Evaluation of a new equation for estimating low-density lipoprotein cholesterol through the comparison with various recommended methods

Introduction The accurate estimation of low-density lipoprotein cholesterol (LDL) is crucial for management of patients at risk of cardiovascular events due to dyslipidemia. The LDL is typically calculated using the Friedewald equation and/or direct homogeneous assays. However, both methods have their own limitations, so other equations have been proposed, including a new equation developed by Sampson. The aim of this study was to evaluate Sampson equation by comparing with the Friedewald and Martin-Hopkins equations, and with a direct LDL method. Materials and methods Results of standard lipid profile (total cholesterol (CHOL), high-density lipoprotein cholesterol (HDL) and triglycerides (TG)) were obtained from two anonymized data sets collected at two laboratories, using assays from different manufacturers (Beckman Coulter and Roche Diagnostics). The second data set also included LDL results from a direct assay (Roche Diagnostics). Passing-Bablok and Bland-Altman analysis for method comparison was performed. Results A total of 64,345 and 37,783 results for CHOL, HDL and TG were used, including 3116 results from the direct LDL assay. The Sampson and Friedewald equations provided similar LDL results (difference ≤ 0.06 mmol/L, on average) at TG ≤ 2.0 mmol/L. At TG between 2.0 and 4.5 mmol/L, the Sampson-calculated LDL showed a constant bias (- 0.18 mmol/L) when compared with the Martin-Hopkins equation. Similarly, at TG between 4.5 and 9.0 mmol/L, the Sampson equation showed a negative bias when compared with the direct assay, which was proportional (- 16%) to the LDL concentration. Conclusions The Sampson equation may represent a cost-efficient alternative for calculating LDL in clinical laboratories.


Introduction
The accurate estimation of low-density lipoprotein cholesterol (LDL) blood concentration is very important because large-scale evidence from randomised trials shows that statin therapy reduces the risk of atherosclerotic cardiovascular disease (ASCVD) proportionally to the absolute achieved reduction in LDL concentration (1,2). Consequently, LDL examination is recommended as the primary lipid analysis method for screening, diagnosis, and management of patients at risk of ASCVD due to dyslipidemia. The 2019 European Society of Cardiology/European Atherosclerosis Society (ESC/ EAS) Guidelines for the management of dyslipidemias recommend treating patients to risk-stratified LDL target concentration: < 1.4 mmol/L, < 1.8 mmol/L, < 2.6 mmol/L, and < 3.0 mmol/L, for patients at very-high, high, moderate, and low AS-CVD risk, respectively, with the 10-year risk of fatal ASCVD being estimated using the Systematic Coronary Risk Evaluation (SCORE) (3).

Martínez-Morillo E. et al. Evaluation of a new equation for estimating low-density lipoprotein
The reference method for LDL determination is the combination of ultracentrifugation and heparin-Mn 2+ precipitation, named generically β-quantification (4). However, most clinical laboratories do not use this assay because it is an expensive, laborious, tough and time-consuming method, that also requires large sample volumes (5). Conversely, LDL is typically calculated using the Friedewald equation, which for the general population is fairly accurate and shows a very strong correlation with homogeneous assays for direct LDL determination (6,7). However, calculated LDL underestimates the actual LDL concentration in patients with high triglycerides (TG) concentration (> 2.0 mmol/L), especially if they show low LDL concentrations (8,9). For this reason, many laboratories provide a direct analysis with homogeneous LDL assays at high TG concentrations, but although direct methods are considered a proper alternative to β-quantification, they have their own limitations in terms of reliability and specificity, specially in patients with atypical lipoproteins (10).
To overcome the limitations of the Friedewald equation, new equations have been proposed over the years (11)(12)(13)

Study design
This was a restrospective study where results of standard lipid profile were obtained from two data sets collected at the biochemistry laboratories of: (i) a tertiary-level hospital (Hospital Universitario Miguel Servet (HUMS)) from Zaragoza (Spain), by enzymatic colorimetric assays using the AU5800 (Beckman Coulter Inc, Brea, USA), with data exported from the laboratory information system (LIS) Modulab (Werfen, Barcelona, Spain); (ii) a secondary-level hospital (Hospital del Oriente de Asturias (HOA)) from Asturias (Spain), by enzymatic colorimetric assays with the Cobas c501 (Roche Diagnostics GmbH, Mannheim, Germany), with data exported from the LIS Omega 3000, Roche Diagnostics. The goal of this design was to verify whether the differences observed between the evaluated methods for estimating LDL concentration were consistent, regardless of the laboratory size, the type of hospital and the manufacturer's test kits. Patient data were extracted and an- onymized. Therefore, informed consent and ethical approval were not required.
Results of total cholesterol (CHOL), high-density lipoprotein cholesterol (HDL) and TG from serum samples assayed routinely at HUMS and HOA were collected. The exclusion criteria were: samples without results for any of the three parameters and samples with TG concentration above 9.0 mmol/L. The data set from HOA also included LDL results obtained with a direct assay (LDLC3, Roche Diagnostics), in serum samples with TG concentration ≥ 3.4 mmol/L, according to an internal protocol, since calculated LDL was considered less acurate in these samples. Direct LDL analysis was not performed at HUMS, so data were not available. Data from HUMS were collected between January 2019 and February 2020, while data collection from HOA was extended from January 2015 to December 2019, in order to obtain a similar number of results from both laboratories.

