Extensive Evidence Supports the Martin–Hopkins Equation as the LDL-C Calculation of Choice Free

This “Point” contends that now is the time for all laboratories to recognize the importance of more accurately reporting clinically valid lipid results, notably low-density lipoprotein cholesterol (LDL-C). In 2013, one of us (S.S.M.) and colleagues introduced a novel solution (1) that has been robustly validated in numerous studies across varying populations globally (2, 3). This “Point” describes the extensive body of work from research and clinical practice supporting the Martin–Hopkins/extended Martin–Hopkins equations that we hope you will soon adopt, if you have not done so already.

One of us (H.W.K.) once lived and worked in Framingham, a western suburb of Boston, Massachusetts, and collaborated with the Framingham Heart Study. Lipid testing was performed on a cohort of Framingham residents who participated in the longitudinal study, which was established in 1948. Beginning in the 1960s, landmark studies from the Framingham Heart Study led to a much deeper understanding and appreciation of the role of lipid testing to assess cardiovascular disease risk (4, 5). At that time, LDL-C testing was cumbersome and not developed for routine clinical laboratory use. Not until 1972 did William Friedewald, Robert Levy, and Donald Frederickson propose a simple equation to estimate LDL-C: LDL-C = total cholesterol—high-density lipoprotein (HDL) cholesterol—triglycerides (TG)/5 in mg/dL (2.2 in mmol/L). The Friedewald equation enabled routine LDL-C assessment based on an estimate (TG/5) of very low-density lipoprotein cholesterol (VLDL-C). That paper (6) became the most cited in the history of Clinical Chemistry.

For decades, clinical laboratories applied the Friedewald equation to estimate LDL-C. However, the Friedewald equation is prone to considerable underestimation when the TG level is elevated (≥150 mg/dL [1.69 mmol/L]) and LDL-C level is low (particularly <100 mg/dL [2.59 mmol/L]) (2, 3). Clinical laboratories generally adopted a TG upper limit of <400 mg/dL (4.52 mmol/L), as suggested in the original Friedewald et al. study, to report calculated LDL-C (6), while some suggested lower TG limits. Indeed, Friedewald et al. acknowledged that TG/5 failed to accurately estimate VLDL-C in any subgroup, although VLDL-C was a relatively small portion of the equation in the setting of typical LDL-C levels in the 1970s (6).

Accurate LDL-C assessment is challenging. The reference measurement procedure for LDL-C is preparative ultracentrifugation, also known as beta quantification. This method is restricted in clinical practice by high cost and arduous implementation. Alternatively, direct chemical LDL-C assays have gained acceptance in clinical practice, yet they are of variable accuracy and add costs (2, 3). Furthermore, the introduction of novel pharmacologic therapies has enabled patients to commonly achieve very low LDL-C levels that were rare in the early 1970s; when the Friedewald equation was introduced, only 35 of 448 Friedewald et al. participants had LDL-C <100 mg/dL [2.59 mmol/L] (6). The Fridewald equation has limitations under certain conditions, primarily when metabolic abnormalities alter the relationship between VLDL-C and TG, such as in patients with diabetes, kidney disease, and other common medical conditions.

To better serve patients in the contemporary treatment era, the Martin–Hopkins equations use an adjustable factor (strata-specific median VLDL-C:TG ratio), essentially moving from a one-size-fits-all to tailored LDL-C calculation (1–3, 7). For patients with TG levels <400 mg/dL (4.52 mmol/L), the original Martin–Hopkins equation defined 174 adjustable factors based on a range of TG and non-HDL-C levels (1). The Martin–Hopkins equation was derived in the Very Large Database for Lipids, which included >1 million patients with population-representative lipid levels who had vertical autoprofile (VAP) ultracentrifugation measurement (validated against beta quantification by twice yearly split sample comparisons at Washington University) (1). Furthermore, for patients with TG levels of 400–799 mg/dL (4.52–9.02 mmol/L), an extended Martin–Hopkins equation defined an additional 240 strata-specific median TG:VLDL-C ratios based on TG and non-HDL-C categories (7). Importantly, performance of the Martin–Hopkins equations did not improve by smoothing the calculation using a greater number of strata or with a continuous equation.

