See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/366070443

Accuracy and Clinical Impact of Estimating Low-Density Lipoprotein-

Cholesterol at High and Low Levels by Different Equations

Article in Biomedicines · December 2022

DOI: 10.3390/biomedicines10123156

CITATIONS READS

4 104

9 authors, including:

Maureen Sampson Anna Wolska

National Institutes of Health National Heart, Lung, and Blood Institute
123 PUBLICATIONS 2,560 CITATIONS 60 PUBLICATIONS 642 CITATIONS

SEE PROFILE SEE PROFILE

Justine Cole Rafael Zubiran

University of Cape Town National Institutes of Health
6 PUBLICATIONS 13 CITATIONS 5 PUBLICATIONS 43 CITATIONS

SEE PROFILE SEE PROFILE

Some of the authors of this publication are also working on these related projects:

ApoA-I-mediated phospholipid efflux View project

ApoC-II mimetic peptides View project

All content following this page was uploaded by Rafael Zubiran on 08 December 2022.

The user has requested enhancement of the downloaded file.

Article

Accuracy and Clinical Impact of Estimating Low-Density

Lipoprotein-Cholesterol at High and Low Levels by
Different Equations
Maureen Sampson 1, Anna Wolska 2, Justine Cole 1, Rafael Zubirán 3, James D. Otvos 2, Jeff W. Meeusen 4,
Leslie J. Donato 4, Allan S. Jaffe 4 and Alan T. Remaley 2,*

1 Department of Laboratory Medicine, Clinical Center, National Institutes of Health,

Bethesda, MD 20892, USA
2 Lipoprotein Metabolism Laboratory, Translational Vascular Medicine Branch, National Heart, Lung and

Blood Institute, National Institutes of Health, Bethesda, MD 20892, USA

3 Salvador Zubirán National Institute of Health Sciences and Nutrition, Mexico City 14080, Mexico

4 Department of Laboratory Medicine and Pathology, Mayo Clinic, Rochester, MN 55902, USA

* Correspondence: aremaley1@nhlbi.nih.gov; Tel.: +1-301-402-9797; Fax: +1-301-402-1885

Abstract: 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
Citation: Sampson, M.; Wolska, A.; regression analysis, error-grid analysis, and concordance with the BQ method for classification into
Cole, J.; Zubirán, R.; Otvos, J.D.; different LDL-C treatment intervals. For triglycerides (TG) < 175 mg/dL, the four LDL-C equations
Meeusen, J.W.; Donato, L.J.; Jaffe, yielded similarly accurate results, but for TG between 175 and 800 mg/dL, the S-LDL-C equation
A.S.; Remaley, A.T. Accuracy and when compared to the BQ method had a lower mean absolute difference (mg/dL) (MAD = 10.66)
Clinical Impact of Estimating than F-LDL-C (MAD = 13.09), M-LDL-C (MAD = 13.16) or eM-LDL-C (MAD = 12.70) equations. By
Low-Density Lipoprotein- error-grid analysis, the S-LDL-C equation for TG > 400 mg/dL not only had the least analytical errors
Cholesterol at High and Low Levels but also the lowest frequency of clinically relevant errors at the low (<70 mg/dL) and high (>190
by Different Equations. Biomedicines
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:
2022, 10, 3156. https://doi.org/
20.0%) equations. The S-LDL-C equation also had the best overall concordance to the BQ reference
10.3390/biomedicines10123156
method for classifying patients into different LDL-C treatment intervals. The S-LDL-C equation is
Academic Editor: Adrian both more analytically accurate than alternative equations and results in less clinically relevant
Wlodarczak errors at high and low LDL-C levels.
Received: 7 November 2022
Accepted: 29 November 2022 Keywords: low-density lipoproteins; cholesterol; triglyceride; cardiovascular disease risk
Published: 6 December 2022

