to be precise and produce accurate LDL-C concentrations even in hypertriglyceridemia [29]. Contrary to all these studies, in the work of Miller et al. they evaluated eight direct methods for measuring LDL-C compared to the BQ method [32]. The Roche LDL-C method minimally exceeded 13.35% over the NCEP error goal of ≤ 12% for the no diseased group. Also, in this study, all LDL-C assays substantially exceeded the total error goal (>20%) for the diseased group. However, the discordant results in the disease group were present between the BQ method and all direct LDL-C measurement methods. The many patients in the working sample had different types of dyslipidemias and rare genetic lipid disorders, with samples of these patients being the dominant cause of discrepant results; the results from these patients may not be representative of the typical performance of direct methods. As such, the NCEP analytical performance goals require that direct LDL-C measurements have a TAE ≤ ± 12% and analytical bias < ± 4 for medical decisions (NCEP) [3]. In our study, the expected analytical goals yielded rather strong results (TAE-6.2%; analytical bias-2.01%). We also determined LDL-C concentrations of nondiseased subjects by homogeneous assay. As indicated in our study, the assay had robust results in healthy individuals [28], [29].

The first factor contributing to underestimation between estimated LDL-C and d-LDL-C measurement is that the formulas of the estimated LDL-C is generally used in terms of three generalities, including TC, TG, and HDL-C. The results of the estimated LDL-C can be impacted because of an error in the measurement of the three analytes. TC and TG measurements are better standardized than HDL-C measurements. Therefore, accurate measurement of HDL-C has a major on LDL calculation. In one study, the effect on the estimated LDL-C of the eight different HDL measurements was examined. In their study, the Roche reagent that was employed in our own work had an average misclassification rate of 5.6% with respect to method-dependent risk classifications [33]. This situation contributed to negative bias as reflected in the LDL calculation in our study. The second reason is that factors such as obesity, race/ethnicity, insulin resistance, and fasting status may change depending on TG concentrations. In our study, a patient information management system was employed during patient selection. If the treatment and clinical conditions of the selected patient are scrupulously examined, there may be incomplete data entry, or some patients may use a lipid-lowering medication off the record. Another reason is that the number of patients is relatively low according to certain studies. When all these reasons are combined, negative bias can lead to higher detection.

There were several limitations of our study. First, as stated earlier, the information featured included obesity, race/ethnicity, insulin resistance, fasting status, incomplete data entry, and other possible determinants that could feature a lack of data. Second, the patients size was relatively low according to some studies and it was a single center study. Third, we did not examine patients with known CVD or other diseases affected by LDL-C concentrations. These equations need to be reevaluated with CVD and healthy persons for large populations in future studies. Other limitations of our study included the fact we did not use reference methods for the measurement of LDL-C. As in the case of our work, the most important similar studies did not use the reference method [11], [26]. However, despite these limitations, the work presented here is a meaningful comparison because it indicates the state of all formulas as applied to a Turkish population. Additionally, we have also compared directly measured LDL-C results with results of variously estimated LDL-C equations for the first time. There have been hardly any studies to date on the use of the all estimated LDL-C equations in Turkish populations. All these reasons elevate the importance of our study.

In conclusion, in the present study, we compared 10 formulas, including the Friedewald formula and others, against measured d-LDL-C in a Turkish population. In this study, although there was a strong correlation between d-LDL-C measurement and predicted LDL formulas, there was a negative bias between these formulas and the d-LDL-C results. Moreover, these results show that there are differences in the results obtained by the estimated and directly measured methods. The most major international guidelines declare an LDL-C target of  <70 mg/dL for high-risk patients. To achieve this goal, the appropriate drug therapy or diet should be adjusted. According to the results of our study, these formulas, which we employed in the calculation of LDL-C according to d-LDL-C measured, indicate a lower risk in the determination of the risk of CAD and planning of treatment strategies. This may lead to delayed lipid-lowering treatment or an inadequate diet for high-risk patients with CAD.