Indeed, the Martin–Hopkins equations have performed superbly in external validation studies and in clinical practice over the past decade (1, 2). These equations have been studied in large (>5 million people) and wide-ranging patient populations that have included various fasting statuses, ages, racial and ethnic groups, and both sexes, as well as populations undergoing PCSK9 inhibitor treatment or those with familial hypercholesterolemia, other dyslipidemias, atherosclerotic cardiovascular disease (ASCVD), hypertension, diabetes, kidney disease, thyroid dysfunction, chronic inflammation, and diabetes mellitus, with and without lipid-lowering drugs, including statins. Of 23 LDL-C equations proposed in the literature, the Martin–Hopkins equation was the most accurate in a large-scale analysis (8) followed by the Sampson-NIH equation (correctly categorizing 90% and 86% of patients, respectively). Table 1 lists the highest quality of evidence since 2020, comparing the Martin–Hopkins equation with the Friedewald, Sampson-NIH, and other equations (7–18). Based on the extensive evidence of superior accuracy, the adoption of the Martin–Hopkins equation in clinical practice is supported by guidelines and expert recommendations around the world, including from AHA/ACC, the European Atherosclerosis Society and European Federation of Clinical Chemistry, National Lipid Association, World Heart Federation, Polish Lipid Association, and Multi-Society Recommendations of Brazil. The Martin–Hopkins equations have been successfully deployed at scale in laboratories globally.

Accurate LDL-C estimation at low LDL-C levels is paramount in current evidence-based hyperlipidemia treatment strategies to prevent ASCVD. The recommendation to treat to very low LDL-C levels (<70 mg/dL [1.81 mmol/L] or <55 mg/dL [1.4 mmol/L]) if at high or very high risk of ASCVD, along with the emergence of newer nonstatin therapies to help achieve these levels, highlight the clinical value provided by the Martin–Hopkins equation. In this setting, the Martin–Hopkins equation has consistently emerged as the LDL-C calculation of choice in high-quality randomized controlled trial data from patients treated with lipid-lowering therapy (e.g., FOURIER (19) and TULIP (10) trials with beta quantification comparators). The FOURIER trial included 56 624 observations in patients achieving low LDL-C with PCSK9 inhibition, finding that the Martin–Hopkins equation closely approximated beta quantification (19). Another large study of 146 106 patients with ASCVD, TG ≥150 mg/dL (1.69 mmol/L), and low LDL-C (<70 mg/dL [1.81 mmol/L]) found the Friedewald and Sampson-NIH equations consistently underestimated LDL-C relative to the Martin–Hopkins equation, and therefore could lead to false reassurance and inappropriate withholding of statin and/or nonstatin therapy, leaving patients at greater ASCVD risk (16).

Bias from the selected derivation population and methodological approach used in the development of the Sampson-NIH equation (20) raised early concerns that have been substantiated by subsequent studies showing suboptimal performance (Table 1). The Sampson-NIH equation uses least squares, nonlinear regression with purported clinical utility in patients with low LDL-C [<100 mg/dL (2.59 mmol/L)] and high TG [≥400 mg/dL (4.52 mmol/L)]. However, the initial analyses of low LDL-C were misleading due to the exclusion of patients with very low LDL-C and due to a statistical approach that suppressed the ability to detect underestimation of LDL-C. Regarding patients with high TG, the mean absolute LDL-C difference was notably large with the Sampson-NIH equation at 24.9 mg/dL (0.64 mmol/L) in the original publication (20); the extended Martin–Hopkins equation provided substantially better performance (7). In contrast to the large, contemporary population used to develop the Martin–Hopkins equations, the initial Sampson et al. study was performed in a niche and small (8656) National Institutes of Health patient population from the 1970s to the 1990s and, thus, is not reflective of the diverse patient population seen in modern clinical practice. The derivation and validation set used for the Sampson-NIH equation excluded specimens with very low LDL-C and was enriched with specimens with very high LDL-C and/or TG compared to the general population. These deficiencies in the Sampson-NIH equation’s development may explain why the Sampson-NIH equation is consistently less accurate than the Martin–Hopkins equation in head-to-head in clinical practice and research comparisons.

