Search for Relevant Studies

The literature published through September 2021 was reviewed by searching PubMed and Web of Science. The following search strategy was developed with the input of a Johns Hopkins Welch Medical Library informationist: (measur*[ti] OR calculat*[ti] OR equation OR formula) AND (low density lipoprotein cholesterol OR LDL-C) in both databases. The initial search yielded 15,477 articles (Supplemental Figure 1), published from 1972 through 2021. Articles were evaluated for their report of new LDL-C equations. The reference lists of the final 23 articles were searched, and no additional LDL-C equations were identified.

Study Population

This study used data from the second harvest of the Very Large Database of Lipids (VLDbL), registered at http://www.clinicaltrials.gov (NCT01698489). The design of the VLDbL has been described in detail previously [19]. Patient samples were acquired by the VAP Diagnostics Laboratory from October 1, 2015 through June 30, 2019 in the United States. The study included both sexes, as well as children (aged <11 years), adolescents (aged 11 to <18 years), and adults (aged ≥18 years). Patient samples largely originated from primary care clinics (85%), with the remainder from inpatient settings and specialty centers. The lipid distributions in the VLDbL have been shown to reflect those in the population-representative National Health and Nutrition Examination Survey [19]. We excluded samples with missing total cholesterol (TC), high density low-density cholesterol (HDL-C), TG, and LDL-C. We included all samples regardless of their fasting status. The Johns Hopkins Institutional Review Board declared our study exempt.

Lipid Measurements

The VLDbL includes direct measurements of TC, LDL-C, very low-density lipoprotein cholesterol (VLDL-C), HDL-C, and other lipoprotein parameters. Measurements were performed by VAP to separate lipoprotein classes by density into all five classes (HDL, LDL-Real [LDL-R; the LDL without Lp(a) and IDL], VLDL, IDL, and Lp(a)) and then measure the cholesterol component via enzymatic analysis and spectrophotometric absorbance. The accuracy of VAP was validated by annual yearly random split-sample comparisons with preparative ultracentrifugation or BQ at the Washington University in St. Louis Core Laboratory for Clinical Studies (r = 0.986, r = 0.969, respectively; bias 0.6%, 1.7%, respectively). Correlation coefficients from an analysis using 40 split serum specimens comparing VAP to BQ were: 0.99 for total cholesterol, 0.99 for HDL-C, 0.98 for LDL-C, and 0.98 for VLDL-C [20]. TG levels were directly measured with the Architect C-8000 system (Abbott Laboratories, IL), which were compared with samples from the University of Alabama School of Medicine for quality assessment.

Equations for Estimating LDL-C

A total of 23 equations for estimating LDL-C are summarized in Supplemental Table 1. One class of LDL-C equations uses a fixed TG:VLDL-C ratio to estimate VLDL-C and extract estimated VLDL-C from non-HDL-C to estimate the LDL-C levels (Friedewald et al. [9], Puavilai et al. [21], Vujovic et al. [22], DeLong et al. [23], Ephraim et al. [24], Ghasemi et al. [25], Bauer et al. [26]). Another class of the equations uses TC, HDL-C, and TG levels as coefficients of linear models to estimate LDL-C (Hattori et al. [27], Anandaraja et al. [28], Chen et al. [29], Cordova et al. [30], Teerakanchana et al. [31], Ahmadi et al. [32], Rao et al. [33], Dansethakul et al. [34], Rasouli et al. [35], Lee & Hu [36], Choi et al. [37], Orejon et al. [38], and Molavi et al. [39]). Other equations use an adjustable factor for TG:VLDL-C ratio based on a lookup table (Martin et al. [40]) or interaction/quadratic terms (Sampson et al. [41], Saiedullah et al. [42]) to account for non-linearity. Furthermore, we used the extended Martin/Hopkins equation [43] for LDL-C estimation at high TG levels (400–799 mg/dL).

Statistical Analysis

We assessed the accuracy of the 23 equations for estimating LDL-C using VAP ultracentrifugation as the reference. Firstly, we compared the concordance in classification according to clinical guideline-based categories (<40, 40–54, 55–69, 70–99, 100–129, 130–159, 160–189, and ≥190 mg/dL) in patients with TG levels up to 399 mg/dL. Concordance was defined as the proportion of ultracentrifugation-measured LDL-C levels falling in the same category as estimated LDL-C. Secondly, we compared the magnitude of error of each equation compared to ultracentrifugation using median differences.

