A Novel LDLC Equation is Superior to the NIH LDLC Equation and the Friedewald Equation

Introduction

A lipid panel that includes triglycerides (TGs), total cholesterol (TC), high-density lipoprotein (HDL) cholesterol (HDLC), and low-density lipoprotein (LDL) cholesterol (LDLC)¹ is used worldwide for routine testing to determine your cholesterol status. Routinely, the LDLC level is estimated by calculation using a formula (eg, the NIH LDLC (LDL_NIH) equation² and the Friedewald (LDL_F) equation).³ However, direct measurement of LDLC is not a routine cholesterol test.⁴ Research indicates⁵ that the direct measurement of LDLC is important for information about CVD risk. However, its advantages are modest when comparing it to LDLC levels calculated using a formula. Because the LDLC calculated formula is a reliable and cost-effective method for routine cholesterol tests,⁶ the LDLC calculated formula still needs to be optimized and improved. We read with interest an article titled “Validating the LDL_NIH equation in a specialized lipid cohort: Does it add up?” by Victoria Higgins et al that was published in Clinical Biochemistry.⁷ The authors focused on which calculation equation is better for LDLC and concluded that the LDL_NIH equation was superior to the LDL_F equation based on ultracentrifugation LDLC. Is this true? It can be seen from the cohort of equations we established that the LDLC calculated by the LDL_NIH and LDL_F equations is lower than that measured by the direct method (Table 1).

Table 1 The Characteristics of Establishment of the LDLC Equation Group

Hence, we established an LDLC equation for estimating LDLC levels using cohorts of healthy individuals base on the direct measurement of LDLC and compared the novel LDLC equations, the LDL_NIH equation, and the LDL_F equation for use in other unselected patient cohorts.

Materials and Methods

Study Cohort and Data Extraction

We obtained a large cohort of data from routine check-ups of healthy individuals from the Shuyang Hospital laboratory information system for retrospective analysis by retrieving the results of serum TC, HDLC, LDLC, and TG tests that were performed over several months (from Jan 2019 to December 2019) to establish an equation group based on health standards from the literature.⁸ Another larger cohort of unselected patient data from Jan 2022 to August 2022 was used for the validation group from The Second People’s Hospital of Lianyungang. LDL_F=TC-HDLC-TG/2.2, in mmol/L.³ LDL_NIH=TC/0.948-HDLC/0.971-TG/3.74-TG*nonHDLC/24.16+TG*TG/79.36–0.244, in mmol/L.⁷ TG*nonHDLC/24.16+TG*TG/79.36–0.244, in mmol/L. This study was approved by the Ethics Committee of Medicine, Shuyang Hospital. The study accordented with the Declaration of Helsinki.

Laboratory Methods and Instruments

Serum TG (GPO-POD method), TC (Enzymatic method), HDLC (direct clearance method), and LDLC (direct clearance method) levels were measured with an AU5800 Modular System (Beckman Coulter, Inc., America). Calibration and verification (TG, TC, HDLC, and LDLC) of the instrument were performed annually, which also included reportable range, precision, and trueness (Table 2). A regular external quality assessment scheme and regular internal quality control procedures were performed throughout the study period. The ethics committee of Shuyang Hospital approved this study.

Table 2 Instrument Performance Parameters (TG, TC, HDL-C, and LDL-C) of AU5821 Chemistry Analyzer

Statistical Analysis

NonHDLC was calculated as TC minus HDLC.⁹ The relationship between two markers was analysed using Spearman’s approach. Establishment of the novel LDLC equations was performed by using the regression equation (y=a + b*x + c*x²) based on the direct measurement of LDLC levels as the reference method. Agreement of the LDLC equations was determined by using Bland‒Altman plot. ROC curve analysis was used to predict LDLC and the accuracy of the LDLC equation for direct LDLC levels at LDLC cut-offs (1.55 mmol/L, 1.80 mmol/L, 2.60 mmol/L, 3.36 mmol/L, 4.12 mmol/L, and 4.90 mmol/L).⁹ We performed statistical analyses by using MedCalc Version 18.1.1 (MedCalc Software, Ostend, Belgium) and Excel Version 2019 (Armonk, NY, USA). A p value below 0.01 was considered statistically significant.

Results

Establishing the LDL_nonHDLC Equation and LDL_TC Equation

The lipid profiles, including the TG, TC, HDLC, and LDLC levels, of 23,226 consecutive healthy individuals were measured at the laboratory of Shuyang Hospital between Jan 1, 2019, and Dec 31, 2019. Among these 23,226 patients, 16,143 individuals had a TG level below 1.71 mmol/L (Table 1 and Figure 1), We established two novel LDLC equations (LDL_nonHDLC =−0.899+1.195*nonHDLC-0.00347*nonHDLC² and LDL_TC =−2.775+1.29*TC-0.00990*TC²) (Figure 2) for predicting TC and nonHDLC levels for various abnormal direct LDLC levels (>1.55 mmol/L, >1.80 mmol/L, >2.60 mmol/L, >3.36 mmol/L, >4.12 mmol/L, and >4.90 mmol/L) by using ROC curve analysis from 19,643 individuals. We obtained 6 points of different TC and nonHDLC with different LDLC levels.

Figure 1 The characteristics of the participants included in the construction of the novel LDLC equations. Abbreviations: TC, total cholesterol; HDL, high-density lipoprotein cholesterol; LDL, low-density lipoprotein cholesterol; TG, triglycerides, in mmol/L.

