

ORIGINAL ARTICLE 

Year : 2019  Volume
: 12
 Issue : 3  Page : 223227 

Derivation of a new formula for the estimation of lowdensity lipoprotein cholesterol
Ravish Huchegowda^{1}, Rajani Kumawat^{2}, Binita Goswami^{3}, Pramod Lali^{3}, Srinivas H Gowda^{3}
^{1} Department of Neurochemistry, NIMHANS, Bengaluru, Karnataka, India ^{2} Department of Biochemistry, AIIMS, Jodhpur, Rajasthan, India ^{3} Department of Biochemistry, Maulana Azad Medical College, New Delhi, India
Date of Web Publication  15Oct2019 
Correspondence Address: Dr. Srinivas H Gowda Department of Biochemistry, Maulana Azad Medical College, New Delhi  110 002 India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/kleuhsj.kleuhsj_86_19
BACKGROUND: Lowdensity lipoprotein cholesterol (LDLc) is a wellknown surrogate marker to assess the cardiovascular health and risk of atherosclerosis. Due to the feasibility of calculating the LDLc from the estimated values of other subfractions of cholesterol, it has been commonly applied in resourcelimited settings. However, calculated LDLc presents with a significant bias, probably due to the lack of relevance of equation in the local population. MATERIALS AND METHODS: A total of 200 samples were assessed for serum lipid profile by automated method. Parallelly, based on the values of subfractions of cholesterol obtained, an equation was derived using polynomial multiregression analysis. We also tested the ability other published equations to accurately predict the LDLc value. RESULTS: We found the best fit equation as LDL_{cal}= (0.88 × total cholesterol) − (0.02 × triglycerides) − (0.03 × highdensity lipoprotein) − 37.48. The equation performed better than most other published equations, including Friedewald's equation. It was also noted that Chen's equation had the best prediction and Ahmidi's equation performed the poorest. CONCLUSION: This study highlights a significant need for improved formulas to estimate serum LDLc based on other cholesterol parameters.
Keywords: Indirect estimation, lowdensity lipoprotein cholesterol, serum cholesterol
How to cite this article: Huchegowda R, Kumawat R, Goswami B, Lali P, Gowda SH. Derivation of a new formula for the estimation of lowdensity lipoprotein cholesterol. Indian J Health Sci Biomed Res 2019;12:2237 
How to cite this URL: Huchegowda R, Kumawat R, Goswami B, Lali P, Gowda SH. Derivation of a new formula for the estimation of lowdensity lipoprotein cholesterol. Indian J Health Sci Biomed Res [serial online] 2019 [cited 2019 Nov 19];12:2237. Available from: http://www.ijournalhs.org/text.asp?2019/12/3/223/269208 
Introduction   
Cholesterol is a sterolbased chemical known to be associated with cellular structure and thus forms an integral part of normal physiological functioning.^{[1]} Cholesterols being insoluble in water are circulated in association with proteins, and hence, they are referred to as lipoproteins. Structurally, these lipoproteins possess a central hydrophobic core of nonpolar lipids surrounded by a hydrophilic membrane consisting of phospholipids, free cholesterol, and apolipoproteins.^{[2]} The lipoproteins are further subclassified based on their density into five major subtypes – very lowdensity lipoprotein (VLDL), intermediatedensity lipoprotein (IDL), lowdensity lipoproteins (LDL), and highdensity lipoprotein (HDL).^{[2],[3]} Of these VLDL, IDL, and LDL are proatherogenic,^{[4],[5],[6]} whereas HDL has antiatherogenic properties.^{[7],[8]}
Of these, LDL cholesterol (LDLc) is used as a laboratory biomarker to indicate cardiovascular health and risk of atherosclerosis.^{[9]} LDLc maybe estimated directly using beta quantification method or by indirect calculation such as using Friedewald's equation. It has been shown that direct measurement is a better marker for LDLc estimation.^{[10],[11]} However, the feasibility of deriving LDLc based on other cholesterol parameters has lead several laboratories to adopt Friedewald's equation.
There are several published equations for deriving the LDLc value. However, each equation provides with a slightly different result. This variation is probably due to the limitations of the population which was used to derive the equation biased by demographic variability, genetic differences, and environmental influences, each of which influences the LDLc production. For example, a study by Osegbe et al. compared 10 different equations and found that Teerankanchana's formula performed the best and Ahmadi's equation had the maximum bias.^{[12]} In a more recent study, a new formula was developed by Ghasemi et al. which showed better performance.^{[13]} These studies indicate the need to develop a more local approach to the formula which can be used to indirectly calculate LDLc.
