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DOI: 10.1055/s00421748628
Comparative Study of Calculated LDLCholesterol Levels with the Direct Assay in Patients with Hypothyroidism
Abstract
Background Hypothyroidism is one among the many factors that predisposes one to coronary artery disease. As lowdensity lipoproteincholesterol (LDLC) is associated with cardiovascular risk, calculated LDLC should have good accuracy with minimal bias. Hypothyroidism alters the lipid composition of lipoproteins by the secretion of triglyceriderich lipoproteins, which affects the calculation of LDLC. The present study aimed to compare 13 different formulae for the calculation of LDLC including the newly derived Martin's formula by direct assay in patients of hypothyroidism.
Method In this analytical crosssectional study, a total of 105 patients with laboratory evidence of hypothyroidism, from January to June 2019, were studied, and blood samples were subjected for lipid profile analysis at central biochemistry laboratory. Calculated LDLC was assessed by different formulae.
Result We observed that calculated LDLC by Friedewald's, Cordova's, Anandaraja's, Hattori's, and Chen's formulae has bias less than ± 5 compared with direct LDLC, with Anandaraja's formula having the lowest bias (2.744) and Cordova's formula having lowest bias percentage (−1.077) among them. According to the Bland–Altman plots, the bias in Friedewald's and Anandraja's were equally distributed below and above the reference line of direct LDLC.
Conclusion This is the first study comparing different formulae for LDLC calculation in patients with hypothyroidism. Anandaraja's formula was as equally effective as Friedewald's formula when used as an alternative costeffective tool to evaluate LDLC in hypothyroid patients. The recently proposed Martin's formula for calculated LDLC had a higher bias when compared with Friedewald's and Anandaraja's formulae in patients with hypothyroidism.
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Keywords
Anandaraja's formula  Friedewald's formula  hypothyroidism  LDL cholesterol  lipid profile  Martin's formulaIntroduction
Thyroid hormones alter lipoprotein metabolism by inducing 3hydroxy3methylglutarylcoenzyme A reductase and also regulate the lowdensity lipoprotein (LDL) receptor (LDLR) expression at the genetic level.[1] [2] In hypothyroidism, the decreased thyroid function would lower the LDLR activity as well as lipoprotein lipase activity leading to decreased catabolism of LDL, intermediatedensity lipoprotein, and decreased clearance of triglyceride (TG)rich lipoproteins.[3] [4] Further, subclinical hypothyroidism leads to the greater secretion of larger TGrich verylowdensity lipoprotein (VLDL) particles from the liver when compared with euthyroid subjects and hyperthyroid subjects.[5] As TG is taken as an indirect marker of VLDL cholesterol, this leads to a bias in the calculation of LDL cholesterol (LDLC). On cardiovascular risk assessment, patients with subclinical hypothyroidism are also found to be at increased risk.[6] Further, an altered lipid profile viz. atherogenic lipid profile was seen in patients with subclinical hypothyroidism when compared with the euthyroid subjects.[7] Therefore, the estimation of lipid profile is necessary to assess the risk of patients for cardiovascular disease and metabolic syndrome which would help in the early initiation of treatment. As LDLC is associated with cardiovascular risk stratification, the formula for the calculation of LDLC should have good accuracy with minimal bias. Different formulae have been devised to calculate the LDLC from the measured lipid profile parameters, i.e., Friedewald et al,[8] Hattori et al,[9] Anandaraja et al,[10] Chen et al,[11] de Cordova and de Cordova,[12] Teerakanchana et al,[13] Ahmadi et al,[14] Delong et al,[15] Rao et al,[16] Martin et al,[17] Hata and Nakajima,[18] Puavilai et al,[19] and Vujovic et al.[20] Among these, the Friedewald formula is the most commonly used formula to calculate LDLC.
The derivation of different formulae for the calculation of LDLC requires these formulae to be validated in different populations as well as in different diseases before final implementation in the clinical practice. Various studies have tested the validity of Friedewald formula in various population groups[21] [22] [23] [24] and in diseasespecific cohort like metabolic syndrome cohort.[25] Attempts toward validation using different formulae in different populations have been undertaken in different countries as evidenced by the work done by Onyenekwu et al, Lee et al, and Alpdemir and Alpdemir.[26] [27] [28] Similarly, various studies have tried to validate different formulae in different diseases. To this extent, studies conducted by Fawwad et al, Karkhaneh et al, Paz et al, and Lin et al have validated them in diabetes, different metabolic health statuses, schizophrenic patients, and patients with coronary heart disease, respectively.[29] [30] [31] [32] Alteration of lipid profile in patients with hypothyroidism has been documented by multiple studies.[33] [34] However, to our knowledge, no studies have been undertaken to validate different formulae for the calculation of LDLC in patients with hypothyroidism.
