Accuracy and Clinical Impact of Estimating Low-Density Lipoprotein-Cholesterol at High and Low Levels by Different Equations

New more effective lipid-lowering therapies have made it important to accurately determine Low-density lipoprotein-cholesterol (LDL-C) at both high and low levels. LDL-C was measured by the β-quantification reference method (BQ) (N = 40,346) and compared to Friedewald (F-LDL-C), Martin (M-LDL-C), extended Martin (eM-LDL-C) and Sampson (S-LDL-C) equations by regression analysis, error-grid analysis, and concordance with the BQ method for classification into different LDL-C treatment intervals. For triglycerides (TG) < 175 mg/dL, the four LDL-C equations yielded similarly accurate results, but for TG between 175 and 800 mg/dL, the S-LDL-C equation when compared to the BQ method had a lower mean absolute difference (mg/dL) (MAD = 10.66) than F-LDL-C (MAD = 13.09), M-LDL-C (MAD = 13.16) or eM-LDL-C (MAD = 12.70) equations. By error-grid analysis, the S-LDL-C equation for TG > 400 mg/dL not only had the least analytical errors but also the lowest frequency of clinically relevant errors at the low (<70 mg/dL) and high (>190 mg/dL) LDL-C cut-points (S-LDL-C: 13.5%, F-LDL-C: 23.0%, M-LDL-C: 20.5%) and eM-LDL-C: 20.0%) equations. The S-LDL-C equation also had the best overall concordance to the BQ reference method for classifying patients into different LDL-C treatment intervals. The S-LDL-C equation is both more analytically accurate than alternative equations and results in less clinically relevant errors at high and low LDL-C levels.


Introduction
Cholesterol in low-density lipoproteins (LDL) (density range: 1.006-1063 g/mL), is causally related to the development of atherosclerosis [1]. Although other biomarkers for risk stratification such as apolipoprotein B (apoB) may be superior [2,3], the accurate measurement of LDL cholesterol (LDL-C) at both low and high levels is still important when following current guidelines for the clinical management of patients for the prevention of atherosclerotic cardiovascular disease (ASCVD) risk [4].
The use of proprotein convertase subtilisin/kexin type 9 serine protease (PCSK9) inhibitors [5,6] has made the measurement of low LDL-C critical for the secondary prevention of ASCVD. Because of its expense, PCSK9-inhibitors are typically reserved for high-risk ASCVD patients who do not achieve LDL-C levels below at least 70 mg/dL on more conventional therapy [4,7,8]. Most clinical laboratories still use the Friedewald equation (F-LDL-C) to calculate LDL-C based on the results of the standard lipid panel (total cholesterol (TC), triglycerides (TG) and high-density lipoprotein cholesterol (HDL-C)) [9,10]. Typically, F-LDL-C closely matches LDL-C as determined by the β-quantification reference method

Results
We first compared the various LDL-C equations against the BQ reference method (BQ-LDL-C) by regression analysis on a large number of patients with a wide range of LDL-C values (Figure 1). Based on their mean absolute difference (MAD) and other metrics of test accuracy (slope, intercept, correlation coefficient (R 2 ) and root mean square error (RMSE)), the S-LDL-C equation ( Figure 1D) showed greater accuracy than the F-LDL-C ( Figure 1A), M-LDL-C ( Figure 1B), or eM-LDL-C equations ( Figure 1C). The eM-LDL-C equation was only slightly more accurate than the original M-LDL-C equation in the whole dataset, but when results with TG 400-800 mg/dL were separately analyzed (Supplemental Figure S1), there was greater improvement over the original Martin equation (M-LDL-C MAD = 27.1, eM-LDL-C MAD = 24.5). Nonsensical negative LDL-C values for high TG samples occurred mostly with the F-LDL-C equation ( Figure 1A). An analysis of all equations by their residual errors as a function of the main independent variables (TG, nonHDL-C and HDL-C) as well as apoB and age also indicated S-LDL-C had the smallest residual errors, followed by eM-LDL-C, M-LDL-C and F-LDL-C (Supplemental Figure S2).
