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An improved method for estimating low LDLC based on the enhanced SampsonNIH equation
Lipids in Health and Disease volume 23, Article number: 43 (2024)
Abstract
Background
The accurate measurement of Lowdensity lipoprotein cholesterol (LDLC) is critical in the decision to utilize the new lipidlowering therapies like PCSK9inhibitors (PCSK9i) for highrisk cardiovascular disease patients that do not achieve sufficiently low LDLC on statin therapy.
Objective
To improve the estimation of low LDLC by developing a new equation that includes apolipoprotein B (apoB) as an independent variable, along with the standard lipid panel test results.
Methods
Using βquantification (BQ) as the reference method, which was performed on a large dyslipidemic population (N = 24,406), the following enhanced SampsonNIH equation (eS LDLC) was developed by leastsquare regression analysis:
Results
The eS LDLC equation was the most accurate equation for a broad range of LDLC values based on regression related parameters and the mean absolute difference (mg/dL) from the BQ reference method (eS LDLC: 4.51, SampsonNIH equation [S LDLC]: 6.07; extended Martin equation [eM LDLC]: 6.64; Friedewald equation [F LDLC]: 8.3). It also had the best areaunderthecurve accuracy score by Regression Error Characteristic plots for LDLC < 100 mg/dL (eS LDLC: 0.953; S LDLC: 0.920; eM LDLC: 0.915; F LDLC: 0.874) and was the best equation for categorizing patients as being below or above the 70 mg/dL LDLC treatment threshold for adding new lipidlowering drugs by kappa score analysis when compared to BQ LDLC for TG < 800 mg/dL (eS LDLC: 0.870 (0.853–0.887); S LDLC:0.763 (0.749–0.776); eM LDLC:0.706 (0.690–0.722); F LDLC:0.687 (0.672–0.701). Approximately a third of patients with an F LDLC < 70 mg/dL had falsely low test results, but about 80% were correctly reclassified as higher (≥ 70 mg/dL) by the eS LDLC equation, making them potentially eligible for PCSK9i treatment. The M LDLC and S LDLC equations had less false low results below 70 mg/dL than the F LDLC equation but reclassification by the eS LDLC equation still also increased the net number of patients correctly classified.
Conclusions
The use of the eS LDLC equation as a confirmatory test improves the identification of highrisk cardiovascular disease patients, who could benefit from new lipidlowering therapies but have falsely low LDLC, as determined by the standard LDLC equations used in current practice.
Background
Cholesterol carried by lowdensity lipoproteins (LDLC) is a key risk marker for Atherosclerotic Cardiovascular Disease (ASCVD) [1] and is commonly calculated based on test results from the standard lipid panel (total cholesterol [TC], highdensity lipoproteincholesterol [HDLC] and triglycerides [TG]) [2]. Until recently, LDLC was almost exclusively calculated by clinical laboratories with the Friedewald equation (F LDLC) [3]. The premise of this calculation method is that in plasma from fasting patients, only three types of lipoprotein particles transport cholesterol, namely LDL, HDL and very lowdensity lipoproteins (VLDL) [4]. A key part of the equation is the estimation of VLDLC, which is done by dividing the concentration of TG by 5 when in mg/dL units. To calculate LDLC, one then simply subtracts the cholesterol that is on HDL and VLDL from TC (LDLC = TC – HDLC – TG/5). By using this formula, it avoids the need for the separation of lipoproteins by ultracentrifugation and allowed for the first time the routine reporting of LDLC by clinical laboratories [3].
In 2013, a more accurate equation called the MartinHopkins equation (M LDLC) was developed [5]. This equation is nearly identical to the F LDLC equation, but it uses a series of variable factors instead of the fixed factor of 5 as the TG denominator for estimating VLDLC. This series of factors can be found in a 180cell table that is grouped by different TG and nonHDLC intervals. These factors were empirically determined based on the Vertical Auto Profile (VAP) ultracentrifugation method [6]. The extended MartinHopkins equation (eM LDLC) uses an additional set of factors for samples with a TG between 400 to 800 mg/dL [5, 7].
In 2020, a bivariate quadratic equation that depends upon nonHDLC and TG was described for estimating VLDLC, which became part of what is known as the SampsonNIH equation for LDLC (S LDLC) [8]. Compared to all other equations, LDLC calculated by this method, particularly for hypertriglyceridemic samples, matched the closest to the βquantitation (BQ) reference method [9, 10], which is used for the standardization of routine diagnostic assays for LDLC.
Besides the ratio of cholesterol to TG, lipoprotein particle number and their sizes are other important determinants for the cholesterol carrying capacity of lipoproteins. Apolipoprotein B (apoB), the main structural protein on LDL and VLDL, is present as a single copy per lipoprotein particle, and hence it can be used to estimate the total number of apoBcontaining lipoprotein [11]. We recently included apoB as an independent variable for improving the estimation of VLDLC in order to diagnose Type III dysbetalipoproteinemia [12], which is characterized as having cholesterol enriched VLDL particles [13].
