Key PointsQuestion
Is it possible to provide a more accurate estimate of low-density lipoprotein cholesterol in patients with hypertriglyceridemia and/or a low level of low-density lipoprotein cholesterol?
Findings
In this decision analytical model, a new low-density lipoprotein cholesterol equation was derived that can be used to more accurately estimate the low-density lipoprotein cholesterol level in patients with plasma triglyceride levels up to 800 mg/dL and is at least equivalent or more accurate than other equations for patients with normolipidemia and a low level of low-density lipoprotein cholesterol.
Meaning
The new low-density lipoprotein cholesterol equation can be readily implemented by clinical laboratories without incurring any additional costs compared with a standard lipid panel and may improve the use of calculated low-density lipoprotein cholesterol in cardiovascular disease risk management.
Importance
Low-density lipoprotein cholesterol (LDL-C), a key cardiovascular disease marker, is often estimated by the Friedewald or Martin equation, but calculating LDL-C is less accurate in patients with a low LDL-C level or hypertriglyceridemia (triglyceride [TG] levels ≥400 mg/dL).
Objective
To design a more accurate LDL-C equation for patients with a low LDL-C level and/or hypertriglyceridemia.
Design, Setting, and Participants
Data on LDL-C levels and other lipid measures from 8656 patients seen at the National Institutes of Health Clinical Center between January 1, 1976, and June 2, 1999, were analyzed by the β-quantification reference method (18 715 LDL-C test results) and were randomly divided into equally sized training and validation data sets. Using TG and non–high-density lipoprotein cholesterol as independent variables, multiple least squares regression was used to develop an equation for very low-density lipoprotein cholesterol, which was then used in a second equation for LDL-C. Equations were tested against the internal validation data set and multiple external data sets of either β-quantification LDL-C results (n = 28 891) or direct LDL-C test results (n = 252 888). Statistical analysis was performed from August 7, 2018, to July 18, 2019.
Main Outcomes and Measures
Concordance between calculated and measured LDL-C levels by β-quantification, as assessed by various measures of test accuracy (correlation coefficient [R^{2}], root mean square error [RMSE], mean absolute difference [MAD]), and percentage of patients misclassified at LDL-C treatment thresholds of 70, 100, and 190 mg/dL.
Results
Compared with β-quantification, the new equation was more accurate than other LDL-C equations (slope, 0.964; RMSE = 15.2 mg/dL; R^{2} = 0.9648; vs Friedewald equation: slope, 1.056; RMSE = 32 mg/dL; R^{2} = 0.8808; vs Martin equation: slope, 0.945; RMSE = 25.7 mg/dL; R^{2} = 0.9022), particularly for patients with hypertriglyceridemia (MAD = 24.9 mg/dL; vs Friedewald equation: MAD = 56.4 mg/dL; vs Martin equation: MAD = 44.8 mg/dL). The new equation calculates the LDL-C level in patients with TG levels up to 800 mg/dL as accurately as the Friedewald equation does for TG levels less than 400 mg/dL and was associated with 35% fewer misclassifications when patients with hypertriglyceridemia (TG levels, 400-800 mg/dL) were categorized into different LDL-C treatment groups.
Conclusions and Relevance
The new equation can be readily implemented by clinical laboratories with no additional costs compared with the standard lipid panel. It will allow for more accurate calculation of LDL-C level in patients with low LDL-C levels and/or hypertriglyceridemia (TG levels, ≤800 mg/dL) and thus should improve the use of LDL-C level in cardiovascular disease risk management.