Materials and Methods   
Study design
The present study was conducted retrospective for 2 years.
Study population
Data of serum samples were obtained from the participants (n = 200) investigated at the Maulana Azad Medical College, New Delhi, from 2014 to 2016. Participants aged between 16 and 70 years, hyperlipidemic patients with cholesterol <200 mg/dL, including newly diagnosed diabetes and hypertension patients not on medication, and healthy population with cholesterol <200 mg/dL and triglyceride <400 mg/dL were also included for analysis. Participants on active medications, including steroids and (or) antioxidants, known history of substance abuse such as tobacco, nicotine, and alcohol, were excluded from the study.
Ethical statement
The study was approved by the MAMC Institutional Ethical Committee, New Delhi (IEC no: F.1/IEC/MAMC/(65/05/2016/No/383 dated 31/12/2018).
Data collection
The demographic details and clinical history were recorded based on the available medical records. Blood sample was collected as per the standard protocol. In brief, samples were collected from participants after overnight fasting in plain vacutainer tubes (#367815; BD; USA). The collected blood samples were allowed to clot for at least 30 min at ambient temperature and centrifuged at 4000 ×g for 10 min to obtain the serum. All the parameters of cholesterol, including total cholesterol by the direct enzymatic endpoint method, triglycerides by GPOPAP method, HDL and LDL were measured by enzymatic end point method using automated Au400 automated analyzer using Randox reagent (UK) as per the manufacturer's instructions.
Baseline statistical analysis
The basic statistical analyses were performed using the R Statistical package 3.5 (R Foundation for Statistical Computing, Vienna, Austria). The sample size was determined using nQuery advisor version 7 (Randox Laboratories Ltd., Crumlin, County Antrim, United Kingdom). The normality distribution of the data was assessed using the Kolmogorov–Smirnov test. Descriptive statistics for each variable were studied as the mean and standard deviation. Pearson's correlation and Spearman's correlation statistics were applied based on the continuous value and categorical values, respectively, as appropriate.
Derivation and validation of the formula
The values obtained from twothirds of patients were randomly assigned to a derivation data set, and polynomial multiregression analysis was done to predict the bestfit equation. Onethird of patients in the study sample were randomly assigned to a validation data set, and the LDLc values were derived based on the new formula. Subsequently, the linearity match between the calculated and the direct LDLc was assessed using Pearson's correlation analysis.
Results   
A total of 200 participants, of which 113 were male and 87 were female, were included in the study. The demographic distribution of participants and their lipid profile by gender are shown in [Table 1]. It was noted that there were no statistically significant differences in lipid profiles between the genders, although the cholesterol levels were slightly higher in females except for HDL.
Polynomial multiregression analysis found the best fit formula as LDL_{cal}= (0.88 × total cholesterol [TC]) − (0.02 × triglycerides [TG]) − (0.03 × HDL) − 37.48. Following derivation and validation, we also checked for correlation of the derived formula against the entire dataset and found a reasonably good performance [Figure 1]; R^{2} = 0.72]. We also analyzed our dataset against multiple other reported formulas and observed for the linear correlation between direct and calculated LDLc. The findings are presented in [Table 2]. [Figure 1] shows the linear correlation between our derived formulae against the direct LDLc indicating the performance.  Figure 1: Correlation of derived formula using polynomial multiregression model against direct estimation of lowdensity lipoprotein cholesterol
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 Table 2: Correlation between direct and calculated lowdensity lipoprotein cholesterol using equations described by others and this study
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It was observed that our formula performed second to Chen's equation. To understand this discrepancy, we probed our data further by analyzing the errors between the direct estimation value and the formula derived value and found that the error ranged from −49 to + 46 units [Figure 2]. Correlation analysis between age, gender, total cholesterol, triglycerides, and HDL was found to be weak against the error in the estimation of LDLc, indicating the error was independent of these variables. We also grouped the samples with triglycerides <150 mg/dL (n = 50) and >150 mg/dL (n = 150) and compared the error; did not find any statistically significant difference (P = 0.32).  Figure 2: Error between the lowdensity lipoprotein cholesterol direct estimation value and the formula derived value
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Discussion   
Cardiovascular diseases represent one of the most commonly preventable clinical condition on a global scale. Periodic estimation of complete serum lipid profile is useful in predicting the cardiovascular health of an individual. However, in recent years, LDLc has replaced total cholesterol as a serumbased biomarker and is a modifiable risk factor used for the assessment of cardiovascular health.^{[14]} It has been largely agreed that a periodic LDLc estimation is useful in predicting the risk of atherosclerosis, though the direct role of LDLc has been challenged recently.^{[15],[16]} Nevertheless, the importance of accurate estimation of serum LDLc in a diagnostic laboratory has been considered to be an invaluable tool.^{[9],[17]} Direct estimation method of LDLc is always superior to calculated estimate. However, the feasibility of calculating LDLc is especially useful in resourcelimited settings. Hence, multiple laboratories over the world use indirect calculation as a method of choice to estimate LDLc.