In this study, we examined whether we could also improve the accuracy for estimating low LDLC with the use of apoB as an independent variable. The clinical rationale for developing a new equation is that with the use of the new more effective lipidlowering drug therapies, it is becoming more common to see patients with extremely low levels of LDLC. In addition, US guidelines recommend that for the secondary prevention of ASCVD, patients should be treated with a proprotein convertase subtilisin/kexin type inhibitor (PCSK9i) and or another type of lipidlowering therapy in conjunction with a statin in order to reach an LDLC below at least 70 mg/dL [1]. For some highrisk patients, even lower LDLC target goals have recently been recommended by some guidelines [14, 15]. The relatively high cost of PCSK9i therapy, however, can create a barrier to reimbursement by insurance companies [16]. The negative bias of the F LDLC equation, particularly for hypertriglyceridemic patients, can lead to falsely low results below the 70 mg/dL target treatment threshold, which can mislead healthcare providers on the eligibility of patients for PCSK9i therapy. Although the newer LDLC equations are more accurate than the F LDLC equation, they are still not as widely used and still have less than ideal accuracy at low LDLC values [9]. The direct measurement of LDLC by homogenous assays may be useful for patients with low LDLC, but they are frequently not offered by clinical laboratories and or can have their own analytical challenges [17]. Therefore, we investigated here whether measuring apoB and including it in a new equation called the enhanced SampsonNIH (eS LDLC) equation can improve the estimation of low LDLC, particularly for highrisk patients who are possibly candidates for new lipidlowering therapies.
Methods
Deidentified lipid and apoB test results from patients for whom the tests were ordered for routine medical care from the Mayo Clinic were used for analysis as previously described [18, 19]. LDLC and other lipid tests were determined by the BQ reference method (N = 39,874) [8]. ApoB was measured in a subset of this population (N = 24,406), using an immunoturbidometric assay on a Cobas c501 analyzer (Roche Diagnostics, IN). Research under this study was considered nonhuman subject research and exempted from IRB review.
The eS LDLC equation was established by least square regression analysis on a randomized training dataset of BQ LDLC test results (N = 12,196) and then tested on a separate validation dataset of BQ LDLC results (N = 12,210). The minimum and maximum of lipid values for the BQ LDLC training dataset are as follows: (HDLC: 2–201 mg/dL, TC: 27–811 mg/dL, TG: 5–1471 mg/dL, nonHDLC: 12–777 mg/dL, BQ LDLC: 9–593 mg/dL, and apoB: 5–401 m/dL)). Regression Error Characteristic analysis was performed as previously described [20]. The agreement between the various LDLC equations with BQ LDLC for classifying patients above and below 70 mg/dL was assessed by the calculation of Kappa scores [21]. LDLC was calculated by the various equations as per their original descriptions [3, 7, 8].
All data analysis was done with JMP software (JMP, Cary, NC) or by Excel (Microsoft, Redmond, WA). Data for key findings and a spreadsheet for performing the new eS LDLC calculation can be downloaded at the NHLBI Fig Share website by searching under the name Sampson.
Results
The new eS LDLC equation was established by least squares regression analysis (Fig. 1), using BQ LDLC as the reference method. As can be seen below, the new equation contains all the same individual variables based on the standard lipid panel like the original Sampson equation but the coefficients for the variables differ. It also contains a new variable for apoB and a new interaction term between apoB and TG.
When the eS LDLC equation was applied to the validation dataset (Fig. 2A), it showed similar accuracy based on standard regression parameters (correlation coefficient [R^{2}], root mean square error [RMSE], and mean absolute difference [MAD]) as the training dataset, indicating that the new equation was not overfitted. Notably, it also matched much better to the BQ LDLC reference method than the original S LDLC equation or when compared to the eM LDLC or F LDLC equations (Fig. 2BD). Unlike the F LDLC equation, it did not result in any nonsensical negative LDLC values for high TG samples. In addition, LDLC from patients with Type III dysbetalipoproteinemia (gray triangle symbols), which showed a clear positive bias for the three other equations, appeared closer to the regression line for the eS LDLC equation.
Next, we determined with the validation dataset the MAD values for different intervals of the independent variables used in the various LDLC equations (Fig. 3). The F LDLC equation showed the largest bias compared to the other equations for hypertriglyceridemic samples, and hence the longstanding recommendation to not use this equation when TG > 400 mg/dL. The eS LDLC equation maintained better accuracy as TG increased compared to other equations. Its MAD scores for TG values up to 1500 mg/dL remained below the maximum recommended error of 25 mg/dL (see solid line), which was established based on the observed error limit found for the F LDLC equation at a TG of 400 mg/dL. Based on this same error limit, S LDLC appears to be suitable for TG values up to 800 mg/dL as previously described [8], whereas the eM LDLC equation exceeded this error limit for TG values slightly greater than 600 mg/dL. A closer examination of lower TG values (see inset) shows that the accuracy advantage of the eS LDLC equation over the other equations approximately starts at TG values greater than 200 mg/dL.
Similar findings, in regard, to the superior accuracy of the eS LDLC equation were found when the other independent variables were examined (Fig. 3). For nonHDLC, the eM LDLC equation showed the greatest bias and based on the 25 mg/dL error limit goal, it should not be used when nonHDLC > 350 mg/dL (Fig. 3B). With respect to HDLC, the F LDLC equation showed the greatest bias when HDLC was low and exceeded the 25 mg/dL error limit when HDLC < 20 mg/dL (Fig. 3C). Not unexpectedly, because it is the only equation that utilizes apoB as an independent variable, the eS LDLC equation showed the lowest MAD scores across a broad range of apoB values (Fig. 3D), although like the other equations its accuracy deteriorated as apoB increased.