Methods
The equations used to calculate the LDL concentration were: Where f -adjustable value (factor) ranging from 3.1 to 11.9 (results in mg/dL), obtained from the 180-cell factor table (14).

Statistical analysis
Data are presented as numbers and percentages, medians with interquartile ranges (IQR), or mean of differences and mean absolute difference (MAD) with standard deviations. Calculation of LDL concentration with the three equations was performed by using the software  (Table 1).
First, a comparison between the LDL concentration provided by the Sampson, Friedewald, and Martin-Hopkins equations was performed ( Figure 1). Thus, differences in LDL concentration were plotted against the TG concentration range (0-9.0 mmol/L). Figure 1 shows as the differences observed between the calculated LDL, although statistically significant (P < 0.001) due to the large sample size, were very similar when data from HUMS and HOA were used. Thus, for instance, the medians of LDL differences between the Sampson and   On the other hand, a comparison between the calculated LDL concentrations and the direct LDL measurement, at TG between 3.4-4.5 mmol/L and 4.5-9.0 mmol/L, respectively, was performed (Figures 4 and 5). The aim was to compare the performance of these equations at TG concentrations below and above 4.5 mmol/L. Figure 4 shows that the Friedewald equation calculated mostly lower LDL concentrations than those obtained with the direct assay, with differences growing from -0.6 mmol/L to -1.3 mmol/L, on average, as TG concentration increased. The Martin-Hopkins equation estimated more similar LDL concentrations than

Discussion
To our knowledge, this is the first study that evaluates the Sampson equation using real data (> 100,000 results from the standard lipid profile)   (20,21). Thus, discrepancies between homogene-ous assays and β-quantification are found mostly in hypertriglyceridemic subjects, with some studies showing positive but minor biases (< 5%, on average), with no consistent pattern for the frequency of discordant LDL results with triglyceride concentration (22)(23)(24). Therefore, the negative bias observed in this study with the Sampson equation when compared with the Martin-Hopkins-calculated LDL and with the directly measured LDL concentrations may not be extensible to the reference method or it is probably less. Sampson et al. also found that the Martin-Hopkins equation, which is based on the Vertical Auto Profile test (an ultracentrifugation density-based separation procedure different to the reference method), misclassified 31.9% of patients with TG concentration between 4.5-9.0 mmol/L into some treatment categories, mainly falsely increasing the LDL result. However, the Sampson equation had a total error of 22.3%, with patients been misclassified in both ways, by falsely increasing or decreasing the LDL result (19).
In conclusion, this study shows that the Sampson equation can be implemented in clinical laboratories, providing an acceptable performance. This equation has several advantages: (i) It can replace the Friedewald equation, since at low TG concentrations (≤ 2.0 mmol/L), when Friedewald equation is trustable, both equations calculate very similar LDL concentrations; (ii) Although this equation is more complicated than other previously published, it can be automatically calculated by most LIS, unlike the Martin-Hopkins equation; (iii) It can be used in patients with TG concentration up to 9.0 mmol/L, saving costs and complying the EAS/ EFLM recommendation to use the same method for on-treatment follow-up, to attenuate errors in treatment decisions due to marked betweenmethods variations (7,25,26). The main disadvantages are: (i) The Sampson-calculated LDL depends upon three laboratory assays (CHOL, HDL, and TG), meaning that three measurement errors are involved which inevitably introduce calculation variability. However, we have obtained very similar results using data from two laboratories obtained with assays from different manufacturers; (ii) The equation appears to have a negative proportional bias respect to the direct assay. The main limitation of this study was not having LDL results obtained by the reference method. However, the obtained results will allow clinical laboratories to estimate which differences could be found if they decide to implement this new equation, based on β-quantification, into their daily routine.