Publisher’s Note: MDPI stays

neutral with regard to jurisdictional
1. Introduction
claims in published maps and
institutional affiliations. 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
Copyright: © 2022 by the authors. when following current guidelines for the clinical management of patients for the
Licensee MDPI, Basel, Switzerland. prevention of atherosclerotic cardiovascular disease (ASCVD) risk [4].
This article is an open access article The use of proprotein convertase subtilisin/kexin type 9 serine protease (PCSK9)
distributed under the terms and inhibitors [5,6] has made the measurement of low LDL-C critical for the secondary
conditions of the Creative Commons prevention of ASCVD. Because of its expense, PCSK9-inhibitors are typically reserved for
Attribution (CC BY) license
high-risk ASCVD patients who do not achieve LDL-C levels below at least 70 mg/dL on
(https://creativecommons.org/license
more conventional therapy [4,7,8]. Most clinical laboratories still use the Friedewald
s/by/4.0/).
equation (F-LDL-C) to calculate LDL-C based on the results of the standard lipid panel

Biomedicines 2022, 10, 3156. https://doi.org/10.3390/biomedicines10123156 www.mdpi.com/journal/biomedicines

Biomedicines 2022, 10, 3156 2 of 18

(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 (BQ), a laborious combined precipitation-
ultracentrifugation procedure [11,12]. The F-LDL-C equation is known, however, to
underperform for hypertriglyceridemic (HTG) samples (TG > 400 mg/dL), because its
TG/5 term overestimates cholesterol on very-low-density lipoproteins (VLDL), leading to
an underestimation of LDL-C [13–16].
Because of the known limitations of the F-LDL-C equation, the current US-Multi-
society Cholesterol Guideline on the Management of Blood Cholesterol [4] recommends
that either a direct LDL-C test or an alternative LDL-C equation be used when LDL-C is
low (<70 mg/dL). Although direct LDL-C tests are now fully automated and widely
available, they can differ from the BQ reference method for various types of dyslipidemia,
including HTG [10]. Because of this issue, which is related to their differential reactivity
to different lipoprotein subfractions, and the extra costs for performing direct LDL-C
testing, most clinical laboratories in the US still calculate LDL-C, according to recent
College of American Pathology proficiency test surveys. In 2018, the US-Multi-society
Cholesterol Guideline [4] recommended “enhanced equations” such as the Martin
equation (M-LDL-C) [15,17] rather than F-LDL-C for estimating LDL-C when
concentrations are low. The M-LDL-C equation, designed to match LDL-C measured by
the vertical auto profile (VAP) ultracentrifugation method [18,19] is identical to the F-
LDL-C equation except for its TG denominator, which varies depending upon the plasma
levels of TG and non-high-density lipoprotein cholesterol (nonHDL-C) [15,17,20].
Recently, a modified Martin equation (extended Martin equation; eM-LDL-C) was
described with a different set of TG denominators for TG between 400 and 800 mg/dL [21].
The accurate measurement of LDL-C at the high end is also clinically relevant,
particularly for primary prevention. According to the US-Multi-society Cholesterol
Guideline [4], patients with LDL-C > 190 mg/dL do not need to undergo any further
ASCVD risk assessment and should be treated with a statin. For patients with HTG, it is
recommended that a nonHDL-C cut-point of 220 mg/dL, which can be accurately
calculated by a simple calculation, be used instead for deciding statin therapy, because of
potential inaccuracies in LDL-C estimation [4]. Some have also advocated more
widespread use of nonHDL-C as an ASCVD biomarker, but current guidelines still focus
most of their recommendations based on LDL-C values.
In 2020, we described a bivariate quadratic equation, called the Sampson equation
(S-LDL-C) [16], designed to match LDL-C measured by the BQ reference method [11,12].
Overall, it was more accurate than the other LDL-C equations when compared to BQ,
particularly for high TG samples up to 800 mg/dL [16]. In this study, we compare the S-
LDL-C equation to the two different versions of the Martin equation and the F-LDL-C
equation against the BQ reference method for both low and high LDL-C values. We also
describe a new method for assessing the clinical impact of inaccuracies in LDL-C
estimation methods, using error-grid analysis [22].

2. Methods
Deidentified LDL-C and other lipid test results were obtained from the clinical
laboratory at Mayo Clinic on patients (N = 40,346) for whom BQ testing was performed as
previously described [23,24]. Samples with detectable Lipoprotein-X by agarose gel
electrophoresis (N = 141), with TG > 2000 mg/dL (N = 172), with TC > 1000 mg/dL (N = 6),
or with Type III hyperlipidemia (TG between 150 and 1000 mg/dL with measured VLDL-
C/TG > 0.3, N = 71) were excluded from analysis. The mean and range of lipid values and
patient demographic information for the final dataset are shown in Supplemental Table
S1.
LDL-C was calculated by the F-LDL-C [9], M-LDL-C [17], eM-LDL-C [21] and S-LDL-
C [16] equations (Supplemental Table S2) by an Excel spreadsheet, which can be
downloaded at the following website: https://figshare.com/articles/software/Sampson_
Biomedicines 2022, 10, 3156 3 of 18

