The Sampson-NIH Equation Is the Preferred Calculation Method for LDL-C

The development of the Martin-Hopkins equation in 2013 (1) was the first major advance in estimating low-density lipoprotein cholesterol (LDL-C) since the Friedewald equation in 1972. We disagree, however, with our colleagues that it is presently the best way to calculate LDL-C. Differences in very low-density lipoprotein cholesterol (VLDL-C) account for the major differences between LDL-C equations. To illustrate this point, the triglyceride (TG)/VLDL-C ratios predicted by the 3 most used equations are plotted in Fig. 1A against TG. In the Friedewald equation, this ratio is fixed at 5; thus, VLDL-C is calculated as simply TG/5. This works well for most samples, but this divisor is too low for hypertriglyceridemia, leading to a positive bias for VLDL-C and a corresponding underestimation of LDL-C. Comparison of LDL-C equations. Panel A shows the factor values used for estimating VLDL-C for samples with a nonHDL-C level of 150 mg/dL (total cholesterol = 195 mg/dL [5.04 mmol/L] and HDL-C = 45 mg/dL [1.16 mmol/L]) at various TG levels. For the Friedewald equation (red), a constant factor of 5 is used for all samples, resulting in a horizontal line. For the Martin-Hopkins equation (purple), the factor varies by TG intervals, which leads to its stairstep appearance. For the Sampson-NIH equation (green), its effective factor values were mathematically derived by setting the Sampson-NIH equation equal to the Friedewald equation and then algebraically solving for its effective factor values. In panel B, the 3 equations are used to calculate VLDL-C for patients with a nonHDL-C of 150 mg/dL (3.87 mmol/L) at different TG levels. In panel C, VLDL-C was calculated at various nonHDL-C and TG values for the different factor cells used by the extended Martin-Hopkins equation (left side) or the Sampson-NIH equation (right side). VLDL-C values are indicated by the color code with green indicating low values, white—intermediate values, and purple—high values. The thin black grid lines in the left panel indicate the factor table cells in the Martin-Hopkins equation. Panels D-G show regression error characteristic curves for LDL-C equations using β-quantification as the reference method for all data (panel D), LDL-C ≤ 70 mg/dL (1.81 mmol/L) (panel E), TG ≥ 175 mg/dL (1.97 mmol/L) (panel F), or for TG ≥ 400 mg/dL (4.52 mmol/L) (panel G). Area under the curve (AUC) is calculated for each equation to provide a single integrated measure of test accuracy. The Martin-Hopkins equation differs from the Friedewald equation in that VLDL-C is calculated using a variable set of TG divisors (180 factors) based on TG and non-high-density lipoprotein cholesterol (nonHDL-C) intervals (1), determined empirically by the vertical autoprofile (VAP) ultracentrifuge method (2). Because the TG/VLDL-C ratio for TG-rich lipoproteins (TRL) is continuous, the quantile nature of the Martin-Hopkins factors (Fig. 1A) leads to either an underestimation or overestimation of VLDL-C at the ends of each factor interval. This creates discontinuities in calculated VLDL-C, particularly at high TG levels, which have larger factor intervals (Fig. 1B). The extended Martin-Hopkins equation uses many more factors for TG >400 mg/dL (4.52 mmol/L) but still does not show a smooth VLDL-C transition throughout the range of TG and nonHDL-C (Fig. 1C). The VLDL-C discontinuous jumps that can drop by 10 mg/dL (0.26 mmol/L) or more as TG increases are likely due to random errors in the factor interval assignments from small sample sizes. The Sampson-NIH equation is a continuous bivariate (nonHDL-C and TG) quadratic equation that was first described in 2020 (3) and overcomes the inherent limitations of the discrete factor approach. It produces a smooth factor line between those produced by the Friedewald and Martin-Hopkins equations (Fig. 1A). The use of a fit equation ensures that estimated LDL-C always changes in a continuous and predictable manner. It also has a practical advantage in simplifying laboratory information system implementation. Most importantly, it was established by fitting to LDL-C values determined by the “gold-standard” β-quantification reference method. The VAP method upon which the Martin-Hopkins equation is based uses proprietary hardware available in only a single testing facility. Unlike β-quantification, which uses a swinging-bucket rotor, the centrifuge tubes always remain in a vertical orientation