Given the altered TG content in subclinical and overt hypothyroidism, the current study aimed to compare 13 different formulae for calculated LDLC with the direct assay in patients with subclinical and overt hypothyroidism. The comparison of calculated LDLC in different forms of thyroid disorder or different chemistry analyzer platforms was out of this study's scope.
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Materials and Methods
Study Design
This was an analytical crosssectional study performed after obtaining approval by the institutional ethics committee on human subjects' research (AIIMS/IEC/2018/690). This study was conducted from January 2019 to June 2019. The frequency of dyslipidemia in primary hypothyroidism was found to be 91%.[35] The calculation was based on the assumption of an α error of 0.05 and a power of 90%. The estimated sample size was 89. Considering the subgroup analysis, 105 patients were recruited for the study. We calculated the sample size using the Open Epi program 9 Open Source Epidemiology statistics for Public Health, version 3.01. The samples were collected from patients with laboratory evidence of subclinical and overt hypothyroidism attending the medicine and endocrinology outpatient department of a tertiary care hospital. Patients with TG values greater than 350 mg/dL and hemolyzed blood samples were excluded from the study.
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Sample Collection and Processing
Thyroid profile reports from the central biochemistry laboratory were analyzed for patients with laboratory evidence of subclinical and overt hypothyroidism. Those blood samples with thyroid hormonal values signifying subclinical and overt hypothyroidism were subjected for lipid profile analysis at the central biochemistry laboratory. The results of TG, total cholesterol (TC), highdensity lipoprotein (HDLC), and LDLC by direct assay were analyzed in the Beckmann AU 680 clinical chemistry analyzer. Calculated LDLC was assessed by the following formulae: LDLC Friedewald et al, LDLC Hattori et al, LDLC Anandaraja et al, LDLC Chen et al, LDLC Cordova and Cordova, LDLC Teerakanchana et al, LDLC Ahmadi et al, LDLC Delong, LDLC Rao et al, LDLC Martin et al, LDLC Puavilai et al, LDLC Hata and LDLC Vujovic.
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Lipoprotein Analysis
The serum was separated by centrifugation and analyzed on the Beckmann AU 680 autoanalyzer. TC and TG were measured enzymatically by CHODPAP and glycerol phosphate oxidaseperoxidase methods, respectively. TC and TG were calibrated using the system multicalibrator provided by Beckman Coulter, Inc., CA, United States. Direct LDLC and HDLC were measured by the selective solubilization method and the selective inhibition method. Direct LDLC and HDLC were calibrated using the calibrator provided with the reagent. Quality control was assessed for TC, TG, direct LDLC, and HDLC using 2 Levels of Liquichek Lipids Control from BioRad Laboratories, Inc.
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Statistical Analysis
The results were described as means, medians, and standard deviations (quantitative variables) or by frequency and percentiles (qualitative variables). Student's t test for paired samples was used to compare the results of LDLC using different formulas and LDLC by direct assay. Linear regression was performed to calculate the slope. Scattergram data, Bland–Altman diagram, and calculation of bias and difference percentage were used to evaluate results obtained using different formulae and direct assay. The underestimated and overestimated LDLC values were compared with the direct assay values based on the existing formulae. A probability of 5% or less was considered significant.
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Results
General Characteristics of the Study Participants
[Table 1] summarizes the characteristics of all 105 study participants of hypothyroidism including general characteristics, lipid profile, and baseline thyroid values.
Abbreviations: HDLC, highdensity lipoprotein cholesterol, IQR, interquartile range; LDLC, lowdensity lipoprotein cholesterol; SD, standard deviation; TSH, thyroidstimulating hormone.
Note: Data expressed as a mean ± standard deviation for normal distribution, median, IQR for nonnormal distribution and number (percent) for categorical variables.