A plot of MAD for the four equations against the BQ reference method for different intervals of TG and nonHDL-C is shown in Figure 2. In HTG samples, greater accuracy was observed for S-LDL-C compared to the other equations (Figure 2A). At a TG interval centered at 400 mg/dL, the F-LDL-C equation had a MAD score of approximately 20 mg/dL, which we used as a benchmark because the Friedewald equation is not recommended for samples with TG exceeding this value because of inaccuracy. The S-LDL-C equation crosses this threshold at a TG level between 800 and 1000 mg/dL, whereas the original Martin equation exceeds this threshold between a TG level of 390 and 410 mg/dL. The extended Martin equation exceeded this threshold at a slightly higher TG level somewhere between 410 and 500 mg/dL. When the different equations were examined for different intervals of nonHDL-C, the S-LDL-C equation again appeared to be the most accurate, particularly for high nonHDL-C samples. The two Martin equations were the least accurate ( Figure 2B). Using the same 20 mg/dL LDL-C error threshold used for the different TG intervals, it appears that the S-LDL-C equation can be used for nonHDL-C values up to at least 350 mg/dL.
To assess the accuracy of the equations for estimating low LDL-C, regression analysis was performed on low LDL-C samples (<100 mg/dL) for those with TG 400-800 mg/dL and <400 mg/dL. By all the different accuracy metrics, S-LDL-C had the best overall performance for HTG samples, followed by eM-LDL-C and M-LDL-C and finally F-LDL-C ( Figure 3). Both the M-LDL-C and eM-LDL-C equations exhibited a fixed positive bias, as can be seen by their relatively large positive intercepts and how their regression lines were above and parallel to the line of identity. In contrast, the F-LDL-C equation showed a negative bias, particularly for HTG patients with low LDL-C values, which sometimes resulted in negative LDL-C values.
When samples with low LDL-C and TG < 400 mg/dL were analyzed (Figure 4), the LDL-C equations were more similar in their performance, but they maintained the same rank order in their accuracy. Note that only results of the M-LDL-C equation are shown, because it yields identical results to the eM-LDL-C equation for TG < 400 mg/dL. Further subdivision of TG to <175 mg/dL versus 175-400 mg/dL revealed a slight negative bias for F-LDL-C for samples with TG 175-400 mg/dL. In contrast, the M-LDL-C equation showed a slight positive bias for those same samples with modest TG elevations.  To evaluate the different LDL-C equations for high LDL-C samples, we performed regression analysis against BQ-LDL-C for LDL-C between 160 and 220 mg/dL to bracket the 190 mg/dL high cut-point recommended for primary prevention screening ( Figure 5). Based on this analysis, all the equations showed better performance at the high LDL-C cutpoint, but the S-LDL-C equation was again slightly better by most of the accuracy metrics followed by the F-LDL-C and then the two Martin equations. When samples with TG 400-800 mg/dL were analyzed separately, it was observed that the M-LDL-C and eMLDL-C equations had a positive bias of at least 20 mg/dL, as can be observed by their positive regression line across the whole LDL-C 160-220 mg/dL test interval. Improved accuracy of the S-LDL-C equation for high LDL-C samples was also demonstrated by analysis of a larger sample set with LDL-C ranging between 100 and 700 mg/dL (Supplemental Figure S3).  The inset shows a close-up for low TG and low nonHDL-C samples. The number of samples within the interval is indicated, as well as the mean value for the interval. Solid black line is the level of the MAD for Friedewald at 400 mg/dL TG (20 mg/dL), which was used as a limit for acceptable accuracy for the other equations.