The clinical management of patients at risk for cardiovascular disease (CVD) is critically dependent on their level of low-density lipoprotein cholesterol (LDL-C).^{1} It is routinely calculated using results from the standard lipid panel (total cholesterol, high-density lipoprotein-cholesterol [HDL-C], and triglycerides [TGs]) by the equation by Friedewald et al^{2} (hereafter referred to as the Friedewald equation): LDL-C = (Total Cholesterol) − (HDL-C) − (TGs/5). The main source of error in this equation is the TGs/5 term, which serves as an estimate of very low-density lipoprotein-cholesterol (VLDL-C). The ratio of cholesterol to TGs in VLDL-C can vary considerably, depending on its size and other factors, which diminishes the accuracy of the equation for high-TG samples.^{2} Although tests for directly measuring LDL-C (dLDL-C) have been developed, it is still common practice to calculate LDL-C because of the extra cost of adding dLDL-C to the lipid panel and the poor analytical performance of some dLDL-C tests.^{3}^{-6}
Many LDL-C equations besides the Friedewald equation have been described,^{7}^{-20} but most are not significantly better than the Friedewald equation compared with the β-quantification reference method, a swinging-bucket ultracentrifugation precipitation-based procedure. Recently, Martin et al^{21}^{,22} developed an equation (hereafter referred to as the Martin equation) based on the Vertical Auto Profile test, which is a vertical-rotor ultracentrifugation-based method.^{23} It replaces the fixed TG denominator of 5 in the Friedewald equation with an empirical denominator (or factor) that varies depending on levels of TGs and non–HDL-C.^{21} It is more accurate than the Friedewald equation, particularly for low–LDL-C samples^{21}^{,22} that are now more common because of more effective lipid-lowering therapy.^{24}^{,25} In 2018, the new American College of Cardiology and American Heart Association guidelines on CVD risk biomarkers recommended the Martin equation as the preferred calculation method for low–LDL-C samples^{26} because of the clinical importance of LDL-C accuracy in the management of patients treated with potent new agents such as proprotein convertase subtilisin/kexin type 9 (PCSK9) inhibitors that can markedly decrease LDL-C levels.^{24}^{,25}
Clinical laboratories usually do not report LDL-C levels for patients with hypertriglyceridemia (TG levels ≥400 mg/dL [to convert to millimoles per liter, multiply by 0.0113]) because of large errors in the Friedewald estimate of VLDL-C.^{4} Instead, dLDL-C or apolipoprotein B testing is often performed, which increases costs. Furthermore, many patients with elevated TG levels have suppressed LDL-C levels, thus making their already low levels of LDL-C even more difficult to accurately estimate because of the greater proportion of error due to VLDL-C. Even for samples with only modest TG elevations, significant errors in estimating the LDL-C level can still occur.^{4}^{,18}^{,27} Now that most CVD guidelines have endorsed the use of nonfasting samples for an initial lipid screening,^{26} the inaccuracy of calculated LDL-C owing to elevated TG levels will be a greater problem in the future. Although the Martin equation has an adjustable factor for dividing TG levels, it has never been validated for patients with hypertriglyceridemia.^{21}^{,22} Moreover, the Vertical Auto Profile method on which it is based may sometimes underestimate the VLDL-C level in high-TG samples.^{23}^{,28}^{,29}
Using β-quantification results from a patient population with a high frequency of hypertriglyceridemia, we developed a new LDL-C equation. It can be used to more accurately estimate the LDL-C level in patients with TG levels up to 800 mg/dL and is also slightly more accurate than other equations for patients with normolipidemia. Furthermore, it correctly classifies more patients from a general population of patients with dyslipidemia into different LDL-C treatment groups than other equations and thus should improve the use of calculated LDL-C in CVD risk management.
Results of β-quantification for LDL-C were obtained from a deidentified data set from 8656 fasting patients tested on multiple occasions at the National Institutes of Health Clinical Center from January 1, 1976, to June 2, 1999. Research under this study was exempted by the National Institutes of Health Institutional Review Board because data were deidentified. Statistical analysis was performed from August 7, 2018, to July 18, 2019. Female patients accounted for 47% of the population (n = 4068), and the mean age was 49 years (range, 1-83 years). The laboratory performing the testing participated in the Centers for Disease Control and Prevention Lipids Standardization Program. Results outside the first and 99th percentiles for each lipid parameter, along with type III hyperlipidemic samples as determined by a VLDL-C to TGs ratio greater than 0.33, were removed from analysis, leaving a total of 18 715 LDL-C test results that were split into equally sized training and validation data sets. The median TG level was 149 mg/dL (interquartile range, 98-253 mg/dL), and 14% of the samples had a TG level of 400 mg/dL or more. The median non–HDL-C level was 190 mg/dL (interquartile range, 144-248 mg/dL) (to convert to millimoles per liter, multiply by 0.0259). The complete distribution of lipid test results for the internal data set and those of the external validation data sets (Mayo Medical Lab, Laboratory Corporation of America Holdings, Prism Health Dx Inc, and Pacific Biomarker) can be seen in the Table and are further described in eAppendix 2 in the Supplement. Dependent variables (TG and non–HDL-C levels) were converted into higher-degree and more complex multivariable terms using Excel (Microsoft Corp) and were used to develop equations for VLDL-C and LDL-C as described in eAppendix 1 in the Supplement by multiple least squares regression analysis with JMP (SAS Institute Inc). Confidence intervals for LDL-C risk level classification were calculated using the Wald test.