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Comparison of an Estimated LDLC Using the Different Formulae and Directly Measured LDLC
Overall, there was a significant difference between calculated LDLC and directly measured LDLC in our study. Mean calculated LDLC was higher than that obtained by directly measured in all formulae except Cordova's, Hattori's, and Hatta's formulae ([Table 2]). All other formulae overestimated LDLC compared with direct LDLC. Also, Anandraja's and Chen's formulae did not show any significant difference in calculated LDLC compared to Friedewald's formula.
Abbreviations: LDLC, lowdensity lipoprotein cholesterol; NA, not applicable; SD, standard deviation.
Note: Data expressed as a mean ± standard deviation of LDLC. The different formulae used are LDL_Friedewald, LDL_Ahmadi, LDL_Cordova, LDL_Anandaraja, LDL_Hattori, LDL_Chen, LDL_DeLong, LDL_Rao, LDL_Teerankanchcna, LDLC Martin el al, LDLC Puavilai et al, LDLC Hata and LDLC Vujovic. Statistical test: Paired ttest.
^{a} Denotes pvalue < 0.05 which is considered as statistically significant.
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Scatter Plots of Estimated LDLC Using the Different Formulae and Directly Measured LDLC
[Fig. 1] depicts the scatter plot of calculated LDLC using Friedewald's formula and direct LDLC, and [Fig. 2] depicts the scatter plot of calculated LDLC using different formulae in comparison with LDL Friedewald and direct LDL. Except for Ahmadi formula, all other formulae appeared to have comparable calculated LDLC values compared to direct LDLC estimation. Further, this comparable relationship was observed to be similar across all the ranges of direct LDLC. LDLC calculated by Ahmadi formula was found to be different from direct LDLC estimation.
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Linear Regression of Estimated LDLC Using the Different Formulae and Directly Measured LDLC
Linear regression analysis showed Ahmadi's formulae having the highest slope (1.247) and lowest r ^{2} value (0.4190). Calculated LDLC using Cordova's formula was found to have the lowest slope (0.8435). In addition to Ahmadi's, calculated LDLC using Friedewald's, DeLong's, Chen's, Puavilai's, and Vujovic's formulae also showed slope more than 1. All formulae found to have a good correlation against directly measured LDLC (r ^{2} > 0.90 and r > 0.95) except Ahmadi's (0.6473) in hypothyroid patients ([Table 3]).
Abbreviations: LDLC, lowdensity lipoprotein cholesterol; SE, standard error.
Note: Linear regression data expressed with slope, standard error, 95% confidence interval, r ^{2} and r value of calculated LDLC.
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Assessment of Bias of Estimated LDLC Using the Different Formulae and Directly Measured LDLC
[Table 4] and [Fig. 3] show the bias of calculated LDLC by different formulae and direct LDLC in the recruited patients. Calculated LDLC using Ahmadi's was found to be the highest bias, and Anandaraja's showed the lowest bias when compared with direct LDLC. On comparison with direct LDLC, calculated LDLC using Cordova's, Hattori's, and Hatta's were found to have a negative bias. The average bias was less than ± 5 for calculated LDLC using Friedewald's, Cordova's, Anandaraja's, Hattori's, Chen's, and Hatta's formulae. The difference percentage was observed to be lowest for Cordova's followed by Friedewald's and Anandaraja's formulae. When compared with Friedewald's and Anandaraja's, Martin's formula exhibited higher bias and difference percentage in the calculation of LDLC in hypothyroid patients.
Abbreviations: LDLC, lowdensity lipoprotein cholesterol; SD, standard deviation.
Note: Data expressed as a mean ± standard deviation of LDLC and difference percentage.
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Bland–Altman Plots for the Method Comparison of Estimated LDLC Using the Different Formulae and Directly Measured LDLC
[Fig. 4A–M] depicts the Bland–Altman plots for estimated LDLC using the different formulae and directly measured LDLC. Bland–Altman plots brought out the bias present for different formulae at various levels of direct LDLC. Friedewald's and Anandaraja's formulae appeared to estimate LDLC levels with minimal bias when compared with direct estimation. Ahmadi's formulae displayed a trend of increasing bias with an increase in LDLC levels. Interestingly, Cordova's formulae displayed a shift of bias from positive to negative with an increase in LDLC levels. DeLong's, Rao's, Teerankanchana's, Martin's, Puavilai's, and Vujovic's formulae were found to have a predominantly positive bias across all levels of direct LDLC.