LDLC_and_VLDLC_calculator/21346893. The overall concordance with the BQ method

for classification by the different equations into LDL-C intervals was determined by either
calculating the balanced-accuracy (BA) index (Sensitivity + Specificity/2) or the
normalized Matthews correlation coefficient (nMCC) index, as previously described [25].
Comparisons among LDL-C equations for the number of potentially clinically relevant
errors were done by pairwise Chi-Square analysis and by calculating their kappa scores.
Research under this study was not considered human subject research and was exempted
from IRB review.

3. 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 (R2) 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.
Biomedicines 2022, 10, 3156 4 of 18

Figure 1. Comparison of estimated LDL-C versus BQ-LDL-C. LDL-C was calculated in patients (N
= 39,956) with a wide range of LDL-C values by F-LDL-C, (Panel A), M-LDL-C (Panel B), eM-LDL-
C (Panel C) and S-LDL-C (Panel D) equations and plotted against LDL-C as measured by BQ
reference method (BQ-LDL-C). Solid lines are 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.
Biomedicines 2022, 10, 3156 5 of 18

Figure 2. Mean Absolute Difference of estimated LDL-C versus BQ-LDL-C. Mean absolute
difference (MAD) score for LDL-C from patients (N = 39,956) with a wide range of LDL-C values is
shown for the F-LDL-C (purple line), the M-LDL-C (orange line), eM-LDL-C (green line) and S-LDL-
C (light blue line) equations for the indicated TG intervals (Panel A) and nonHDL-C intervals (Panel
B). 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.
Biomedicines 2022, 10, 3156 6 of 18

Figure 3. Comparison of estimated LDL-C versus BQ-LDL-C for HTG samples with low LDL-C.
LDL-C was calculated from patients (N = 1115) with LDL-C < 100 mg/dL and TG 400–800 mg/dL
values by F-LDL-C (Panel A), M-LDL-C (Panel B), eM-LDL-C, (Panel C) and S-LDL-C (Panel D)
equations and plotted against LDL-C as measured by the BQ reference method (BQ-LDL-C). 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.

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.
Biomedicines 2022, 10, 3156 7 of 18

Figure 4. Comparison of estimated LDL-C versus BQ-LDL-C for low TG samples with low LDL-C.
LDL-C was calculated for patients (N = 13,415) with LDL-C < 100 mg/dL and TG < 400 mg/dL values
by F-LDL-C (Panel A), M-LDL-C (Panel B), and S-LDL-C (Panel C) equations and plotted against
LDL-C as measured by the BQ reference method (BQ-LDL-C). 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 TG < 175 mg/dL indicated in blue and samples with TG between 175 and 400 mg/dL in red.
Biomedicines 2022, 10, 3156 8 of 18

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
cut-point, 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).

Figure 5. Comparison of estimated LDL-C versus BQ-LDL-C for samples with high LDL-C. LDL-C
was calculated for patients (N = 5060) with LDL-C between 160 and 220 mg/dL by F-LDL-C (Panel
A), M-LDL-C (Panel B), eM-LDL-C (Panel C) and S-LDL-C (Panel D) equations and plotted against
LDL-C as measured by BQ reference method (BQ-LDL-C). Solid red lines are the linear fits for the
indicated regression equations for samples with TG > 400 mg/dL. Dotted lines are lines of identity.
Biomedicines 2022, 10, 3156 9 of 18

Results are color coded by TG level with TG < 400 mg/dL indicated in blue and TG 400–800 mg/dL
in red.