To derive a more accurate LDL-C equation, we first improved the estimation of VLDL-C. The following bivariate quadratic equation was developed by multiple least squares regression, using β-quantification test results that contained a broad range of TG (38-3162 mg/dL) and non–HDL-C (53-734 mg/dL) values.
As with the Friedewald equation, Equation 1 contains a TG term, but it is divided by 8.59 instead of 5:
This term captures the linear component of the association between the TG level and the VLDL-C level (eFigures 1 and 2 in the Supplement). The (TG × Non–HDL-C) term accounts for the interaction between the 2 independent variables. Its maximum value occurs in the upper right corner of the VLDL-C contour plot (eFigure 1D in the Supplement) owing to cholesterol enrichment by the cholesteryl ester transfer protein.^{30} The TG^{2} term can be considered a correction factor. It adjusts for the fact that patients with the most extreme elevations of TGs have proportionally more chylomicrons and nascent VLDL enriched in TGs rather than cholesterol.^{31}
In Equation 1, VLDL-C level is more accurately calculated than by the Friedewald or Martin equations (Figure 1) or by alternative equations (eTable and eFigure 3 in the Supplement), particularly for patients with hypertriglyceridemia. Equation 1 has a higher correlation coefficient (R^{2}) and a lower root mean square error (RMSE) than other equations, and these parameters were almost identical between the training and validation set, indicating that the regression model was not overfitted. The residual error plots for TG levels (eFigure 4A-C in the Supplement) and non–HDL-C levels (eFigure 4D-F in the Supplement) show that the Friedewald and Martin equations can lead to both falsely high and falsely low VLDL-C values owing to improper factor adjustment for TG and non–HDL-C levels. The Friedewald equation most often shows a positive bias against TG levels. In contrast, the Martin equation shows a slight negative bias for TG levels less than 700 mg/dL, but a positive bias for TG levels of 700 mg/dL or more (eFigure 5 in the Supplement). Although the HDL-C level was not directly used as a variable in Equation 1, residual errors for this parameter are also more closely centered around zero than for the other equations (eFigure 4G-I in the Supplement).
To determine the effective factor for each equation, we divided the TG level by either the measured (β-quantification) or calculated VLDL-C level and made contour plots for the mean factor at each possible TG and non–HDL-C level. For β-quantification, the mean factor ranged from 2 to more than 26 (eFigure 2 in the Supplement). Samples requiring the highest factors occurred in the lower right corner of the plot with the highest TG to non–HDL-C ratios. These high-factor values are consistent with the known TG to cholesterol ratios of chylomicrons and nascent VLDL-C and are the types of samples that lead to falsely elevated VLDL-C levels by the other equations. In contrast, high non–HDL-C samples in the upper left corner of the plot require much lower factors and can be falsely low by other equations. Compared with the other equations, the factor values for Equation 1 match the β-quantification factor plot much better.
When we restricted our analysis to just normolipidemic samples (TG level <400 mg/dL and non–HDL-C level <220 mg/dL), we found that the 180-cell factor table used in the Martin equation yielded very similar VLDL-C results to Equation 1 (eFigure 6 in the Supplement) and could be fitted by a slight modification to Equation 1 (eFigure 5 in the Supplement). Unlike Equation 1, results for the Martin equation did not always vary smoothly with respect to TG and non–HDL-C levels owing to the quantile nature of its table and likely because of a less-than-optimum factor assignment for some data cells. The fitted equation for the factor table used in the Martin equation also did not perform well when applied to hypertriglyceridemic samples.