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Comparison of Frequency of Underestimated and Overestimated LDLC Samples Using the Different Formulae and Directly Measured LDLC
[Fig. 5] depicts frequency of underestimated and overestimated calculated LDLC samples using different formulae and direct LDLC. DeLong's, Rao's, Teerankanchana's, Martin's, Puavilai's, and Vujovic's formulae consistently overestimated LDLC when compared with direct LDLC. Chen's, Anandaraja's, and Cordova's showed approximately equal number of underestimated and overestimated samples. Using Friedewald's formula for the calculation of LDLC, samples were overestimated when compared with direct LDLC.
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Discussion
National Cholesterol Education Program (NCEP) Adult Treatment PanelIII (ATP) guidelines classify patients for cholesterollowering treatment including dietary therapy based on LDLC levels. Hence, it is of utmost importance to accurately estimate LDLC levels in patients prone to dyslipidemia. Increased risk for cardiovascular diseases in hypothyroidism patients due to altered lipid profiles makes it imperative to have a method of estimation of LDLC with minimal bias. The reference method for LDLC estimation is β quantification, but it is timeconsuming and expensive which makes it not suitable for routine laboratory testing.[36] [37] In 1972, Friedewald's et al published a landmark report describing a formula to estimate LDLC as an alternative to tedious ultracentrifugation and results of estimated LDLC highly correlated with β quantiﬁcation method. Over the past few years, many homogenous methods have been developed which are expensive and have also failed to show clear advantages in terms of performance when compared with Friedewald's calculation.[38] [39] [40] Although Friedewald's formula is the most widely used to estimate LDLC in a clinical setup, it has its wellknown limitations.[41] [42] Since then, numerous efforts have been directed to address the limitations of Friedewald's formula in the general population as well as in diseasespecific scenarios.[8] [9] [10] [11] [12] [13] [14] [15] The present study was designed to evaluate the performance of 13 different formulae for calculated LDLC in a set of Indian patients with subclinical and overt hypothyroidism.
Overall, there was a significant difference between calculated LDLC and directly measured LDLC in our study. We have found calculated LDLC to be higher than directly measured LDLC using Friedewald's, Ahmadi's, Anandaraja's, Chen's, DeLong's, Rao's, Teerankanchana's, Martin's, Puavilai's, and Vujovic's, except Cordova's, Hattori's and Hatta's formulae ([Table 2]). Although no similar study has been undertaken in the hypothyroid disease cohort, Sahu et al[40] and Gasko[43] have reported similar findings, i.e., an overestimation of LDLC by Friedewald's and Anandaraja's formulae in the general population. Some studies have reported an underestimation with calculated LDLC to measured LDLC.[44] [45] [46] [47] We have found a correlation of greater than 0.950 in all calculated LDLC and directly measured LDLC except Ahmadi's (0.6473) in hypothyroid patients. Anandaraja et al reported the correlation of 0.97 between LDLC measured by their formula and direct LDLC and 0.88 between Friedewald's and directly measured LDLC in the general population.^{9} In our study in the hypothyroid disease cohort, this correlation was found to be 0.950, 0.981, and 0.976, respectively, for Anandraja's, Friedewald's, and Martin's ([Table 3]). Other studies have reported a correlation 0.88,[39] 0.786,[45] and 0.86,[48] respectively, in general population but not a diseasespecific.
