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Despite the availability of several homogenous LDL-C assays, calculated Friedewald’s LDL-C equation remains the widely used formula in clinical practice. Several novel formulas developed in different populations have been reported to outperform the Friedewald formula. This study validated the existing LDL-C formulas and derived a modified LDL-C formula specific to a Ghanaian population. In this comparative study, we recruited 1518 participants, derived a new modified Friedewald’s LDL-C (M-LDL-C) equation, evaluated LDL-C by Friedewald’s formula (F-LDL-C), Martin’s formula (N-LDL-C), Anandaraja’s formula (A-LDL-C), and compared them to direct measurement of LDL-C (D-LDL-C). The mean D-LDL-C (2.47±0.71 mmol/L) was significantly lower compared to F-LDL-C (2.76±1.05 mmol/L), N-LDL-C (2.74±1.04 mmol/L), A-LDL-C (2.99±1.02 mmol/L), and M-LDL-C (2.97±1.08 mmol/L) p < 0.001. There was a significantly positive correlation between D-LDL-C and A-LDL-C (r=0.658, p<0.0001), N-LDL-C (r=0.693, p<0.0001), and M-LDL-C (r=0.693, p<0.0001). M-LDL-c yielded a better diagnostic performance [(area under the curve (AUC)=0.81; sensitivity (SE) (60%) and specificity (SP) (88%)] followed by N-LDL-C [(AUC=0.81; SE (63%) and SP (85%)], F-LDL-C [(AUC=0.80; SE (63%) and SP (84%)], and A-LDL-C (AUC=0.77; SE (68%) and SP (78%)] using D-LDL-C as gold standard. Bland–Altman plots showed a definite agreement between means and differences of D-LDL-C and the calculated formulas with 95% of values lying within ±0.50 SD limits. The modified LDL-C (M-LDL-C) formula derived by this study yielded a better diagnostic accuracy compared to A-LDL-C and F-LDL-C equations and thus could serve as a substitute for D-LDL-C and F-LDL-C equations in the Ghanaian population.

Cardiovascular diseases (CVDs) are the leading cause of morbidity and mortality globally [

Since the inception of Friedewald’s LDL-C equation in 1972, it has been used most widely to estimate LDL-C in clinical practice as well as in health screenings [

Ultracentrifugation and beta-quantitation are the gold standards for LDL-C measurement [

Previous studies have shown that the formula underrates LDL-C and CV risk stratification even when triglyceride levels are below 4.52 mmol/l [

The heterogeneity of population, as well as differences in dietary habits, calls for a more population-specific LDL-C formula that will be generic, accurate, and precise. The scarcity of literature on modified LDL-C formula in a West African population makes it necessary that we begin to document and validate existing formulas in our setting. Research in this direction will provide the breakthrough in combating the burden of atherosclerosis and serve as a useful guide for stakeholders in the management and control of cardiovascular diseases in Ghana. Using fasting lipid profile data from patients who visited the laboratory department of the National Cardiothoracic Centre, this study validated the existing LDL-C formulas and derived a modified LDL-C formula specific to a Ghanaian population.

This was a comparative study for the estimation of LDL-C using three different formulas and direct estimation by a homogenous assay. Data was collected for the lipid profile samples received in the laboratory unit of the National Cardiothoracic Centre (NCC) in Accra from December 2016 to April 2017. The NCC in Korle Bu, Accra, is one of the few functioning referral centres in West Africa where complete evaluation of cardiothoracic diseases is not only possible but very safe and of a standard comparable internationally.

This study was approved by the Committee on Human Research, Publication and Ethics (CHRPE) of School of Medical Sciences, KNUST. The subjects were adequately informed of the purpose, procedures, nature, risks, and minimal discomfort of the study. Participants were coded and assured of strict anonymity, confidentiality, and the freedom to exit or decline participation at any time without penalty.

Samples for lipid profile analysis were collected from patients visiting the laboratory unit of the NCC over the period stated. This was after participants had given their consent. Of a total of 1540 samples analysed, 22 were excluded because they had triglyceride levels greater than 4.52mmol/l (400mg/dl). The sample size of 1518 (N=1518) was comprised of 782 males and 736 females.

Participants with no evidence of metabolic conditions (diabetes, chronic renal failure) as per clinical history and had observed at least ten (10) hours of overnight fasting were included. Samples with triglyceride levels greater than 4.52mmol/l (400mg/dl) were excluded.