We separated the equations based on whether they performed better than Friedewald (Figure 1). We then conducted secondary analyses for the top equations as well as the Friedewald equation with ultracentrifugation as reference. We first compared the concordance of each equation in patients with TG levels of 150–399 mg/dL and 400–799 mg/dL. We further evaluated LDL-C equations stratified by age (<18, 18–59, ≥60), sex, and fasting status. We also performed analyses stratified by ASCVD (ICD-9 code 410.XX, 414.0X, 411.1, 433.XX, 434.XX, 435.9, 440.2X, 443.9) and hypertension (ICD-9 code 401.XX), and in patients with available laboratory data, we performed analyses stratified by kidney disease (eGFR <60 mL/min/1.73 m²), diabetes (ICD-9 250.XX, A1c >6.5%, or fasting glucose ≥126 mg/dL), inflammation (high-sensitivity C-reactive protein ≥ 2 mg/L), and thyroid dysfunction (TSH <0.5 or >4.5 uIU/mL). Finally, we evaluated the percentage of patients with Friedewald LDL-C <70 mg/dL correctly reclassified (confirmed by ultracentrifugation) to LDL-C >70 mg/dL using the other top performing equations.

All statistical analyses were performed in Stata (StataCorp), version 15.1. Graphs were plotted using R (R Core Team) version 4.0.3.

Characteristics of the Study Population

A total of 5,051,467 patients were analyzed with 4,939,528 patients included in the primary analyses of patients with TG levels up to 399 mg/dL. The mean (SD) age was 56±16 years and 53.3% of patients were women. The median directly measured LDL-C was 114 (IQR: 90–141) mg/dL and the median TG level was 116 (IQR: 82–169) mg/dL. Considering fasting status, 11.9% of patients were non-fasting, 19.4% were fasting, and we did not have data on fasting status for 68.7% of patients (Table 1). For patient subgroups, 32,223 had ASCVD, 274,286 had hypertension, 361,079 had kidney disease, 212,671 had diabetes, 417,561 had inflammation, 39,515 had TSH <0.5 uIU/mL and 27,350 had TSH ≥4.5 uIU/mL.

Concordance According to Clinical LDL-C Classification Guidelines

Among the LDL-C estimation methods, the Martin/Hopkins algorithm most accurately classified LDL-C to the correct clinical category (89.6%), followed by the Sampson (86.3%), Chen (84.4%), Puavilai (84.1%), Delong (83.3%), and Friedewald (83.2%) equations (Table 2). The other 17 equations were less accurate than Friedewald, with accuracy as low as 35.1%.

Magnitude of Patient-Level Error

The median error of equations ranged from –10.8 to 18.7 mg/dL, and was best optimized using the Martin/Hopkins equation (0.3, IQR–1.6 to 2.4 mg/dL) (Table 3). In comparison, other equations that demonstrated higher overall accuracy compared to Friedewald had median differences of 1.7 mg/dL (Sampson), 3.3 mg/dL (Puavilai), 4.1 mg/dL (Delong), and –2.9 mg/dL (Chen). In patients with TG levels <400 mg/dL, 68.6% of patients had less than 5 mg/dL error using Friedewald compared to 70.8% and 82.8% using Sampson and Martin/Hopkins, respectively.

Accuracy of Top Performing Equations at High Triglyceride Levels

In patients with TG levels 150–399 mg/dL, the Martin/Hopkins continued to be the best performing equation with accuracy of 83.5%, followed by Chen (81.3%), DeLong (80.0%), Puavilai (79.4%), Sampson (79.3%), and Friedewald (67.8%) (Supplemental Table 2). In patients with TG levels 400–799 mg/dL (n = 111,939), the extended Martin/Hopkins [43] had the highest accuracy (60.3%), followed by Martin/Hopkins (59.2%) and Chen (57.7%) (Supplemental Table 3). Some equations that demonstrated greater accuracy in patients with TG levels <400 mg/dL performed poorly in patients with hypertriglyceridemia. DeLong had a concordance of 42.2% and Sampson had a concordance of 37.3%.