With the same terms for VLDL-C as Equation 1, the following Equation 2 can be used to calculate LDL-C:
Equation 2 is similar to the Friedewald equation in that VLDL-C and HDL-C are subtracted from total cholesterol, but the inclusion of an intercept and allowing the coefficients to vary for each term resulted in a better fit with β-quantification than the other equations (Figure 2). Negative LDL-C values sometimes occurred for both the Friedewald and Martin equations owing to their negative bias for hypertriglyceridemic samples, but negative LDL-C values rarely occurred for Equation 2 (Figure 2).
To compare all the different LDL-C equations with a single integrated index of accuracy, we calculated the mean absolute difference (MAD) from β-quantification at different TG and non–HDL-C cutpoints (eFigure 7 in the Supplement). When only hypertriglyceridemic samples were analyzed, Equation 2 had the lowest MAD value. For TG levels less than 400 mg/dL, Equation 2 was again the most accurate, but differences between the top equations were relatively minor. Similar improvements in the accuracy of Equation 2 were found when results were stratified by non–HDL-C level. When compared with β-quantification, the new equation was more accurate than other LDL-C equations (slope, 0.964; RMSE = 15.2 mg/dL; R^{2} = 0.9648; vs Friedewald equation: slope, 1.056; RMSE = 32 mg/dL; R^{2} = 0.8808; vs Martin equation: slope, 0.945; RMSE = 25.7 mg/dL; R^{2} = 0.9022), particularly for patients with hypertriglyceridemia (MAD = 24.9 mg/dL; vs Friedewald equation: MAD = 56.4 mg/dL; vs Martin equation: MAD = 44.8 mg/dL).
To further validate Equation 2, we tested it on 2 external β-quantification data sets. The first was from patients from a large national reference laboratory that should be representative of dyslipidemia in the general population (eFigure 8A-C in the Supplement). For TG levels less than 400 mg/dL, all 3 equations were similar in accuracy, but based on its MAD value, Equation 2 had a slight advantage and showed an even greater advantage for hypertriglyceridemic samples. This was particularly true for the Friedewald equation, which, in 0.4% of the cases, yielded negative LDL-C values for hypertriglyceridemic samples. The second β-quantification data set was from patients treated with a statin with or without a cholesteryl ester transfer protein inhibitor (eFigure 8D-F in the Supplement). There was only a limited number of hypertriglyceridemic samples, and 68% of samples had LDL-C levels less than 100 mg/dL, but as before, Equation 2 was more accurate than the other equations.
We also compared the LDL-C equations with 2 commonly used dLDL-C tests in a general population. For the Roche dLDL-C (Figure 3A-C), both Equation 2 and the Martin equation closely matched the dLDL-C results, although the Martin equation showed a negative bias for TG levels of 1000 mg/dL or more. The Friedewald equation showed a much poorer concordance with the Roche dLDL-C test owing to its much larger negative bias and had many more negative LDL-C test results than the other equations. Similar results were found for the Beckman dLDL-C test (eFigure 8G-I in the Supplement). Whether the Roche dLDL-C test was used only in male vs female individuals or only in fasting vs nonfasting individuals, the linear fit with Equation 2 was nearly identical (eFigure 9 in the Supplement), indicating that Equation 2 is unaffected by sex or fasting state.
Using the large external β-quantification data set (n = 27 646), we determined the MAD score for various TG or non–HDL-C intervals (Figure 4A and B) to provide a population-independent estimate of accuracy. For TG intervals less than 400 mg/dL, all 3 equations had similar MAD scores, although the score for Equation 2 was slightly better for TG levels between 200 and 400 mg/dL. For TG levels of 400 mg/dL or more, the Friedewald equation shows a marked increase in MAD values with increasing TG levels because its fixed factor of 5 is too low for these types of samples. The Martin equation is slightly more accurate than the Friedewald equation at higher TG levels, but its factor values are still too low for specimens with the most elevated TG levels. The MAD values for Equation 2 also increase with increasing TG levels, but to a lesser degree, and stay below 30 mg/dL up to a TG level of 1000 mg/dL (Figure 4A). When analyzed by non–HDL-C intervals (Figure 4B), Equation 2 also had lower MAD values than the other equations, particularly at higher intervals.