A volume of at least 3 mL of venous blood was taken into plain tubes after a 12-hour or minimum of 8-hour overnight fast via phlebotomy. The blood could clot, and serum was separated by centrifugation (2000g for 10mins) and analysed on URIT 8210 automatic chemistry analyser by TC and TG were measured enzymatically by CHOD-PAP and Glycerol phosphate peroxidase-PAP methods, respectively, using reagent kit obtained from Human Diagnostic Worldwide, Germany. TC and TG were calibrated using general chemistry calibrator provided by Human Diagnostic. The reagent kit for direct LDL-C assay, the Chema LDL direct FL test, was manufactured by Hospitex Diagnostics, Italy. HDL-c measurement was performed using a direct homogenous method without precipitation with the use of enzymatic colorimetric assay provided by Human Diagnostic, Germany. LDL-C concentration was directly determined by enzymatic assays.

LDL-C concentrations were also calculated by Friedewald’s, Anandaraja’s and Martin’s formula as follows:

Re-examination of Friedewald’s formula for LDL-C determination in our setting is based on the current results, following the procedure which led to Friedewald’s formula derivation. Factor for VLDL-C concentration estimation was recalculated. Total cholesterol, TG, LD-C, and HDL-C concentration measurements were used in the initial group to calculate the VLDL-C/TG ratio for a Ghanaian population. The sum of HDL-C and LDL-C was subtracted from TC for each person. This accounted for the assessment of VLDL-C concentration for each person. Afterwards, to determine the mean of the ratio, the TG concentration was divided by the corresponding calculated VLDL-C. The mean ratio, TG/ VLDL, was 4 compared to 2.2 according to Friedewald, M-LDL-C (mmol/L) =TC-HDL-C-TG/4.0 [

Data collected were stored in MS Excel spread sheet. Using the Statistical Package for Social Sciences program (SPSS, version 21.0 for Windows) and GraphPad prism (Version 5 for windows, Inc. 2007), statistical analyses were carried out. Results are expressed as means ± SD and percentages in parenthesis. Unpaired t-test and one-way ANOVA were used to compare mean values of continuous variables for two and more than two categories. Person’s correlation analysis was used to determine the association between directly measured LDL-C and calculated LDL-C. The Bland-Altman plots for comparison were used to determine level of bias and agreement of the calculated LDL-C to direct LDL-C. Linear regression analysis was used to generate linear models for the estimation of LDL-C. For all statistical comparisons, a

Lipoprotein concentrations and their distributions in the validation group are given in Table

Distribution of basic lipoprotein measurements.

| | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|

| | | | | | | | | |

Mean | 4.60 | 1.02 | 1.38 | 3.22 | 2.47 | 2.76 | 2.74 | 2.99 | 2.97 |

SD | 1.20 | 0.57 | 0.36 | 1.13 | 0.71 | 1.05 | 1.04 | 1.02 | 1.08 |

1st Quartile | 3.77 | 0.65 | 1.13 | 2.45 | 1.94 | 2.03 | 2.03 | 2.30 | 2.23 |

Median | 4.45 | 0.88 | 1.33 | 3.09 | 2.43 | 2.64 | 2.63 | 2.87 | 2.64 |

3rd Quartile | 5.21 | 1.23 | 1.59 | 3.78 | 2.90 | 3.28 | 3.26 | 3.54 | 3.28 |

The mean %ΔLDL between calculated LDL-Cs compared to the direct method was 12.39 ± 27.34% for Friedewald’s formula, 11.74 ± 29.25% for Martin’s formula, 23.54 ± 30.45% for Anandaraja’s formula, and 21.33± 28.43% for modified formula (Table

Mean percentage difference between D-LDL-C and calculated LDL-C.

| | | | |
---|---|---|---|---|

Mean | 12.39 | 11.74 | 23.54 | 21.33 |

SD | 27.34 | 29.25 | 30.45 | 28.43 |

1st Quartile | 4.33 | 5.07 | 1.39 | 3.63 |

Median | 13.79 | 13.51 | 23.84 | 23.8 |

3rd Quartile | 29.63 | 28.55 | 44.81 | 39.11 |

SD: standard deviation; ΔA-LDL-C: mean percentage difference for Friedwald’s formula; ΔA-LDL-C: mean percentage difference for Martin formula; ΔA-LDL-C: mean percentage difference for Anandaraja’s formula; ΔA-LDL-C: mean percentage difference for modified formula. Mean percentage difference was calculated as [(calculated LDL-C)-(D-LDL-C)]

The ability of the formulas to correctly classify subjects at the clinical decision cut-off points in specific subgroups is shown in Table

Means ± SDs and percentages of correctly classified subjects in risk categories regarding TC, TG and D-LDL-C concentrations given by NCEP ATP III.