for VAP (2), which reduces the time needed for centrifugation. It causes, however, the adherence of TRLs (including VLDL) to the sides of the tubes, leading to their poor recovery in hypertriglyceridemic samples, which was acknowledged by the inventors of the method as its “major drawback” (2). In the papers cited by our colleagues about the rigorous validation of VAP against β-quantification, we could not find sufficient documentation on this important issue. Only data from a single, small (n = 40) study is described, and no information is provided on the type of samples tested. Furthermore, only precision data and the correlation coefficient are provided and none of the other standard measures of regression analysis, such as slope and intercept, which are necessary to determine if there is a systematic difference between the 2 methods. In the only published study that we are aware of on this issue, an external laboratory found for hypertriglyceridemic samples that VAP underestimated VLDL-C by as much as 40% compared to β-quantification (4). This is consistent with our own findings when we compared the original and extended Martin-Hopkins equations to β-quantification (5). In our view, the accuracy of any LDL-C equation can only be definitively established by comparison against the β-quantification reference method, which has long been used throughout the world for standardizing LDL-C assays. The main comparator assay in most of the studies cited by our colleagues in their table supporting the purported superior accuracy of the Martin-Hopkins equation was a direct LDL-C assay or the VAP method itself. As many Clinical Chemistry readers are already aware, direct LDL-C methods vary by as much as 30% between platforms and some like the Martin-Hopkins equation show a positive bias on hypertriglyceridemic samples (6). Besides the studies cited in the table, there are several other reports on how the Sampson-NIH equation is either superior or at least equivalent to the Martin-Hopkins equation when compared against some direct LDL-C methods. These seemingly contradictory results may be explained by the 2 equations yielding similar values for most samples. It has also been found that the accuracy of the different equations may depend on the manufacturer of the lipid tests used as inputs to the equations (7). The only cited study showing an advantage of the Martin-Hopkins equation when compared to β-quantification was a small study (n = 364) of a cholesterol ester transfer protein-inhibitor, a non-FDA approved drug that changes the TG/cholesterol ratio on lipoproteins and could, therefore, differentially affect the performance of the equations. A much larger Protein Convertase Subtilisin/Kexin Type 9 (PCSK9) inhibitor (alirocumab) trial (n = 17 077) not cited in the table reported that the Sampson-NIH equation was better than the Friedewald and the Martin-Hopkins equations in matching β-quantification when TG > 150 mg/dL (1.69 mmol/L) (8). A group at the University of Toronto confirmed by β-quantification the improved accuracy of the Sampson-NIH equation over the Friedewald equation (Martin-Hopkins equation not tested) (9), which led, in part, to a recent recommendation by the Canadian Society of Clinical Chemists to propose it as the preferred calculation method (10). Our colleagues have questioned the older β-quantification database we used to establish our equation because it contained a limited number of low LDL-C patients. In our original study (3), however, the accuracy of our equation was validated using 2 different contemporary β-quantification databases with much larger numbers of low LDL-C patients. There have also been differences in our statistical approaches. In our analysis for test misclassifications into different LDL-C treatment intervals, we first classified patients based on β-quantification and then by the different equations. Our colleagues typically do the reverse. In our approach, we were essentially testing sensitivity, whereas they were testing positive predictive value. When using a test as a binary classifier one needs, of course, to assess both sensitivity and specificity (or positive and negative predictive value) simultaneously to account for both false positives and false negatives. We found that the mean of sensitivity and specificity and the Matthew correlation coefficient, another way to combine sensitivity and specificity, were higher for the Sampson-NIH equation than other equations in