To assess the potential association of the improved accuracy of Equation 2 with the clinical management of patients, we calculated the misclassification rate for the categorization of patients into different LDL-C treatment groups (Figure 4C and D). We did this for patients with TG levels from 400 to 800 mg/dL because we observed that the misclassification rate of 29% for Equation 2 for the TG interval of 600 to 800 mg/dL (mean, 677 mg/dL; n = 221) nearly approached the same misclassification rate of 29% for the Friedewald equation at the 350 to 450 mg/dL TG interval (mean, 394 mg/dL; n = 418). Equation 2 had 35% fewer misclassifications than the Friedewald equation, which showed a clear negative bias for low LDL-C levels, and 30% fewer misclassifications than the Martin equation, which showed an overall positive bias. Equation 2 also had less misclassifications that crossed 2 LDL-C treatment thresholds than the other equations. For TG levels less than 400 mg/dL, Equation 2 was similar in its misclassification rate to the Martin equation but showed a more substantial advantage over the Friedewald equation, which still had a negative bias for low LDL-C values (Figure 4D). Similar results regarding the improved accuracy of Equation 2 vs the other equations could also be observed by comparing its concordance to β-quantification in almost the entire range of LDL-C risk-level categories (eFigure 10 in the Supplement).
The derivation of a more accurate LDL-C equation for patients with hypertriglyceridemia and/or low LDL-C levels has practical value. The new equation uses results only from the standard lipid panel and has no intellectual property restrictions, so it will not increase the cost of testing. It is more complicated than other equations, but the result can be automatically calculated by most laboratory information systems without any additional software changes, unlike those that may be needed to implement the 180-cell factor table used by the Martin equation.^{21} Because the new equation is only slightly more accurate than the other equations for patients with normolipidemia, it can be reserved only for patients with hypertriglyceridemia and/or low LDL-C levels. From a practical standpoint, however, it may be simpler to use the new equation for all patients rather than use 2 different equations for calculating LDL-C levels.
Another important advantage of Equation 2 is that it is based on β-quantification, the reference method for LDL-C level. The Vertical Auto Profile test, on which the Martin equation is based, is also an ultracentrifugation density-based separation procedure. However, it is less well suited for hypertriglyceridemic samples because TG-rich lipoproteins can adhere to the sides of the vertical centrifugation tubes, leading to an underestimation of VLDL-C level.^{23}^{,28}^{,29} This possibility could account for the positive LDL-C bias for the Martin equation for TG levels less than 700 mg/dL, but at higher TG levels, the Martin equation, like the Friedewald equation, shows a negative bias owing to factor values that are too low.
Instead of not reporting any LDL-C test results or using a dLDL-C test, Equation 2 makes feasible the calculation of LDL-C for TG levels up to 800 mg/dL with a misclassification rate comparable to that of the Friedewald equation at 400 mg/dL. Equation 2 should therefore be suitable for almost all patients because a TG level of 800 mg/dL is greater than the 99th percentile in the general population. Use of the new equation was associated with 35% fewer misclassifications of patients with hypertriglyceridemia into different LDL-C treatment categories compared with the Friedewald equation and thus should improve the clinical management of patients. Misclassified patients, particularly those who cross more than 1 LDL-C treatment threshold, may not receive the correct lipid-lowering therapy and may have worse clinical outcomes. In part because of the limitations in the accuracy of LDL-C, non–HDL-C was recommended by the American College of Cardiology and American Heart Association as the main lipid biomarker in patients with hypertriglyceriemia.^{32} The most recent guidelines,^{26} however, are based primarily on LDL-C, so a more accurate calculated LDL-C could be useful for risk management in this population. Equation 2 could also be used to partition non–HDL-C into cholesterol in LDL-C vs TG-rich lipoproteins. In several large population studies, TG-rich lipoprotein cholesterol has been found to be more strongly associated with CVD than LDL-C,^{33}^{,34} but this association depends on correctly measuring LDL-C level.