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TC (mmol/L) | n | D-LDL-C | F-LDL-C | N-LDL-C | A-LDL-C | M-LDL-C | F | N | A | M |

≤4.13 | 586 | 2.01±0.53 | 1.91±0.40 | 1.89±0.40 | 2.11±0.38 | 2.09±0.41 | 77.6% | 77.9% | 92.6% | 86.4% |

4.14-5.16 | 536 | 2.49±0.51 | 2.79±0.41 | 2.77±0.39 | 3.04±0.31 | 2.99±0.40 | 78.1% | 77.9% | 84.1% | 78.9% |

5.17-6.20 | 272 | 2.92±0.50 | 3.52±0.45 | 3.52±0.41 | 3.80±0.36 | 3.78±0.42 | 72.4% | 76.4% | 65.6% | 64.6% |

6.21-7.24 | 89 | 3.44±0.65 | 4.45±0.49 | 4.43±0.44 | 4.66±0.38 | 4.72±0.45 | 65.8% | 70.3% | 56.9% | 48.1% |

≥ 7.25 | 35 | 3.90±0.66 | 6.16±2.18 | 6.17±2.18 | 6.37±1.84 | 6.53±2.21 | 63.8% | 68.9% | 59.6% | 50.8% |

TG (mmol/L) | ||||||||||

≤1.13 | 1055 | 2.40±0.69 | 2.63±0.90 | 2.57±0.89 | 2.92±0.91 | 2.78±0.91 | 75.2% | 79.1% | 73.0% | 80.6% |

1.14-1.69 | 324 | 2.61±0.70 | 2.96±0.90 | 3.10±0.93 | 3.10±0.99 | 3.24±0.96 | 30.2% | 32.4% | 29.3% | 29.6% |

1.70-2.25 | 76 | 2.75±0.69 | 3.18±1.20 | 3.30±0.89 | 3.29±1.20 | 3.58±1.19 | 19.7% | 23.7% | 25.0% | 22.4% |

2.26-2.82 | 40 | 2.68±0.75 | 3.49±2.82 | 3.74±2.74 | 3.51±2.49 | 4.01±2.82 | 11.4% | 5.0% | 2.5% | 10.0% |

2.83-4.52 | 23 | 2.74±1.01 | 3.00±1.05 | 3.43±0.96 | 3.03±1.02 | 3.75±1.07 | 4.3% | 8.7% | 8.7% | 17.4% |

LDL-C (mmol/L | ||||||||||

≤2.59 | 903 | 2.01±0.38 | 2.33±0.65 | 2.31±0.65 | 2.61±0.68 | 2.53±0.67 | 80.0% | 80.4% | 80.0% | 81.4% |

2.60-3.35 | 447 | 2.92±0.22 | 3.05±0.90 | 3.04±0.89 | 3.23±0.88 | 3.27±0.92 | 41.4% | 42.9% | 31.7% | 34.1% |

3.36-4.12 | 142 | 3.62±0.18 | 3.98±0.91 | 3.95±0.92 | 4.18±0.93 | 4.22±0.97 | 31.9% | 31.4% | 19.2% | 22.6% |

4.13-4.89 | 21 | 4.36±0.21 | 5.68±2.54 | 5.64±2.57 | 5.72±2.26 | 5.94±2.26 | 8.2% | 9.5% | 9.8% | 42.5% |

≥4.90 | 5 | 5.54±0.44 | 6.08±2.12 | 6.06±2.69 | 6.07±2.69 | 6.40±2.06 | 10.6% | 8.8% | 3.5% | 7.7% |

From Table

Diagnosis performances of the various formulas.

| | | | | | | |
---|---|---|---|---|---|---|---|

F-LDL-C | 2.92 | 0.80 | 0.78-.83 | 0.63(0.60-0.67) | 0.84(0.82-0.87) | 0.87 | 0.74 |

N-LDL-C | 2.92 | 0.81 | 0.78-.83 | 0.63(0.60-0.66) | 0.85(0.82-0.87) | 0.87 | 0.78 |

A-LDL-C | 2.96 | 0.77 | .75-.78 | 0.68(0.65-0.72) | 0.73(0.70-0.77) | 0.68 | 0.73 |

M-LDL-C | 3.23 | 0.81 | .78-.83 | 0.60(0.56-0.64) | 0.88(0.85-0.90) | 0.72 | 0.72 |

AUC: area under curve; CI: confidence interval; NPV: negative predictive value; PPV: positive predictive value; FLDL-C, LDL-C calculated by Friedewald’s formula; N-LDL-C, LDL-C calculated by Martin’s formula; A-LDL-C, LDL-C calculated by Anandaraja’s formula; M-LDL-C, LDL-C calculated by modified formula.