Several factors may be creating false barriers to implementation of the Martin–Hopkins equations. First, there has been misinformation about licensing (21). The Martin–Hopkins equations have no licensing requirement and are free of charge; no change is anticipated. The previously filed patent was abandoned by Johns Hopkins University to allow widespread use without intellectual property restrictions. Second, concern has been expressed for under-recovery of VLDL by VAP ultracentrifugation (21). Yet, Martin–Hopkins LDL-C agrees strongly with VAP ultracentrifugation measured LDL-C, with LDL separating in the middle of the centrifuge tube, well away from VLDL (22). This shows the lack of significance of this concern, as do the studies discussed previously in which Martin–Hopkins LDL-C values have shown high accuracy compared with beta quantification. Third, implementing the table-based approach to LDL-C calculation has been a perceived challenge. However, this table-based approach can be programmed in a straightforward manner to provide an automated calculation in laboratory information systems. Programmers we have encountered prefer table look-up compared to equations. The ease of implementation is demonstrated by the widespread use of the Martin–Hopkins equation in diverse laboratories throughout the world ranging from a full-scale implementation across a large commercial laboratory (Quest Diagnostics), across hospitals and health systems, and across nationalized health systems.

Variation in the reporting and estimation of LDL-C in contemporary practice can introduce unintended disparities in clinical care. In a meta-analysis including 49 trials of cardiovascular disease outcomes (23), the method of LDL-C estimation was unspecified in 32 studies and 11 others used the Friedewald equation. The remaining 6 studies used beta quantification, a direct enzymatic LDL-C assay, or a combination of the Friedewald with the Martin–Hopkins or Sampson-NIH equations. Patient care and clinical studies are best served when we converge on the optimal approach for LDL-C estimation.

Our “Point” is based on the overwhelming evidence available: to simplify, standardize, allow widespread implementation, and ensure the highest accuracy of LDL-C calculation, the original and extended Martin–Hopkins equations should be universally adopted in clinical and research practice as the LDL-C calculation of choice.

Nonstandard Abbreviations

LDL-C, low-density lipoprotein cholesterol; HDL-C, high-density lipoprotein cholesterol; TG, triglycerides; VLDL-C, very low-density lipoprotein cholesterol; VAP, vertical autoprofile; ASCVD, atherosclerotic cardiovascular disease.

Author Contributions

The corresponding author takes full responsibility that all authors on this publication have met the following required criteria of eligibility for authorship: (a) significant contributions to the conception and design, acquisition of data, or analysis and interpretation of data; (b) drafting or revising the article for intellectual content; (c) final approval of the published article; and (d) agreement to be accountable for all aspects of the article thus ensuring that questions related to the accuracy or integrity of any part of the article are appropriately investigated and resolved. Nobody who qualifies for authorship has been omitted from the list.

Jelani K. Grant (Conceptualization-Equal, Formal analysis-Equal, Writing—original draft-Lead), Harvey W. Kaufman (Conceptualization-Equal, Supervision-Equal, Writing—review & editing-Equal), and Seth S. Martin (Conceptualization-Equal, Supervision-Equal, Writing—review & editing-Equal).

Authors’ Disclosures or Potential Conflicts of Interest

Upon manuscript submission, all authors completed the author disclosure form.

Research Funding

None declared.

Disclosures

H.W. Kaufman, employed by and owns stock in Quest Diagnostics. S.S. Martin reports grant funding from the American Heart Association, PCORI, NIH, Google, and Merck, and receipt of equipment from Apple; consulting fees from Amgen, AstraZeneca, BMS, Chroma, Kaneka, New Amsterdam, Novartis, Novo Nordisk, and Sanofi; stock in Corrie Health.

Acknowledgments

The authors thank Dr. Roger Blumenthal for his insightful comments during the drafting of this manuscript.

References