Next, for patients with TG 400-800 mg/dL, we used error grid analysis [22] to compare the analytic errors of the different LDL-C equations for their potential to change clinical management decisions. As shown in Figure 6A, differences between estimated LDL-C and BQ-LDL-C that were greater than the 12% proportional total allowable error goal for LDL-C [10] but not expected to change clinical management (no change in classification at the low (70 mg/dL) and high (190 mg/dL), were categorized as pure analytical errors. Errors that resulted in the incorrect classification of a patient at either the low or high LDL-C cut-point were classified as clinically relevant errors regardless of the magnitude of the difference between the estimated and BQ LDL-C values. For TG 400-800 mg/dL, only approximately half of the S-LDL-C results were analytically correct (within the 12% total allowable error goal), but this was much better than the other equations ( Figure 6F). Likewise, the S-LDL-C equation had the least analytically incorrect results. Its errors were also more balanced than the other equations. F-LDL-C more often underestimated true LDL-C, whereas M-LDL-C and eM-LDL-C more frequently overestimated LDL-C. In terms of clinically relevant errors ( Figure 6H), a total of 13.5% of the S-LDL-C results would be predicted to potentially change the management of patients, which was statistically less than for F-LDL-C (23.0%), M-LDL-C (20.5%) and eM-LDL-C (20.0%) (Supplemental Table  S3). The clinically relevant errors for F-LDL-C tended to underestimate LDL-C at the low LDL-C cut-point, whereas M-LDL-C and eM-LDL-C more often overestimated LDL-C at both the low and high LDL-C cut-points. When samples with low LDL-C and TG < 400 mg/dL were analyzed (Figure 4), the LDL-C equations were more similar in their performance, but they maintained the same rank order in their accuracy. Note that only results of the M-LDL-C equation are shown, because it yields identical results to the eM-LDL-C equation for TG < 400 mg/dL. Further   metrics followed by the F-LDL-C and then the two Martin equations. When samples with TG 400-800 mg/dL were analyzed separately, it was observed that the M-LDL-C and eM-LDL-C equations had a positive bias of at least 20 mg/dL, as can be observed by their positive regression line across the whole LDL-C 160-220 mg/dL test interval. Improved accuracy of the S-LDL-C equation for high LDL-C samples was also demonstrated by analysis of a larger sample set with LDL-C ranging between 100 and 700 mg/dL (Supplemental Figure S3). Similar error-grid analysis performed for patients with TG < 400 mg/dL indicated smaller differences between the equations (Figure 7). Much higher percentages of results were analytically correct ( Figure 7D) and fewer were analytically incorrect with limited clinical impact ( Figure 7E). In terms of clinically relevant errors at the high LDL-C cut-point, all 4 equations were similar in performance ( Figure 7F). A greater percentage of clinically relevant errors was observed at the low LDL-C cut-point, but again all equations were similar in performance except for F-LDL-C, which statistically had the greatest frequency of errors due to an underestimation of LDL-C (Supplemental Table S3).  Finally, we calculated in Table 1 the concordance of the four equations for classification of patients into a variety of previously recommended LDL-C treatment intervals [4,26]. For each LDL-C interval, spanning low to high LDL-C values, we calculated true positive, true negative, false positive and false negative test results when compared against the BQ reference method. Using these four possible test outcomes, we also calculated the positive and negative predictive value for each equation, as well as their sensitivity and specificity for correctly classifying patients into their true LDL-C interval as determined by the BQ reference method. For an overall index, we calculated the BA and nMCC index scores. For TG < 400 mg/dL, S-LDL-C had the best BA index for all LDL-C intervals. Similarly, the S-LDL-C equation had the best nMCC index for all LDL-C intervals except for 40-69 mg/dL, which was slightly better for the M-LDL-C equation. In general, all four equations showed relatively good performance for low TG samples and classification differences between the different equations were relatively small. In contrast, for samples with TG 400-800 mg/dL, the S-LDL-C equation was more concordant with the BQ reference method for all of the LDL-C intervals tested based on both the BA and nMCC indices.

Discussion
Because of the clinical need to accurately measure both high and low LDL-C, it is a challenge to develop a single equation that shows adequate accuracy on both ends of the LDL-C reference range. In fact, the Friedewald equation was first developed over 50 years ago when the main clinical concern was only high LDL-C [9]. Only recently with new effective therapies such as PCSK9-inhibitors have we been able to routinely lower LDL-C below 70 mg/dL or even lower, which has now become a goal for secondary prevention [4].