On analysis of bias of calculated LDLC by different formulae and direct LDLC, Ahmadi's had the highest and Anandaraja's had the lowest bias in hypothyroid patients. Calculated LDLC using all 13 different formulae had positive bias compared to direct LDLC except Cordova's, Hattori's, and Hatta's. Contradictorily, in the general population, Gupta et al[44] had reported negative bias in calculated LDLC by Anandraja's and Friedewald's compared to direct LDLC. In our study, the average bias was within ± 5 for calculated LDLC using Friedewald's, Cordova's, Anandaraja's, Hattori's, Chen's, and Hatta's formulae ([Table 4]). We found newer formulae like Martin's to have a higher bias (7.328) in patients with hypothyroidism in estimating LDLC. We also observed that, in hypothyroid patients, Friedewald and Anandaraja formulae appeared to have a minimal bias when compared with direct estimation at different LDLC levels. However, in the general population, Rim et al have demonstrated that Friedewald formula generally overestimates at low LDLC range and underestimates at high LDLC levels.[24] In contrast to our findings in hypothyroid patients, Vujovic et al have demonstrated that Anandaraja formula tends to have a negative bias on the estimation of LDLC in the general population.[20]
From the present study, we found that apart from Friedewald's, calculated LDLC using Anandaraja's, Chen's, and Cordova's also yield comparable results in hypothyroid patients. Both Anandaraja's and Chen's have a comparable slope and minimal bias. Further, both these formulas have a comparable number of underestimated and overestimated samples. Although Cordova's had the lowest difference percentage and minimal bias, the linear regression slope was observed to be 0.8435. This decreased slope for Cordova's was corroborated in Bland–Altman plot where the bias shifted from positive to negative with an increase in LDLC levels. In contrast, calculated LDLC using Friedewald's and Martin's, both having a slope of near to 1, had a higher number of overestimated samples. We also observed that formulae for the calculation of LDLC displayed different characteristics viz. bias and correlation, in the hypothyroid disease cohort when compared with the general population. This corroborates the need for larger studies for the validation of the different formulae in overt and subclinical hypothyroid disease cohort given the altered lipoprotein metabolism and TG content in this specific disease cohort.
In the case of Anandaraja, as the formula considers only two analytes—TC and TG for calculation, it may diminish the total random error when compared with the other formulae. Since the formula does not require HDL cholesterol estimation for calculation, it can prove to be more economical also. Due to these favorable factors, Anandaraja's formula has already been approved for use in general population in Brazilian and Greek subjects.[43] [49]
The present study also had several limitations that need to be addressed. First, the βquantification method, which is considered the gold standard method for measuring LDLC, has not been used. The data regarding treatment for hypothyroidism or any other comorbidities for the recruited subjects were not available for the study. The study needs to be validated within a larger study population.
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Conclusion
As no study till now has compared the various formulae for LDLC in hypothyroidism, this is the first such attempt to bring out the differing characteristics of formulae for LDLC in patients with hypothyroidism when compared with the general population. All 13 formulae for calculated LDLC have differed significantly from direct LDLC in hypothyroid patients. When compared with Friedewald's, Anandaraja's, Chen's, and Cordova's formulae showed comparable calculated LDLC results. Newer formulae like Martin's had higher bias and more samples were being overestimated in hypothyroidism. In conclusion, Friedewald's and Anandaraja's formulae outperformed others for estimating LDLC against a direct measurement with Anandaraja's having a lesser bias. The Anandaraja's formulae could be used as an alternative costeffective tool to Friedewald's to measure LDLC when the direct measurement cannot be afforded in hypothyroid patients. The differing characteristics of various formulae in hypothyroid patients, when compared with the general population, bring into attention the role of altered lipoprotein metabolism in hypothyroidism in the calculation of LDLC and cardiovascular risk assessment and this needs to be validated in a larger study population.
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Conflict of Interest
None declared.

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Article published online:
01 June 2022
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References
 1 Bakker O, Hudig F, Meijssen S, Wiersinga WM. Effects of triiodothyronine and amiodarone on the promoter of the human LDL receptor gene. Biochem Biophys Res Commun 1998; 249 (02) 517521
 2 Shin DJ, Osborne TF. Thyroid hormone regulation and cholesterol metabolism are connected through sterol regulatory elementbinding protein2 (SREBP2). J Biol Chem 2003; 278 (36) 3411434118
 3 Nikkilä EA, Kekki M. Plasma triglyceride metabolism in thyroid disease. J Clin Invest 1972; 51 (08) 21032114
 4 Abrams JJ, Grundy SM. Cholesterol metabolism in hypothyroidism and hyperthyroidism in man. J Lipid Res 1981; 22 (02) 323338
 5 Fabbrini E, Magkos F, Patterson BW, Mittendorfer B, Klein S. Subclinical hypothyroidism and hyperthyroidism have opposite effects on hepatic verylowdensity lipoproteintriglyceride kinetics. J Clin Endocrinol Metab 2012; 97 (03) E414E418
 6 Pesic MM, Radojkovic D, Antic S, Kocic R, StankovicDjordjevic D. Subclinical hypothyroidism: association with cardiovascular risk factors and components of metabolic syndrome. Biotechnol Biotechnol Equip 2015; 29 (01) 157163
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