The greatest clinical benefit of Equation 2 may be for patients with low LDL-C levels. The Martin equation is also more accurate than the Friedewald equation for such patients,^{21}^{,22} which is the reason many clinical laboratories have switched to this equation. Low LDL-C levels were once rare but are much more common with the use of anti-PCSK9 therapy.^{24}^{,25} Given the high cost of anti-PCSK9 therapy, the initial eligibility of patients for this type of therapy critically depends on the accurate measurement of LDL-C levels. Even once a patient is using anti-PCSK9 therapy, it is important to accurately monitor LDL-C levels. Because of the overestimation of the VLDL-C level by the Friedewald equation and some of the other equations, these patients can have falsely low or even nonsensical negative LDL-C results, which may discourage more aggressive lipid-lowering therapy that has been shown to be beneficial in high-risk patients.^{25} However, apolipoprotein B and other particle measures of LDL are more closely tied to residual CVD risk than LDL-C when these measures are discordant, a difference that will likely persist no matter how accurately LDL-C is measured.^{35}
This study has some limitations. One limitation is that a relatively unique population with a high frequency of hypertriglyceridemia was used to establish Equation 2, but it was validated with large numbers of external samples (>250 000) in multiple populations. Another limitation is that patients with type III hyperlipidemia were excluded from analysis because their lipoproteins contain an abnormal lipid composition, but the frequency of this disorder in the general population is less than 1%.^{28} β-Quantification is also not specific for LDL-C and can sometimes include cholesterol from chylomicron remnants, intermediate-density lipoprotein, and lipoprotein(a), but these are also proatherogenic, and thus this bias may not significantly diminish the association of calculated LDL-C with CVD.
We developed a more accurate LDL-C equation for patients with hypertriglyceridemia (TG level ≤800 mg/dL) and/or a low level of LDL-C that also performs well for patients with normolipidemia. Additional studies are needed in other populations, particularly those with low LDL-C levels, to more fully validate the equation and to better understand its clinical utility.
Accepted for Publication: December 10, 2019.
Published Online: February 26, 2020. doi:10.1001/jamacardio.2020.0013
Correction: This article was corrected on March 25, 2020, to fix an error in Figure 1A, Figure 3A, and Figure 4A and B.
Corresponding Author: Alan T. Remaley, MD, PhD, Lipoprotein Metabolism Laboratory, Translational Vascular Medicine Branch, National Heart, Lung, and Blood Institute, National Institutes of Health, 10 Center Dr, Bldg 10/Room 2C433, Bethesda, MD 20892 (aremaley1@nhlbi.nih.gov).
Author Contributions: Ms Sampson and Dr Remaley had full access to all the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis. Ms Sampson and Dr Ling contributed equally.
Concept and design: Sampson, Warnick, Jaffe, Shamburek, Remaley.
Acquisition, analysis, or interpretation of data: Sampson, Ling, Sun, Harb, Ashmaig, Warnick, Sethi, Fleming, Otvos, Meeusen, Delaney, Shamburek, Amar, Remaley.
Drafting of the manuscript: Sampson, Harb, Warnick, Shamburek, Remaley.
Critical revision of the manuscript for important intellectual content: Sampson, Ling, Sun, Harb, Ashmaig, Sethi, Fleming, Otvos, Meeusen, Delaney, Jaffe, Shamburek, Amar, Remaley.
Statistical analysis: Sampson, Ling, Sun, Fleming, Delaney, Remaley.
Obtained funding: Remaley.
Administrative, technical, or material support: Sampson, Ling, Sun, Ashmaig, Warnick, Fleming, Meeusen, Shamburek.
Supervision: Jaffe, Remaley.
Conflict of Interest Disclosures: Dr Jaffe reported receiving personal fees from Abbott, Beckman, Siemens, Roche, ET Healthcare, Sphingotec, Brava, Quidel, Blade, and Novartis outside the submitted work. No other disclosures were reported.
Funding/Support: This research was supported by the Intramural Research Program of the National Heart, Lung, and Blood Institute at the National Institutes of Health.
Role of the Funder/Sponsor: The funding source had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.
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