Low-density lipoprotein (LDL) cholesterol is a measure of the cholesterol mass transported within LDL and plays a prominent role in the pathogenesis of atherosclerotic cardiovascular disease. Although it can be measured directly in the laboratory, laboratories usually calculate LDL cholesterol using the Friedewald formula (FF) in persons whose plasma triglyceride concentrations are below 4.52 mmol/L.¹ The FF obviates the need for the time-consuming, laborious and expensive preparative ultracentrifugation previously required for the determination of LDL cholesterol.² Furthermore, the ease of using the formula, its cost effectiveness, convenience and relatively good accuracy in most clinical scenarios led to its global adoption and continued wide usage in most routine laboratories over the last 50 years.³ The availability of direct assays for LDL cholesterol in the late 1990s had minimal impact on this practice, as their introduction to laboratory operations meant an additional testing step and, consequently, increased costs. These direct assays also demonstrated susceptibility to significant interferences from hypertriglyceridaemia.^4,5

There are, however, challenges with the use of the FF. Firstly, its inability to accurately estimate LDL cholesterol when the triglycerides are ≥ 4.52 mmol/L means that the laboratory needs to have an alternative means of determining and reporting LDL cholesterol in such scenarios. It has also been shown that the assumption in the formula of a fixed ratio of triglyceride levels to very low-density lipoprotein (VLDL) cholesterol of 5:1, when triglycerides are < 4.52 mmol/L, is physiologically inaccurate. According to the Lipid Research Clinics Prevalence Study, this ratio may actually vary between 5 and 9.⁶ A further implication of the above is that the FF may not be suitable when chylomicrons are present in the circulation. This may be particularly problematic with the increasing adoption of non-fasting specimens for initial lipid testing.^7,8 The FF is also unsuitable for use in persons with dysbetalipoproteinaemia (type III hyperlipoproteinaemia).²

In response to these limitations, several alternative equations have been developed. Of these, the Martin-Hopkins (MH) equation⁹ and the Sampson-National Institutes of Health (NIH) equation¹⁰ are the most recent and pre-eminent. Unlike the FF, these two equations do not use a fixed factor for the triglycerides:VLDL cholesterol ratio. The original MH equation, published in 2013,⁹ determines the factor based on the ratio of triglyceride to non-high-density lipoprotein (HDL) cholesterol, and could be used with triglycerides levels up to 4.51 mmol/L. An updated version of the MH equation, which is able to report LDL cholesterol up to a triglycerides of 9.04 mmol/L, was subsequently released in 2021.¹¹ The Sampson-NIH equation, released in 2020, also determines VLDL cholesterol from the triglycerides and non-HDL cholesterol, and has been reported to be accurate even with triglycerides up to 9.04 mmol/L.¹⁰ The reliability and accuracy of these equations is also contributed to by the fact that their derivation involved the use of much larger sample sizes and study populations that were more diverse with regard to health status and LDL cholesterol concentrations compared to those used for the FF.^1,9,10

The majority of the laboratories in Nigeria continue to use the FF for the calculation of LDL cholesterol. For samples with a triglycerides value exceeding 4.51 mmol/L, either direct LDL cholesterol assays are employed, or no value is reported for LDL cholesterol and a comment is entered into the report. Adoption of either of these two formulae (MH or Sampson-NIH) would mean that the laboratory would be able to report LDL cholesterol for a larger percentage of its clients without additional cost. This study compared LDL cholesterol results obtained with the MH and Sampson-NIH equations against that of the FF. It examined any clinically significant differences in the results obtained with the three equations from lipid profile values from a Nigerian population. Furthermore, for samples with a triglycerides value exceeding 4.51 mmol/L, an assessment of the comparability of the results obtained with the MH and Sampson-NIH equations in this population was also performed.

The findings in this study indicate that about 95.4% of the LDL cholesterol estimates by FF were within 0.26 mmol/L of those by the MH equation, and 99.4% for the Sampson-NIH equation. This represents a less than 15% difference for an LDL cholesterol concentration of 1.81 mmol/L. Furthermore, the recently updated set of quality requirements for acceptable performance in proficiency testing programmes released by the Clinical Laboratory Improvements Act has a target value + 20% for LDL cholesterol.¹² Finally, estimates of the reference change value for LDL cholesterol, derived from biological variation data have been reported to be as high as 19%.¹³ The above suggests that, for the vast majority of LDL cholesterol estimates by the FF, the difference from the estimates by the newer equations may not have been clinically significant. This agrees with the observation of Wang et al. among a large US cohort.¹⁴ These would suggest that the Friedewald-calculated LDL cholesterol provides a reasonable estimation of LDL cholesterol and could guide treatment decisions for most patients, in addition to providing support for the recommendations of current guidelines on the continued use of this formula.