In Fig. 4, we compared the accuracy of the different equations by Regression Error Characteristic analysis [20]. When the complete validation dataset was analyzed, the eS LDLC equation was the most accurate and the F LDLC the least accurate, which can be seen by a visual inspection of the plots or by comparing the AUC values of each equation (Fig. 4A). When we only analyzed LDLC values below 100 mg/dL (Fig. 4B), an even greater accuracy advantage was observed for the eS LDLC equation over the other equations. The eS LDLC equation also provided superior accuracy when evaluating result in samples with either moderately or highly elevated triglycerides (Fig. 4C, D, respectively).
Next, we compared the different equations for estimating low LDLC values by restricting the analysis to those patients with an LDLC < 100 mg/dL and a TG < 800 m/dL. As before when a broader set of LDLC values were tested, the eS LDLC equation had the best linear regressionbased parameters of accuracy for low LDLC samples when compared to BQ LDLC (Fig. 5). Notably, the eS LDLC equation had a slope of nearly 1.0 and an intercept of almost zero. A clear negative bias could be observed for the F LDLC equation for high TG samples, whereas a positive bias for these same samples were observed for the eM LDLC equation. This was less apparent when only samples with TG < 400 mg/dL were analyzed (Supplemental Figure 1).
In Table 1, we tabulated the different types of classification errors by the standard LDLC equations and the new eS LDLC equation for categorizing patients as being above or below the 70 mg/dL cutpoint. True positives were defined as correctly identifying patients as being below the 70 mg/dL treatment threshold based on the BQ LDLC test result. Sensitivity (for detecting patients with LDLC < 70 mg/dL), and specificity, as well as positive predictive value (PPV) and negative predictive value (NPV) were calculated. As expected because of its negative bias, the F LDLC equation showed the best sensitivity, but it had the lowest specificity. Correspondingly, it had the lowest PPV but a relatively high NPV. The eS LDLC equation had the highest specificity at all three TG levels with a sensitivity almost as high as the F LDLC equation. Based on the normalized Matthews Correlation Coefficient (nMCC), which combines sensitivity and specificity to obtain a single metric of accuracy [22], the eS LDLC equation had the highest overall accuracy for all three TG levels, followed by the S LDLC, eM LDLC and F LDLC equations. A similar rank order in accuracy was also found for the LDLC equations when assessed for their agreement to the BQ reference method by their kappa scores (Fig. 6), another way to determine overall test accuracy [21].
In Fig. 7, we examined the impact of first measuring LDLC by the three currently used LDLC equations in routine practice and then subsequently confirming the result with the eS LDLC equation to simulate what might be done before deciding whether a highrisk patient is truly eligible or not for PCSK9i therapy. Based on BQ reference method, in about a third of patients with TG < 400 mg/dL, an LDLC result below 70 mg/dL by the F LDLC equation was falsely low (Fig. 5A). An even greater fraction of patients had falsely low test results by the F LDLC equation when samples with TG up to 800 mg/dL were analyzed (Fig. 5B). When the eS LDLC equation was applied to these patients, approximately 80% of the patients with falsely low results below 70 mg/dL were correctly reclassified as being higher, making them potentially eligible for PCSK9i therapy. The application of the eS LDLC equation, however, resulted in a decrease in the number of truly low test results from 1011 to 949 (Fig. 5A, TG < 400 mg/dL), which could result in some highrisk patients unnecessarily receiving PCSK9i therapy. There was, however, an overall net gain of 340 patients (Fig. 5A, TG < 400 mg/dL) that were correctly identified as being eligible for PCSK9i therapy by the eS LDLC equation. Similarly, the use of the eS LDLC equation as a confirmatory test also decreased the number of falsely low results when applied to the M LDLC (Fig. 6C) and S LDLC (Fig. 6D) equations for TG values up to 800 mg/dL, but to a lesser degree than for the F LDLC equation, because these newer equations had less falsely low results to begin with. Like for the F LDLC equation, using the eS LDLC equation as a confirmatory test resulted in net gain of correctly classified patients for these other two equations as well. Consistent with its higher PPV but lower NPV (Table 1), the eM LDLC equation had a lower number of false low test results than the S LDLC equation but also a lower number of true low test results.
Discussion
In this study, we describe the development and validation of a new equation for LDLC that includes apoB as an independent variable. The new eS LDLC equation outperforms, in terms of accuracy, all the other commonly used equations for calculating LDLC. It is suitable for samples with TG values up 1500 mg/dL, which is much higher than the other equations. It also had the best performance in patients with low LDLC.
In the United States, nearly 9 million adults with ASCVD fail to achieve optimal LDLC levels, despite the use of maximally tolerated statin therapy [23]. It is currently recommended that highrisk patients that do not attain an LDLC value below 70 mg/dL be treated with an additional lipidlowering drugs, such as PCSK9i therapy [1]. When it was first approved by the FDA, as many as half to three quarters of all eligible patients were initially denied insurance coverage for PCSK9i therapy [24]. Although the current reimbursement situation is much improved, highrisk patients with a falsely low LDLC below 70 mg/dL are still not likely to receive this relatively expensive treatment if the current guidelines and eligibility criteria for reimbursement are strictly followed. Due to the recognized limitations of the F LDLC equation, particularly its negative bias in hypertriglyceridemia patients, the USMultiSociety cholesterol guidelines recommended in 2018 [1] the use of either a direct LDLC test or the M LDLC equation for low LDLC values to mitigate this problem.