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.
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).
Biomedicines 2022, 10, 3156 10 of 18

Figure 6. Error Grid Analysis for high TG samples. Definition of type of errors are shown in (Panel
A). a: Within 12% proportional error and below regression line, b: Within 12% proportional error
and above regression line, c: Greater than 12% proportional error but no impact on patient
Biomedicines 2022, 10, 3156 11 of 18

management and below regression line, d: Greater than 12% proportional error but no impact in
patient management and above regression line, e: Underestimation of LDL-C at high LDL-C cut-
point leading to error in patient management, f: Overestimation of LDL-C at high LDL-C cut-point
leading to error in patient management, g: Underestimation of LDL-C at low LDL-C cut-point
leading to error in patient management, h: Overestimation of LDL-C at low LDL-C cut-point leading
to error in patient management. Numbers in colored zones (e, f, h and g) indicate total number of
clinically relevant misclassifications. Error grid analysis was performed on patients (N = 2274) with
TG 400–800 mg/dL and BQ-LDL-C ≤ 300 mg/dL for LDL-C calculated by the S-LDL-C (Panel B), F-
LDL-C (Panel C), M-LDL-C (Panel D), and eM-LDL-C (Panel E) equations. Percent of analytically
correct results within 12% proportional error (Panel F, Zones a + b) and incorrect analytical results
(Panel G, Zones c + d) are shown. Clinically relevant errors affecting classification at high (Zones e
+ f) and low (Zones g + h) LDL-C cut-points are shown in (Panel H).

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.
Biomedicines 2022, 10, 3156 12 of 18

Figure 7. Error Grid Analysis for low TG samples. Definition of type of errors are the same as shown
in Figure 6A. Error grid analysis was performed for patients (N = 37,088) with TG < 400 mg/dL and
BQ-LDL-C ≤ 300 mg/dL for LDL-C calculated by the S-LDL-C (Panel A), F-LDL-C (Panel B), M-LDL-
C (Panel C) equations. Percent of analytically correct results within 12% proportional error (Panel
D, Zones a + b) and incorrect analytical results (Panel E, Zones c + d) are shown. Clinically relevant
errors affecting classification at low (Zones e + f) and high (Zones g + h) LDL-C cut-points are shown
in (Panel F).
Biomedicines 2022, 10, 3156 13 of 18

Table 1. Concordance of LDL-C equations with BQ for classification into LDL-C intervals.

TG 0–400 mg/dL
TP TN FP FN ppv npv Sensitivity Specificity BA nMCC
BQ-LDL-C 40–69
mg/dL
F-LDL-C 2719 32,342 1495 594 64.5 98.2 82.1 95.6 88.8 0.849
M-LDL-C 2675 33,077 760 638 77.9 98.1 80.7 97.8 89.2 0.886
S-LDL-C 2770 32,912 925 543 75.0 98.4 83.6 97.3 90.4 0.885
BQ-LDL-C 70–99
mg/dL
F-LDL-C 7320 25,613 2173 2044 77.1 92.6 78.2 92.2 85.2 0.850
M-LDL-C 7471 26,108 1678 1893 81.7 93.2 79.8 94.0 86.9 0.872
S-LDL-C 7544 26,248 1538 1820 83.1 93.5 80.6 94.5 87.5 0.879
BQ-LDL-C 100–129
mg/dL
F-LDL-C 8405 24,196 1807 2742 82.3 89.8 75.4 93.1 84.2 0.851
M-LDL-C 8643 23,944 2059 2504 80.8 90.5 77.5 92.1 84.8 0.852
S-LDL-C 8765 24,342 1661 2382 84.1 91.1 78.6 93.6 86.1 0.868
BQ-LDL-C 130–159
mg/dL
F-LDL-C 5636 28,282 1447 1785 79.6 94.1 75.9 95.1 85.5 0.862
M-LDL-C 5747 27,857 1872 1674 75.4 94.3 77.4 93.7 85.6 0.852
S-LDL-C 5886 28,113 1616 1535 78.5 94.8 79.3 94.6 86.9 0.868
BQ-LDL-C 160–189
mg/dL
F-LDL-C 2620 32,848 759 923 77.5 97.3 73.9 97.7 85.8 0.866
M-LDL-C 2680 32,592 1015 863 72.5 97.4 75.6 97.0 86.3 0.856
S-LDL-C 2785 32,665 942 758 74.7 97.7 78.6 97.2 87.9 0.871
TG 401–800
mg/dL
TP TN FP FN ppv npv sensitivity specificity BA nMCC
BQ-LDL-C 40–69
mg/dL
F-LDL-C 111 1543 312 283 26.2 84.5 28.2 83.2 55.7 0.555
M-LDL-C 110 1814 41 284 72.8 86.5 27.9 97.8 62.9 0.695
eM-LDL-
103 1815 40 291 72.0 86.2 26.1 97.8 62.0 0.687
C
S-LDL-C 218 1736 119 176 64.7 90.8 55.3 93.6 74.5 0.760
BQ-LDL-C 70–99
mg/dL
F-LDL-C 224 1354 249 422 47.4 76.2 34.7 84.5 59.6 0.606
M-LDL-C 205 1371 232 441 46.9 75.7 31.7 85.5 58.6 0.599
eM-LDL-
236 1357 246 410 49.0 76.8 36.5 84.7 60.6 0.617
C
S-LDL-C 374 1384 219 272 63.1 83.6 57.9 86.3 72.1 0.727
BQ-LDL-C 100–129
mg/dL
F-LDL-C 241 1497 191 320 55.8 82.4 43.0 88.7 65.8 0.674
M-LDL-C 197 1283 405 364 32.7 77.9 35.1 76.0 55.6 0.554
Biomedicines 2022, 10, 3156 14 of 18