Accuracy of Top Performing Equations in Patient Subgroups

The Martin/Hopkins equation was consistently the highest performing equation after stratifying by age, sex, and fasting status. The same pattern was observed when stratifying by ASCVD, hypertension, kidney disease, diabetes, inflammation, and thyroid dysfunction (Supplemental Table 4).

Percentage of Patients with Friedewald LDL-C <70 mg/dL Reclassified to LDL-C >70 mg/dL Using the Top Performing Equations

In patients with Friedewald LDL-C <70 mg/dL and TG levels <400 mg/dL, 19.8% were correctly reclassified to LDL-C >70 mg/dL using Martin/Hopkins, 17.6% using Chen, 17.4% using DeLong, 15.4% using Puavilai, and 13.9% using Sampson (Figure 2). In patients with Friedewald LDL-C <70 mg/dL and TG levels 150–399 mg/dL, a considerably greater percentage of patients were correctly reclassified to LDL-C >70 mg/dL, with the Martin/Hopkins having the highest reclassification percentage of 45.6%.

Approaches to LDL-C Determination

LDL-C is defined as TC – HDL-C – VLDL-C according to the landmark Friedewald equation [9] and the Centers for Disease and Prevention (CDC) definition of LDL-C. The two variables that are directly measured are TC and HDL-C, whereas VLDL-C is estimated. The Friedewald equation estimates VLDL-C using a fixed factor, thus assuming a consistent relationship between VLDL-C and TG levels. Some equations retain the basic backbone of Friedewald, which translates into a permutation of equations that substitute the factor 5 in mg/dL units with other predetermined ratios. For example, DeLong et al. proposed dividing TG levels by 6 [23] while Chen et al. in 2010 suggested that LDL-C = TC × 0.9 – HDL- C × 0.9 – TG × 0.1 [29]. These approaches do not account for heterogeneity in TG:VLDL-C ratios, which limits the capacity for substantial accuracy enhancement.

Other equations have deviated from the structure of the Friedewald equation.De Cordova et al. proposed that LDL-C = 3/4 (TC – HDL-C), which eliminated TG levels as an input variable and VLDL-C estimation [29, 30]. Some equations, such as Anandaraja and Lee & Hu, do not include HDL-C as a component in their equations [28, 36]. These equations seek to estimate LDL-C directly, which is unlike the focus of Friedewald on estimating VLDL-C to determine LDL-C. Friedewald LDL-C has guided key clinical trials that have shaped treatment recommendations for ASCVD patients [44]. Therefore, direct LDL-C estimation, which drifts away from the standard set by Friedewald, is inconsistent with our clinical standard for LDL-C.

In our analysis, all the equations that estimated LDL-C directly, except Sampson, performed poorly compared to Friedewald. Sampson used a bivariate equation, which included all the input variables used in Friedewald, unlike other equations that dropped key components of the original formula. Although Sampson demonstrated better accuracy than Friedewald, its deviation from the structure of Friedewald still poses the risk of a fundamental discrepancy—the definition of LDL-C used in treatment guidelines would not align with the one used in LDL-C calculation under Sampson. Furthermore, a subset of the equations assumed a non-zero baseline value by adding a y-intercept in their calculation of LDL-C from TC [28, 31, 32, 34, 38, 42]. Such an approach implies that patients present with a standard pre-existing level of cholesterol, an assumption that may not have merit.

Of the 23 equations, the Martin/Hopkins demonstrated the highest accuracy across strata by age, sex, fasting status, and triglyceride levels, as well as in patients with atherosclerotic cardiovascular disease, hypertension, diabetes, kidney disease, inflammation, and thyroid dysfunction. The Martin/Hopkins equation has been validated extensively on a global scale [11, 16, 45, 46, 47]. Martin/Hopkins is the only formula to preserve the structure of Friedewald while leveraging an adjustable factor that improves VLDL-C estimation, catalyzing a more personalized risk assessment [40]. It thus maintains the same LDL-C definition that guided treatment trials, which offers internal consistency in treatment recommendations and calculation methods. The Martin-Hopkins equation was further validated across a wide spectrum of LDL-C levels, including LDL-C <70 mg/dL, using BQ in large-scale studies [10, 48]. Given the development of the Martin-Hopkins equation based on VAP, these studies provide further validation of the VAP method.