Friedewald et al., in 1972, originally defined formula to calculate the LDLc levels in serum based on other cholesterol subfractions, including TC, HDL, and TG levels. The original formula was defined as LDLc (mg/dL) = TC (mg/dL) – HDL (mg/dL) − TG (mg/dL)/5. Subsequently, several limitations of the Friedewald's formula were realized.^{[18],[19]} For example, the formula assumes that the triglyceride to cholesterol ratio is constant. Hence, it is not applicable if the subject is not fasting, known status of hyperlipoproteinemia, type II diabetes mellitus, nephrotic syndrome, and alcohol abuse since in all these conditions, the triglyceridetocholesterol ratio in VLDL is significantly altered.^{[12]}
In this study, we sought to derive a new formula which could be potentially used in the laboratory to calculate the LDLc value for routine diagnostic application. A total of 200 samples were evaluated for their lipid profile. The study sample involved a reasonable age group of both genders as shown in [Table 1].
The normal range of serum lipoproteins include <200 mg/dl of total cholesterol, <150 mg/dl of triglycerides, >60 mg/dl of HDL, and <130 mg/dl of LDL.^{[20],[21]} In context, it was noted that the cholesterol profile was approximately normal in most of the studied cases. The lipoprotein levels were lower in males as compared to females except for HDL, which is in accordance with the understanding that female are at a higher risk of cholesterol.^{[22]}
Based on the collected data, we performed a polynomial multiregression analysis and derived the formula as LDL_{cal}= (0.88 × TC) − (0.02 × TG) − (0.03 × HDL) − 37.48. To estimate the performance of our derived equation against other derived equations, we compared the linear agreement between the direct estimate and calculated LDLc value. The linear fit modal is the best suited model to generate new formula for LDL.^{[23]} The equation derived in this study performed better than most of the other equations in context with agreement except for Chen's formula which was found to be superior [Table 2]. However, we observed that Chen's formula uniformly underestimated the LDLc value [Figure 2]. In comparison, our new formula was similar to Friedewald's formula with a uniformly distributed error but performed better. It was also noted that Ahmidi's equation performed the poorest among all the tested formulas.
The direct LDLc values were estimated to be 89.94 ± 34.54 mg/dL as compared to the calculated value of 90.2 ± 32.87. The newly derived formula had a range of error units within ± 50 units, and 90% of these errors (n = 180) were between ± 29 units. Further, the formula is not significantly influenced by triglycerides at levels of >150 mg/dl. This indicates that the bias of estimation observed using the newly derived formula is unlikely to impact the clinical decision since most of the error units are below the standard deviation of the direct estimate.
There are a few limitations of this study. Ignoring the fact that the newly derived formula did not perform the best, we were unable to find the possible source of error in calculation with reference to the direct estimate value. We envision that this could be due to other factors such as VLDL or chylomicrons not estimated in this study. Hence, we advocate that direct estimation should be the method of choice for estimating LDLc, especially in critical clinical settings.
Conclusion   
The newly derived equation was found to be reasonably accurate along with Chen's formula in estimating serum LDLc levels. We also highlight the need for better prediction equations to estimate the serum LDLc based on other cholesterol parameters. Finally, we strongly indicate that the direct estimation of LDLc should be the method of choice.
Acknowledgments
We wish to acknowledge MAMC laboratory technical staff, and Binu VS, Department of Biostatistics, NIMHANS who have provided help with statistics.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2]
[Table 1], [Table 2]