eM-LDL-
250 1282 406 311 38.1 80.5 44.6 75.9 60.3 0.598
C
S-LDL-C 306 1452 236 255 56.5 85.1 54.5 86.0 70.3 0.705
BQ-LDL-C 130–159
mg/dL
F-LDL-C 121 1819 122 187 49.8 90.7 39.3 93.7 66.5 0.683
M-LDL-C 146 1567 374 162 28.1 90.6 47.4 80.7 64.1 0.615
eM-LDL-
181 1616 325 127 35.8 92.7 58.8 83.3 71.0 0.673
C
S-LDL-C 175 1752 189 133 48.1 92.9 56.8 90.3 73.5 0.720
BQ-LDL-C 160–189
mg/dL
F-LDL-C 66 2027 81 75 44.9 96.4 46.8 96.2 71.5 0.711
M-LDL-C 55 1920 188 86 22.6 95.7 39.0 91.1 65.0 0.617
eM-LDL-
58 1977 131 83 30.7 96.0 41.1 93.8 67.5 0.653
C
S-LDL-C 78 2015 93 63 45.6 97.0 55.3 95.6 75.5 0.733

4. 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 [10,27–29] 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
Biomedicines 2022, 10, 3156 15 of 18

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
Biomedicines 2022, 10, 3156 16 of 18

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.

Supplementary Materials: The following supporting information can be downloaded at:

https://www.mdpi.com/article/10.3390/biomedicines10123156/s1, Figure S1: Comparison of
estimated LDL-C versus BQ-LDL-C. LDL-C was calculated for patients (N=2267) with a wide range
of LDL-C values and TG 400–800 mg/dL by the M-LDL-C (panel A), and eM-LDL-C (Panel B) and
plotted against LDL-C as measured by BQ reference method (BQ-LDL-C). Solid lines are the linear
fit for 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. Figure S2.
Residual error plots 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=39,956) with a wide range of LDL-C values
by F-LDL-C (Panel A, E, I, M and Q), M-LDL-C (Panels B, F, J, N and R), eM-LDL-C (Panels C, G, K,
O and S) and S-LDL-C (Panels D, H, L, P and T). 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.
Author Contributions: Conceptualization, M.S., A.W., J.C., R.Z., J.D.O., J.W.M., L.J.D., A.S.J. and
A.T.R.; Data curation, M.S., J.W.M. and L.J.D.; Formal analysis, M.S. and A.T.R.; Funding
acquisition, J.W.M. and A.S.J.; Methodology, J.D.O., J.W.M. and A.T.R.; Project administration,
A.T.R.; Software, M.S.; Supervision, A.T.R.; Visualization, M.S.; Writing—original draft, A.T.R.;
Writing—review and editing, M.S., A.W., J.C., R.Z., J.D.O., J.W.M., L.J.D., A.S.J. and A.T.R. All
authors have read and agreed to the published version of the manuscript.
Funding: Research by A.W., J.D.O. and A.T.R. is supported by intramural research funds from the
National Heart, Lung and Blood Institute under grant number HL006275-01.
Institutional Review Board Statement: Not applicable.
Biomedicines 2022, 10, 3156 17 of 18

Informed Consent Statement: Not applicable.