Although the M-LDL-C equation was first reported in 2013 [20], recent College of American Pathologist Clinical Chemistry Surveys indicate that the majority of clinical laboratories still use the F-LDL-C equation. In 2018, the Multi-society Cholesterol Guidelines [4] specifically recommended that the M-LDL-C equation [15,20] be used for low LDL-C samples but did not comment on the use of F-LDL-C equation for other types of samples. Results from this study and now many other studies [10,[27][28][29] have clearly shown that the F-LDL-C equation does not offer any advantages over more recently developed equations for calculating LDL-C. It may take a more explicit recommendation from future US guidelines discouraging the use of the F-LDL-C equation, at least for samples with more than modest elevations in TG, before more clinical laboratories will switch their LDL-C calculation method. An expert panel from the Canadian Society of Clinical Chemists did recently recommend that the F-LDL-C equation be replaced with the S-LDL-C equation for routine use [30].
There are two potential barriers that may have slowed the replacement of the F-LDL-C equation by the M-LDL-C or eM-LDL-C equations, which are not an issue with the S-LDL-C equation. First, the S-LDL-C equation can be directly and easily implemented by most clinical laboratory information systems, because they are all typically designed for user entry of novel equations. In contrast, custom software changes for some laboratory information systems may be needed to implement the 180-cell look-up tables of TG denominators that are required for the M-LDL-C and eM-LDL-C equations. Secondly, the S-LDL-C equation is in the public domain and is free to use without any fees or other type of restrictions. The method for calculating LDL-C by the M-LDL-C equation has been patented and is licensed to Quest Diagnostics.
In terms of accuracy, the Martin and Sampson equations appear to yield similarly accurate results for most samples, but S-LDL-C appears to have a clear advantage for HTG samples even when compared to the new eM-LDL-C equation. As we show by error-grid analysis, the S-LDL-C equation also results in fewer clinically relevant errors compared to the other equations, particularly for HTG samples. The improved accuracy of the S-LDL-C equation over the M-LDL-C and eM-LDL-C equations may be a consequence of the method used to measured LDL-C when developing the Martin equations. The S-LDL-C equation was trained against the BQ reference method, whereas the original and new enhanced Martin equations were based on the VAP method [19]. Both VAP and BQ utilize ultracentrifugation to separate lipoproteins; however, the VAP method has been reported to under-recover TG-rich lipoproteins (VLDL and intermediate-density lipoproteins (IDL)) compared to the BQ reference method and was the reason that this method was not recommended for HTG samples when first developed [19,31,32]. Because LDL-C is calculated by the M-LDL-C equation by subtracting HDL-C and VLDL-C from TC, any under-recovery of VLDL-C by the VAP method would be expected to lead to the observed positive bias in LDL-C for high TG samples by both Martin equations.
When possible, it is, of course, always best to evaluate a method by comparing it to its reference method, which ideally all routine test methods in the field are traced against. Furthermore, in the case of lipids, almost all initial clinical trials of lipid-lowering agents utilized the BQ reference method for establishing the link between lipid lowering and clinical outcomes. Many recent studies [33], however, comparing the different LDL-C equations, have used a direct LDL-C assay to assess accuracy and have sometimes come to different conclusions about the relative accuracy of different equations. Although direct LDL-C assays are sometimes used for HTG samples because of their improved accuracy, they can nevertheless still have significant positive or negative biases [34], which can lead to differences in the interpretation of the accuracy of the various LDL-C equations. Given that the various LDL-C equations yield similar results for most samples, it is also important to evaluate a relatively large number of samples, as was done in this study. It is particularly important to assess patients with HTG and other types of dyslipidemia to fully evaluate the accuracy of the different LDL-C equations [34]. In terms of the difference between the M-LDL-C and eM-LDL-C equations, we found only a relatively modest improvement in the accuracy of the eM-LDL-C equation for HTG samples when both methods were compared against the BQ reference method. Again, this highlights the importance of evaluating any new method for estimating LDL-C against the BQ reference method, which was not done when initially developing the eM-LDL-C equation [21].