In 2020, the S LDLC equation was developed and like the M LDLC equation, it is more accurate than the F LDLC equation, particularly for patients with hypertriglyceridemia [8, 9]. It differs from the M LDLC equation in that it was developed using the BQ reference method, a swinging bucket ultracentrifuge procedure that also includes an LDL precipitation step. All routine diagnostic assays for LDLC are standardized against this reference method by the Centers for Disease Control and Prevention (CDC). It should be noted that the BQ reference method for LDLC can sometimes include cholesterol from Lp(a) and from some denser remnant particles, but these lipoprotein subfractions are also believed to be proatherogenic. The M LDLC equation used the VAP method as its reference method, a rapid ultracentrifugation method that can result in the under recovery of VLDLC on hypertriglyceridemic samples [6, 13], leading to an overestimation of LDLC. When compared against the BQ reference method, the S LDLC equation is slightly more accurate than the original Martin or eM LDLC equations [8,9,10]. It still, however, has less than ideal accuracy for low LDLC samples [9], which prompted us to develop the new eS LDLC equation.
Not unexpectedly, the inclusion of apoB as an independent variable in the eS LDLC equation substantially improved its accuracy. It likely does so by providing the particle count of all apoBcontaining lipoproteins. Although, this includes not only LDL but also VLDL particles (or remnants), the great majority of apoB is on LDL for most patients. Thus, inclusion of apoB likely improved the prediction of LDLC by providing information related to the number of LDL particles present. ApoB, however, does not provide information related to the size of lipoprotein particles, another important determinant of the cholesterol carrying capacity of lipoproteins, but this information is provided, at least in part, by the total TG level, which is used in the new equation. When TG are greatly elevated as in patients with Type I hyperlipidemia [25], very large size VLDL particles or chylomicrons (in nonfasting samples) are markedly increased from deficient lipolysis, but because of their high TG carrying capacity, the concentration of apoB may not be correspondingly increased [11]. In contrast, apoB is typically elevated in patients with moderate hypertriglyceridemia, because of the increased number of small dense LDL particles in these patients due to CETPmediated lipid exchange and the subsequent increased lipolysis of LDL [26]. LDLC, however, is often normal or even decreased as measured by the BQ reference method or by other methods in patients with moderate hypertriglyceridemia. This is because large size LDL particles, which are inversely related to the TG level, typically account for the majority of the cholesterol that is transported on LDL. Thus, the use of apoB for estimating LDLC adjusts for this complex relationship between TG and LDLC and improves the accuracy of the eS LDLC equation.
A major limitation of our new equation is that it involves additional laboratory testing, namely the measurement of apoB, and hence increases the cost for estimating LDLC compared to the other equations. If used, however, as described in this study to only confirm low LDLC values below 70 mg/dL on highrisk patients being considered for adding new lipidlowering therapy, it would not increase overall costs too much because of the relatively low number of these type of patients. It is also worth noting that many studies have now shown that apoB and nonHDLC are superior to LDLC for ASCVD prediction and monitoring [27, 28]. Furthermore, treatment to apoB target goals, which typically involves more aggressive lipidlowering therapy, reduces ASCVD events to a greater extent than treatment goals based on LDLC [10, 21, 28, 29]. Eventually, LDLC should possibly be replaced with apoB or another more predictive biomarker, but in the meantime until guidelines change and insurance companies change their reimbursement policies, using apoB in the eS LDLC equation for reducing the number of patients with falsely low LDLC can be a useful interim approach. It is also worth noting that the cost of apoB testing is relatively trivial (typically under 50 US dollars) compared to the cost of PCSK9i therapy, which typically costs several thousand dollars a year and are usually recommended for the life of a patient [30, 31].
Conclusions
The eS LDLC equation, which utilizes apoB as an independent variable, is the most accurate method for estimating LDLC. When used to confirm low LDLC values that were first determined by any of the three commonly used LDLC equations in routine practice, it can reduce the number of highrisk patients with falsely low LDLC results, who may not otherwise be treated with the new more effective and potentially lifesaving lipidlowering therapies. Furthermore, the more accurate measurement of LDLC with the use of apoB should improve the adherence to current guidelines for using PCSK9i therapy based on LDLC values, and should, therefore, be cost effective [30] and reduce ASCVD events, which costs the healthcare system in the US between 30–40 billion dollars a year.
Availability of data and materials
Data for key findings and a spreadsheet for performing the new eS LDLC calculation can be downloaded at the NHLBI Fig Share website by searching under the name Sampson.
Abbreviations
 LDLC:

Lowdensity lipoprotein cholesterol
 PCSK9:

Proprotein convertase subtilisin/kexin type 9
 PCSK9i:

PCSK9 inhibitors
 eS LDLC:

Enhanced SampsonNIH equation
 BQ:

β Quantification reference method
 S LDLC:

SampsonNIH equation
 F LDLC:

Friedewald equation
 M LDLC:

MartinHopkins equation
 eM LDLC:

Extended MartinHopkins equation
 ASCVD:

Atherosclerotic Cardiovascular Disease
 TC:

Total cholesterol
 HDLC:

Highdensity lipoproteincholesterol
 TG :

Triglycerides
 VLDL:

Very lowdensity lipoproteins
 VAP:

Vertical Auto Profile
 apoB:

Apolipoprotein B
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Additional file 1: Supplemental Figure 1.
Comparison of estimated LDLC versus BQLDLC at low levels. LDLC was calculated in patients with LDLC ≤ 100 mg/dL and TG ≤ 400 mg/dL by FLDLC (Panel A, N=9,483), eMLDLC (Panel B, N=9,483), SLDLC (Panel C, N=9,483), and eSLDLC (Panel D, N=3,894) equations and plotted against LDLC as measured by BQ reference method (BQLDLC). 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 values indicated in the legend (mg/dL).
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Coverdell, T.C., Sampson, M., Zubirán, R. et al. An improved method for estimating low LDLC based on the enhanced SampsonNIH equation. Lipids Health Dis 23, 43 (2024). https://doi.org/10.1186/s1294402402018y
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DOI: https://doi.org/10.1186/s1294402402018y