Our data revealed that, as triglycerides levels increased, the percentage difference between LDL cholesterol values calculated by FF and that calculated by MH increased. A similar pattern was observed between values calculated by FF and by Sampson NIH. This is probably because of the metabolism of VLDL, the main contributor to fasting plasma triglycerides, and the structure of the different formulae. As plasma triglycerides increase, there is a change in the relative concentrations of the two VLDL particle types. The proportion of large VLDL1 particles, which contain about 70% triglycerides, significantly outstrip that of the smaller VLDL2 particles, which consist of about 30% triglycerides. This difference in their relative concentrations widens with increasing triglycerides concentrations.¹⁵ Consequent to this, the FF, which has a fixed triglycerides:cholesterol ratio, will increasingly underestimate the concentration LDL cholesterol compared to the MH and Sampson-NIH, which adjust their estimate of VLDL cholesterol based on triglycerides concentrations. This triglycerides-influenced gradient in the difference between these equations has also been reported by others.^16,17 Hypertriglyceridaemia of at least 1.68 mmol/L was present in over 1 in 10 of the profiles retrieved for this study.

In the context of primary prevention of atherosclerotic cardiovascular disease, hypertriglyceridaemia-related underestimation of LDL cholesterol could impact clinical decision-making. LDL cholesterol levels define the clinical category that is used to identify persons for whom statin therapy should be initiated, as well as those who are achieving the goal of therapy.¹⁸ From our data, about 50% of LDL cholesterol categorisation by FF as < 1.81 mmol/L, with triglycerides > 1.69 mmol/L, were classified in the > 1.81 mmol/L category by the MH equation. The implication of this is that persons either requiring the initiation or an intensification of therapy may not be offered the same. These findings are very similar to several other reports and indicate a major limitation to the continued and unqualified use of the FF for primary prevention of atherosclerotic cardiovascular disease.^19,20,21 Recognising this limitation of the FF, guidelines on the management of blood cholesterol for the primary prevention of atherosclerotic cardiovascular disease recommend the measurement of direct LDL cholesterol or the use of another equation, such as the MH or NIH, to improve accuracy of risk assessment when LDL cholesterol is less than 1.81 mmol/L.^1,22 Although present to a lesser degree, significant and clinically consequential underestimation of LDL cholesterol was also observed at higher LDL cholesterol concentrations and with the NIH equation.

For the clinical laboratory seeking to improve its support for atherosclerotic cardiovascular disease primary prevention efforts and to replace the FF formula, there are items to consider. Firstly, the laboratory must decide which of the several available formulae is to be adopted. A key consideration for this decision should be scientific evidence of superior analytical accuracy in determining the concentration of LDL cholesterol as compared to the gold standard method of beta quantification. With regard to the two pre-eminent equations used in this study, there are claims and counterclaims of superior accuracy. Concerns have been raised over accuracy of the variant of the gold standard technique used, the population used for the development of the formulae, as well as the basis and reliability of the factor used in estimating the cholesterol content of VLDL.^23,24 For primary prevention efforts, what may be of more importance is the classification of individuals into the appropriate LDL cholesterol treatment category, especially in the above discussed context when there is hypertriglyceridaemia. From our data, although the level of agreement between the two equations with each other in this scenario was better than with the Friedewald equation, there were still significant differences, especially when LDL cholesterol was < 1.81 mmol/L. Very similar to our findings, Sajja et al.,²⁵ following their review of the electronic health record data from patients with atherosclerotic cardiovascular disease, reported clinically significant discordance in a pairwise comparison of the Sampson-NIH equation and the MH equation of about 23% at LDL cholesterol values of ≥ 1.81 mmol/L. At triglycerides > 4.52 mmol/L, our data indicate only fair agreement between the two equations. These suggest that the LDL cholesterol estimates from these two equations are not interchangeable. Based on these, it has been suggested that laboratories should indicate on their report which equation they are using to calculate their LDL cholesterol estimates or, if feasible, report the estimates of multiple equations.²⁶

Another major consideration for the laboratory seeking to replace the FF is the ease of implementing the new formula. The FF is a simple arithmetic formula that requires little expertise to incorporate into a laboratory information system software. The Sampson-NIH equation is a more mathematical bivariate quadratic equation developed by multiple least squares regression. The actual equation may require marginally higher expertise than the FF, but should still be easily implementable.¹⁰ The MH equation is more complex than the above two. It is similar to the FF, but uses an adjustable factor to divide the triglycerides instead of the fixed 5. It is rendered as LDL cholesterol = total cholesterol – HDL cholesterol – (triglycerides/adjustable factor). The adjustable factor is sourced from a 240-cell stratification of triglycerides and non-HDL cholesterol. Implementation of this formula would require some coding.⁹ In essence, implementation of the Sampson-NIH equation might be easier for the majority of laboratories.