Another important issue is the best way to assess the accuracy of classifying patients into different LDL-C treatment intervals. The M-LDL-C equation was previously assessed for its classification concordance with the BQ reference method by its ratio of true positives over true positives plus false positives [15], which is its positive predictive value. By itself, positive predictive value is known, however, to be a potentially misleading index of test classification accuracy. It does not take into account false negative test results and is, therefore, unaffected by prevalence [35]. If one does use positive predictive value for this purpose, it is then important to also consider negative predictive value in conjunction with positive predictive value. Alternatively, sensitivity in conjunction with specificity can also be used to assess test concordance with a reference method and is the more conventional way for evaluating diagnostic test performance [36]. There are, however, several different indices of overall test accuracy, each with their own advantages and disadvantages [37]. We used both the BA index, which weighs sensitivity and specificity equally, and the nMCC index, which can weigh sensitivity and specificity differently to account for any imbalance in the number of true positive and true negatives [25]. In our case, both metrics yielded a similar interpretation, indicating an advantage of the S-LDL-C equation over the other equations, particularly for HTG samples.
Another way to assess the accuracy of LDL-C equations is by error-grid analysis [22], which was previously used for evaluating glucose monitors, but we modified it for LDL-C equation assessment. It is a hybrid approach that allows one to separately consider purely analytical errors versus clinically relevant errors. Based on this analysis, the S-LDL-C equation resulted in fewer clinically relevant errors than the other equations for HTG at the low (LDL-C < 70 mg/dL) and high (LDL-C > 190 mg/dL) cut-points. For TG < 400 mg/dL, S-LDL-C and M-LDL-C had similar frequency of clinically relevant errors and F-LDL-C had the most. These results are consistent with a recent report based on the Canadian Health Measure Survey showing that the replacement of F-LDL-C with the S-LDL-C equation is justified based on the number of patients for whom it would affect either the initial decision to treat with a statin or statin dose [38].
In summary, the F-LDL-C equation does not appear to have any advantages over the other LDL-C equations and should be replaced with one of the newer alternative LDL-C equations. The use of more accurate alternative LDL-C equations would likely most benefit those patients who may need to receive a second lipid-lowering agent in order to reduce any remaining high residual risk. For most samples, the alternative LDL-C equations showed similar performance, but S-LDL-C is the most accurate on samples with more than moderate levels of HTG and has several practical advantages in terms of ease of implementation. A limitation of our study is that we only have information on the age and sex of our patients, so it will be important to assess the different LDL-C equations in different ethnic populations and in patients with specific medical disorders to determine if our results are generalizable. Additionally, even though the BQ method is the reference method, it is important to note that cholesterol in the fraction it classifies as LDL also includes cholesterol on Lp(a) and some remnant lipoproteins too. In the future, it would, therefore, be important to directly assess the different LDL-C equations, which may be affected differently by cholesterol on these other lipoproteins, for their impact in the clinical management of patients and for their ability to predict future ASCVD events. The difference from LDL-C as measured by the BQ reference method was plotted for the indicated independent variables. Results are color coded by nonHDL-C level (Panels A-D), triglyceride level (Panels E-P) with the value in the legend (mg/dL) indicating the start of each interval or by sex (Panels Q-T, blue = male, red = female). Figure S3. Comparison of estimated LDL-C versus BQ-LDL-C. LDL-C was calculated from the results of a standard lipid panel from a general population (N = 25,311) with a wide range of LDL-C >100 mg/dL by F-LDL-C (Panels A, B), M-LDL-C (Panels C, D), eM-LDL-C (Panels E, F) and S-LDL-C (Panels G, H) equations and plotted against LDL-C as measured by BQ reference method (BQ-LDL-C) for low TG <400 mg/dL (N = 24,142,Panels A, C, E G) and for high TG 400-800 mg/dL (N = 1169, Panels B, D, F and H). Solid lines are the linear fits for the indicated regression equations. Dotted lines are lines of identity. Results are color coded by TG level with the value in the legend (mg/dL) indicating the start of each interval. Supplemental Table S1. Lipid values and demographic characteristics of dataset. Supplemental Table S2. Equations for calculating LDL-C. Supplemental Table S3. Comparison between equations for accuracy.

Informed Consent Statement: Not applicable.
Data Availability Statement: All data available upon request.

Conflicts of Interest:
The authors declare no conflict of interest. Proprotein convertase subtilisin/kexin type 9 HTG Hypertriglyceridemia/hypertriglyceridemic