The adjustable factor in the Martin/Hopkins, which can range from 3.1 to 9.5 in patients with TG levels <400 mg/dL, was derived from an analysis of TG-to-VLDL-C ratios in more than 1.3 million people, as opposed to the Friedewald equation which was derived in a sample of 448 patients [9, 40]. Other independent, multi-national groups have reported that the Martin/Hopkins equation was more accurate than Friedewald in racially diverse populations [11, 45, 49] as well as for LDL-C values <70 mg/dL [11, 47], and in patients taking proprotein convertase subtilisin/kexin (PCSK9) inhibitors [10], patients with diabetes [50], and patients with familial combined hyperlipidemia [51].

Various large laboratories have adopted the Martin/Hopkins equation, and the AHA/ACC/Multi-society Cholesterol Guideline provided a Class IIa recommendation for using the equation in patients with LDL-C <70 mg/dL [12]. The Martin/Hopkins equation has been supported by the National Lipid Association (NLA) [52], a consensus recommendation in Brazil [53], a joint consensus panel of the European Atherosclerosis Society (EAS), and the European Federation of Clinical Chemistry and Laboratory Medicine (EFLM) [54]. It was also supported by the World Heart Federation Cholesterol Roadmap in 2022 [55]. It can be installed on lab information systems in a straightforward manner using line-by-line code for automatic calculation of LDL-C. There are no intellectual property restrictions. Laboratories can contact JHTT-Communications@jh.edu for assistance in implementation.

LDL-C Risk Reclassification at Low LDL-C Levels

We found that if a clinical laboratory were to switch from Friedewald to Martin-Hopkins, almost half of the patients with Friedewald LDL-C <70 mg/dL and TG levels 150–399 mg/dL would be correctly reclassified to LDL-C >70 mg/dL using Martin/Hopkins. Doing so would facilitate opportunities to further optimize LDL-C and ASCVD risk. Our results are consistent with prior studies reporting LDL-C underestimation using Friedewald estimation [10, 47, 56].

LDL-C Estimation in Hypertriglyceridemia

In patients with TG levels up to 799 mg/dL, the extended Martin/Hopkins performance was the most accurate. However, at such elevated TG levels, the clinical priority is to immediately reduce TG levels to prevent pancreatitis. Our results align with a previous study demonstrating that while the extended Martin/Hopkins is the most accurate of our LDL-C estimation tools at high TG levels, caution with LDL-C estimation in this elevated TG range should still be taken [43].

Limitations

This study has some limitations. Data on race and ethnicity or other clinical factors such as body mass index were not available for analysis due to using a clinical laboratory dataset. Our data also comes entirely from a US population. However, multiple national and international studies, including the ELSA Brazil study and a clinical trial conducted in 49 countries, reported results consistent with ours, which serves as an external validation of our findings [10, 47, 57]. Furthermore, we did not have patient treatment data. Accuracy of LDL-C estimation is important, nonetheless, both pre-treatment and on-treatment. A PCSK9 inhibitor trial and a CETP inhibitor trial showed better accuracy with Martin/Hopkins compared to Friedewald estimation [10, 47].

Some studies suggested that LDL-C levels may vary by patients’ clinical characteristics [58, 59, 60]. We were able to use common biomarkers, such as HbA1c, hsCRP, TSH, and eGFR, as well as ICD codes to assess equation accuracy in subgroup analyses. We found consistent results across these groups. Finally, we used the VAP method as opposed to BQ to directly measure LDL-C. As noted above, studies have demonstrated excellent agreement between the two methods, which are both based on ultracentrifugation. Limited, inconclusive data has raised concern regarding the VAP method and its tendency to underestimate VLDL-C in samples with high TG due to adherence of TG-rich lipoproteins to the walls of test tubes [41, 61, 62]. However, this concern applies to all forms of ultracentrifugation and is only relevant at TG levels beyond the range in our analysis.