Figure

ROC curves depicting the accuracy of the different forms of LDL-C measurements.

Correlation analysis between various formulas is used to estimate the LDL-C concentrations. With respect to the Pearson correlation coefficient (r) and coefficient of determination (R^{2}), various formulas were strongly positive correlated with each other (p<0.0001) (Table

Pearson correlation coefficient (r) (bold) and coefficient of determination (R^{2}) (italics) between formulas.

Formulas | F-LDL | N-LDL | A-LDL | M-LDL | D-LDL-C |
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F-LDL-C (mmol/L) | | | | | |

| | | | ||

N-LDL-C (mmol/L) | | | | | |

| | | | ||

A-LDL-C (mmol/L) | | | | | |

| | | | ||

M-LDL-C (mmol/L) | | | | | |

| | | | ||

D-LDL-C (mmol/L) | | | | | |

| | | |

FLDL-C, LDL-C calculated by Friedewald’s formula; N-LDL-C, LDL-C calculated by Martin’s formula; A-LDL-C, LDL-C calculated by Anandaraja’s formula; M-LDL-C, LDL-C calculated by modified formula.

Figure

Bland and Altman plot of the different forms of LDL-C measurements (F-LDL-C, N-LDL-C, A-LDL-C, and M-LDL-C).

Currently, the NCEP guidelines focus on diagnosis and treatment of TC and LDL-C. It is therefore relevant to accurately estimate LDL-C, as it has significant implications on cardiovascular risk stratification and can affect therapy and outcomes. The gold standard methods for quantifying LDL-borne cholesterol in serum are laborious and thus poorly suited to the modern laboratory [

Lipoprotein concentrations and their distributions were analyzed in this study and we found significant differences between the mean values of F-LDL-C, N-LDL-C, A-LDL-C, and M-LDL-C with respect to D-LDL-C mean values. M-LDL-C values were significantly higher compared to the rest of the formulas except A-LDL-C (Table

Reports from the original study for the development of Friedewald’s formula provided a simple division of blood plasma TG by 5 for mg/dL or 2.2 for mmol/L [

The difference between calculated LDL-C and directly measured LDL-C results can be important regarding risk classification for coronary heart disease among patients [

F-LDL-C had a sensitivity of 63.0% and specificity of 84.0% with negative predictive value of 87.0% and positive predictive 74.0% with a cut-off of 2.92 mmol/L in this study. M-LDL-C had a sensitivity of 0.60 and specificity of 0.88 with a cut-off value of 3.23mmol/L. These findings contrast with reports from a study by Martin et al. in South Africa. In their work, they recorded a higher sensitivity and specificity with a cut-off of 2.5 mmol/L [

In general, there were strong correlations among the various formulas for estimating LDL-C concentrations. However, moderate correlations were observed between the directly measured LDL-C and the various methods. Among the three formulas used in this study, the Anandaraja’s formula showed the least correlation with the directly measured LDL-C (Table

Bland-Altman graphs showed a clear relationship between both the directly measured LDL-C and the calculation formulas. The observed low bias can be well appreciated in all plots though the bias between N-LDL-C and D-LDL-C was the lowest. This indicates that the calculation formulas and the directly measured LDL-C methods are systematically producing similar results (Figure

This study has strength being the first study to compare different methods of estimating LDL-c concentration in Ghana and the West African subregion. However, our study is limited by the fact that both derived models must be further scrutinized and validated bearing in mind the differences in race and the specific character of the applied method of measurement.

The modified LDL-c (M-LDL-c) formula derived by this study yielded a better diagnostic accuracy compared to A-LDL-c and F-LDL-c equation and thus could serve as a substitute for D-LDL-c and F-LDL-c equation in the Ghanaian population. Taking into consideration the racial variances as well as the specific character of the applied method of measurement, the study findings underscore the need for scrutiny, validation, and reliability evaluations of the generated models, to ascertain their clinical use. Further work should also examine the performance of rick calculations by the various formulae.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest.

The authors would like to thank the patients, management, and staff of laboratory unit of the National Cardiothoracic Centre (NCC) Korle-bu Teaching Hospital Accra for making this a successful work.