Data Availability Statement: All data available upon request.
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
apoB Apolipoprotein B
ASCVD Atherosclerotic Cardiovascular Diseases
BQ β-quantification reference method
eM-LDL-C Extended Martin equation for LDL-C
F-LDL-C Friedewald equation for LDL-C
S-LDL-C Sampson equation for LDL-C
LDL-C Low-density lipoprotein-cholesterol
M-LDL-C Martin equation for LDL-C
PCSK9 Proprotein convertase subtilisin/kexin type 9
HTG Hypertriglyceridemia/hypertriglyceridemic

References
1. Ference, B.A.; Ginsberg, H.N.; Graham, I.; Ray, K.K.; Packard, C.J.; Bruckert, E.; Hegele, R.A.; Krauss, R.M.; Raal, F.J.; Schunkert,
H.; et al. Low-density lipoproteins cause atherosclerotic cardiovascular disease. 1. Evidence from genetic, epidemiologic, and
clinical studies. A consensus statement from the European Atherosclerosis Society Consensus Panel. Eur. Heart J. 2017, 38, 2459–
2472.
2. Sniderman, A.D.; Thanassoulis, G.; Glavinovic, T.; Navar, A.M.; Pencina, M.; Catapano, A.; Ference, B.A. Apolipoprotein B
Particles and Cardiovascular Disease: A Narrative Review. JAMA Cardiol. 2019, 4, 1287–1295.
3. Cole, J.; Otvos, J.D.; Remaley, A.T. A Translational Tool to Facilitate Use of Apolipoprotein B for Clinical Decision-Making. Clin.
Chem. 2022. https://doi.org/10.1093/clinchem/hvac161.
4. Grundy, S.M.; Stone, N.J.; Bailey, A.L.; Beam, C.; Birtcher, K.K.; Blumenthal, R.S.; Braun, L.T.; de Ferranti, S.; Faiella-Tommasino,
J.; Forman, D.E.; et al., 2018 AHA/ACC/AACVPR/AAPA/ABC/ACPM/ADA/AGS/APhA/ASPC/NLA/PCNA Guideline on the
Management of Blood Cholesterol: A Report of the American College of Cardiology/American Heart Association Task Force
on Clinical Practice Guidelines. Circulation 2019, 139, e1082–e1143.
5. Chaudhary, R.; Garg, J.; Shah, N.; Sumner, A. PCSK9 inhibitors: A new era of lipid lowering therapy. World J. Cardiol. 2017, 9,
76–91.
6. Everett, M.B.; Smith, R.J.; Hiatt, W.R. Reducing LDL with PCSK9 Inhibitors—The Clinical Benefit of Lipid Drugs. N. Engl. J.
Med. 2015, 373, 1588–1591.
7. Lloyd-Jones, D.M.; Morris, P.B.; Ballantyne, C.M.; Birtcher, K.K.; Covington, A.M.; DePalma, S.M.; Minissian, M.B.; Orringer,
C.E.; Smith, S.C., Jr.; Waring, A.A.; et al. 2022 ACC Expert Consensus Decision Pathway on the Role of Nonstatin Therapies for
LDL-Cholesterol Lowering in the Management of Atherosclerotic Cardiovascular Disease Risk: A Report of the American
College of Cardiology Solution Set Oversight Committee. J. Am. Coll. Cardiol. 2022, 80, 1366–1418.
8. Visseren, F.L.; Mach, F.; Smulders, Y.M.; Carballo, D.; Koskinas, K.C.; Bäck, M.; Benetos, A.; Biffi, A.; Boavida, J.-M.; Capodanno,
D.; et al. 2021 ESC Guidelines on cardiovascular disease prevention in clinical practice: Developed by the Task Force for
cardiovascular disease prevention in clinical practice with representatives of the European Society of Cardiology and 12 medical
societies With the special contribution of the European Association of Preventive Cardiology (EAPC). Eur. Heart J. 2021, 42,
3227–3337.
9. Friedewald, T.W.; Levy, R.I.; Fredrickson, D.S. Estimation of the concentration of low-density lipoprotein cholesterol in plasma,
without use of the preparative ultracentrifuge. Clin. Chem. 1972, 18, 499–502.
10. Wolska, A.; Remaley, A.T. Measuring LDL-cholesterol: What is the best way to do it? Curr. Opin. Cardiol. 2020, 35, 405–411.
11. Hainline, A., Jr. Manual of Laboratory Operations : Lipid and Lipoprotein Analysis, 2nd ed; National Heart and Lung Institute, Lipid
Research Clinics Program, National Insitutes of Health: Bethesda, MD, USA, 1982.
12. Bachorik, S.P.; Ross, J.W. National Cholesterol Education Program recommendations for measurement of low-density
lipoprotein cholesterol: Executive summary. The National Cholesterol Education Program Working Group on Lipoprotein
Measurement. Clin. Chem. 1995, 41, 1414–1420.
13. Nauck, M.; Warnick, G.R.; Rifai, N. Methods for measurement of LDL-cholesterol: A critical assessment of direct measurement
by homogeneous assays versus calculation. Clin. Chem. 2002, 48, 236–254.
14. Fukuyama, N.; Homma, K.; Wakana, N.; Kudo, K.; Suyama, A.; Ohazama, H.; Tsuji, C.; Ishiwata, K.; Eguchi, Y.; Nakazawa, H.;
et al. Validation of the Friedewald Equation for Evaluation of Plasma LDL-Cholesterol. J. Clin. Biochem. Nutr. 2008, 43, 1–5.
Biomedicines 2022, 10, 3156 18 of 18