classifying patients into a broad range of different LDL-C intervals (5). We also modified the Clarke error grid for LDL-C and found that the Sampson-NIH equation for hypertriglyceridemic samples had the least analytical and clinically relevant misclassification errors at high and low LDL-C values (5). We also used what is, to our knowledge, the largest reported β-quantification dataset (n = 40 144) and applied regression error characteristic curve analysis to test the accuracy of the different equations (Fig. 1D-G). When all the data were considered, the Sampson-NIH equation showed only a small improvement over the other equations, but its superiority was readily apparent when just low LDL-C or hypertriglyceridemic samples were analyzed. We recently reported on a new equation that is even more accurate than our original equation called the enhanced Sampson-NIH equation, which includes apolipoprotein B (apoB) as an independent variable (11). It can also be used for diagnosing type III dysbetalipoproteinemia (12). In a large dyslipidemic population, approximately one third of all patients identified as having LDL-C < 70 mg/dL (1.81 mmol/L) by the Friedewald equation were correctly reclassified into a higher LDL-C category using this new equation. Although apoB testing is required, its use could facilitate reimbursement decisions by insurance companies that typically deny coverage for expensive PCSK9 inhibitors when LDL-C < 70 mg/dL (1.81 mmol/L). In the ODYSSEY OUTCOMES trial, treatment with a PCSK9 inhibitor to apoB target goals was even more effective than treating to LDL-C goals (13). Many studies have also shown that when apoB and LDL-C (or nonHDL-C) are discordant, cardiovascular outcomes more closely follow apoB (14). Thus, greater use of apoB is already warranted and eventually LDL-C may be replaced with apoB. Another emerging risk marker is small-dense LDL-C, which tends to increase with higher TG unlike total LDL-C. A direct test for small-dense LDL-C has been approved by the FDA and was shown in several studies to be better than measured or calculated LDL-C as a risk marker. We have described an equation for estimating small-dense LDL-C (15), which uses the same lipid parameters as the standard LDL-C equations, but it was a better predictor of future cardiovascular events than any of the total LDL-C equations. In summary, the Sampson-NIH and Martin-Hopkins equations yield similar results for most patients, but the fact that the Sampson-NIH equation is based on the reference method and has accuracy advantages for low LDL-C and hypertriglyceridemic samples provides, in our view, strong justification for its preferential use. Unfortunately, most clinical laboratories are still using the outmoded Friedewald equation, so there is a clear need for better education in this area. Explicit recommendations in national/international guidelines to discontinue use of this calculation method are certainly warranted. We note, however, that LDL-C as estimated by any equation will likely ultimately give way to the use of better cardiovascular biomarkers for refining therapeutic decision-making. LDL-C, low-density lipoprotein cholesterol; VLDL-C, very low-density lipoprotein cholesterol; TG, triglyceride; nonHDL-C, non-high-density lipoprotein cholesterol; VAP, vertical autoprofile; apoB, apolipoprotein B. 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. Alan Remaley (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Funding acquisition-Equal, Investigation-Equal, Methodology-Equal, Supervision-Equal, Writing—original draft-Equal, Writing—review & editing-Equal), Maureen Sampson (Conceptualization-Supporting, Formal analysis-Lead, Investigation-Equal, Writing—review & editing-Supporting), Anna Wolska (Conceptualization-Supporting, Data curation-Supporting, Writing—original draft-Supporting, Writing—review & editing-Supporting), Jeffrey Meeusen (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Writing—original draft-Supporting, Writing—review & editing-Supporting), and James Otvos (Conceptualization-Supporting, Data curation-Supporting, Formal analysis-Supporting, Writing—original draft-Supporting, Writing—review & editing-Equal). Upon manuscript submission, all authors completed the author disclosure form. Research was supported by the Intramural Research Program of the NHLBI at the National Institutes of Health. A.T. Remaley has CRADA research grants with AstraZeneca and Nissui. J. Otvos, consulting fees from Labcorp.