15. Martin, S.S.; Blaha, M.J.; Elshazly, M.B.; Brinton, E.A.; Toth, P.P.; McEvoy, J.W.; Joshi, P.H.; Kulkarni, K.R.; Mize, P.D.;
Kwiterovich, P.O.; et al. Friedewald-estimated versus directly measured low-density lipoprotein cholesterol and treatment
implications. J. Am. Coll. Cardiol. 2013, 62, 732–729.
16. Sampson, M.; Ling, C.; Sun, Q.; Harb, R.; Ashmaig, M.; Warnick, R.; Sethi, A.; Fleming, J.K.; Otvos, J.D.; Meeusen, J.W.; et al. A
New Equation for Calculation of Low-Density Lipoprotein Cholesterol in Patients With Normolipidemia and/or
Hypertriglyceridemia. JAMA Cardiol. 2020, 5, 540–548.
17. Martin, S.S.; Giugliano, R.; Murphy, S.A.; Wasserman, S.M.; Stein, E.A.; Ceška, R.; Lopez-Miranda, J.; Georgiev, B.; Lorenzatti,
A.J.; Tikkanen, M.J.; et al. Comparison of Low-Density Lipoprotein Cholesterol Assessment by Martin/Hopkins Estimation,
Friedewald Estimation, and Preparative Ultracentrifugation: Insights From the FOURIER Trial. JAMA Cardiol. 2018, 3, 749–753.
18. Brinton, E.A. Management of Hypertriglyceridemia for Prevention of Atherosclerotic Cardiovascular Disease. Endocrinol. Metab.
Clin. North Am. 2016, 45, 185–204.
19. Chung, B.H.; Wilkinson, T.; Geer, J.C.; Segrest, J.P. Preparative and quantitative isolation of plasma lipoproteins: Rapid, single
discontinuous density gradient ultracentrifugation in a vertical rotor. J. Lipid. Res. 1980, 21, 284–291.
20. Martin, S.S.; Blaha, M.J.; Elshazly, M.; Toth, P.P.; Kwiterovich, P.O.; Blumenthal, R.S.; Jones, S.R. Comparison of a Novel Method
vs the Friedewald Equation for Estimating Low-Density Lipoprotein Cholesterol Levels From the Standard Lipid Profile. JAMA
2013, 310, 2061–2068.
21. Sajja, A.; Park, J.; Sathiyakumar, V.; Varghese, B.; Pallazola, V.A.; Marvel, F.A.; Kulkarni, K.; Muthukumar, A.; Joshi, P.H.;
Gianos, E.; et al. Comparison of Methods to Estimate Low-Density Lipoprotein Cholesterol in Patients With High Triglyceride
Levels. JAMA Netw. Open 2021, 4, e2128817–e2128817.
22. Clarke, W.L.; Cox, D.; Gonder-Frederick, L.A.; Carter, W.; Pohl, S.L. Evaluating clinical accuracy of systems for self-monitoring
of blood glucose. Diabetes Care 1987, 10, 622–628.
23. Meeusen, J.W.; Lueke, A.J.; Jaffe, A.S.; Saenger, A.K. Validation of a proposed novel equation for estimating LDL cholesterol.
Clin. Chem. 2014, 60, 1519–1523.
24. Meeusen, J.W.; Snozek, C.L.; Baumann, N.A.; Jaffe, A.S.; Saenger, A.K. Reliability of Calculated Low-Density Lipoprotein
Cholesterol. Am. J. Cardiol. 2015, 116, 538–540.
25. Chicco, D.; Tötsch, N.; Jurman, G. The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy,
bookmaker informedness, and markedness in two-class confusion matrix evaluation. BioData Min. 2021, 14, 13.
26. Stone, N.J.; Robinson, J.G.; Lichtenstein, A.H.; Bairey Merz, C.N.; Blum, C.B.; Eckel, R.H.; Goldberg, A.C.; Gordon, D.; Levy, D.;
Lloyd-Jones, D.M.; et al. 2013 ACC/AHA Guideline on the Treatment of Blood Cholesterol to Reduce Atherosclerotic
Cardiovascular Risk in Adults. Circulation 2014, 129 (Suppl. S2), S1–S45.
27. Ginsberg, H.N.; Rosenson, R.S.; Hovingh, G.K.; Letierce, A.; Samuel, R.; Poulouin, Y.; Cannon, C.P. LDL-C calculated by
Friedewald, Martin-Hopkins, or NIH equation 2 versus beta-quantification: Pooled alirocumab trials. J. Lipid Res. 2022, 63,
100148.
28. Higgins, V.; Leiter, L.A.; Delaney, S.R.; Beriault, D.R. Validating the NIH LDL-C equation in a specialized lipid cohort: Does it
add up? Clin. Biochem. 2022, 99, 60–68.
29. Li, J.; Xin, Y.; Li, J.; Meng, M.; Zhou, L.; Qiu, H.; Chen, H.; Li, H. Evaluation of Sampson equation for LDL-C in acute coronary
syndrome patients: A Chinese population-based cohort study. Lipids Health Dis. 2022, 21, 39.
30. Habeeb, N.M.W.-A.; Higgins, V.; Venner, A.A.; Bailey, D.; Beriault, D.R.; Collier, C.; Adeli, K. Canadian Society of Clinical
Chemists Harmonized Clinical Laboratory Lipid Reporting Recommendations on the Basis of the 2021 Canadian
Cardiovascular Society Lipid Guidelines. Can. J. Cardiol. 2022, 38, 1180–1188.
31. Hopkins, N.P.; Brinton, E.A.; Nanjee, M.N. Hyperlipoproteinemia type 3: The forgotten phenotype. Curr. Atheroscler Rep. 2014,
16, 440.
32. Kulkarni, K.R.; Garber, D.W.; Marcovina, S.M.; Segrest, J.P. Quantification of cholesterol in all lipoprotein classes by the VAP-
II method. J. Lipid Res. 1994, 35, 159–168.
33. Martins, J.; Rossouw, H.M.; Pillay, T.S. How should low-density lipoprotein cholesterol be calculated in 2022? Curr. Opin.
Lipidol. 2022, 33, 237–256.
34. Miller, W.G.; Myers, G.L.; Sakurabayashi, I.; Bachmann, L.M.; Caudill, S.P.; Dziekonski, A.; Edwards, S.; Kimberly, M.M.;
Korzun, W.J.; Leary, E.T.; et al. Seven Direct Methods for Measuring HDL and LDL Cholesterol Compared with
Ultracentrifugation Reference Measurement Procedures. Clin. Chem. 2010, 56, 977–986.
35. Ioannidis, J.P. Why most published research findings are false. PLoS Med. 2005, 2, e124.
36. Glaros, G.A.; Kline, R.B. Understanding the accuracy of tests with cutting scores: The sensitivity, specificity, and predictive
value model. J. Clin. Psychol. 1988, 44, 1013–1023.
37. Shreffler, J.H.M. Diagnostic Testing Accuracy: Sensitivity, Specificity, Predictive Values and Likelihood Ratios. 2022 Updated 9
March 2022. Available online: https://www.ncbi.nlm.nih.gov/books/NBK557491/ (accessed on 17 October 2022).
38. Zhao, J.P.; Hegele, R.A. The impact of low-density lipoprotein equation changes on cholesterol treatment in Canada. CJC Open
2022. https://doi.org/10.1016/j.cjco.2022.09.007.

View publication stats