Figure 2 We obtained two novel LDLC equations. Abbreviations: Direct_LDLC and LDL-C (direct clearance method) were tested with an AU5800 Modular System (Beckman Coulter, Inc., America). TC, total cholesterol; HDL, high-density lipoprotein cholesterol; NonHDLC=TC-HDL, in mmol/L.

Validating That the LDL_nonHDLC Equation and LDL_TC Equation are Superior to the LDL_NIH Equation

The unselected outpatient cohort (Figure 3) included 21,168 subjects.

Figure 3 The histogram of the characteristics of the unselected patient cohort. Abbreviations: TC, total cholesterol; HDL, high-density lipoprotein cholesterol; LDL, low-density lipoprotein cholesterol; TG, triglycerides; LDL_F, LDL-C calculated using the Friedewald equation; LDL_NIH, LDL-C calculated using the NIH equation; LDL_nonHDLC-equation=−0.899+1.195*nonHDLC-0.00347*nonHDLC2 and LDL_TC-equation=−2.775+1.29*TC-0.00990*TC2, in mmol/L.

LDL_F, LDL_NIH, LDL_nonHDLC, and LDL_TC levels were significantly positively correlated with direct LDLC levels (Figure 4).

Figure 4 Scatter plots for the direct low-density lipoprotein cholesterol (LDLC) and LDLC equations. Their relationship was analysed using Spearman’s approach. Abbreviations: LDL (direct clearance method) was tested with an AU5800 Modular System (Beckman Coulter, Inc., America); LDL_F, LDL-C calculated using the Friedewald equation; LDL_NIH, LDL-C calculated using the NIH equation; LDL_nonHDLC-equation=−0.899+1.195*nonHDLC-0.00347*nonHDLC2 and LDL_TC-equation=−2.775+1.29*TC-0.00990*TC2, in mmol/L.

Figure 5 shows the ROC curves of LDL_F, LDL_NIH, LDL_nonHDLC, and LDL_TC for predicting the 6 different direct LDLC levels. As listed in Figure 5, these novel LDLC equations (LDL_nonHDLC and LDL_TC equations) are superior to the LDL_NIH equation and the Friedewald equation.

Figure 5 Receiver operating characteristic curves of the LDLC equations for predicting direct low-density lipoprotein cholesterol (direct LDLC levels are >1.55 mmol/L, >1.80 mmol/L, >2.60 mmol/L, >3.36 mmol/L, >4.12 mmol/L, and >4.90 mmol/L). Abbreviations: LDL (direct clearance method) was tested with an AU5800 Modular System (Beckman Coulter, Inc., America); LDL_F, LDL-C calculated using the Friedewald equation; LDL_NIH, LDL-C calculated using the NIH equation; LDL_nonHDLC-equation=−0.899+1.195*nonHDLC-0.00347*nonHDLC2 and LDL_TC-equation=−2.775+1.29*TC-0.00990*TC2, in mmol/L.

The Bland‒Altman plot (Figure 6) showed that the number of overestimated LDLC and underestimated LDLC of LDL_F and LDL_NIH was greater than that of LDL_nonHDL and LDL_TC. Overestimation with LDL_F and LDL_NIH occurred at low LDLC levels, and several paired data points fell below 5 mmol/L.

Figure 6 Bland‒Altman plot of LDLC from four LDLC equations. Abbreviations: LDL (direct clearance method) was tested with an AU5800 Modular System (Beckman Coulter, Inc., America); LDL_F, LDL-C calculated using the Friedewald equation; LDL_NIH, LDL-C calculated using the NIH equation; LDL_nonHDLC-equation=−0.899+1.195*nonHDLC-0.00347*nonHDLC2 and LDL_TC-equation=−2.775+1.29*TC-0.00990*TC2, in mmol.

Discussion

Here, we describe the performance of the Friedewald equation, the LDL_NIH equation, and two novel LDL equations in the clinical setting using direct-LDL (direct clearance method) as a reference method. This study has three novel aspects: 1) it is the first publication to use ROC for establishing LDL-equations using direct-LDL as a reference method, 2) the overestimation for LDLC is better than the underestimation from three different perspectives of analysis for clinical significance, and 3) we established the equations with a healthy cohort and validated the equations with an unselected patient cohort.

In this study, we analysed direct LDLC measurements and LDLC equations and their correlations in a large, unselected outpatient cohort. We found that the novel LDLC equations were positively correlated with direct LDLC measurements, and the correlation coefficient between the novel LDLC equation and direct LDLC measurements was greater than the correlation coefficient between the NIH LDLC equation and the Friedewald equation and the direct LDLC measurements. The ROC of these four LDLC-equations at the cutoffs of clinical decision limits of 1.55 mmol/L, 1.80 mmol/L, 2.60 mmol/L, 3.36 mmol/L, 4.12 mmol/L, and 4.90 mmol/L indicated that the AUC of our novel LDLC-equations were greater than the AUCs of the NIH LDLC-equation and the Friedewald equation. Our results are consistent with Victoria Higgins’s findings.⁷

However, all LDLC equations overestimate and underestimate LDLC.¹⁰ Underestimating results in a false negative, a misdiagnosis, and this is undesirable.^10,11 Overestimation results in a false-positive and can be corrected by using more specific methodologies. Therefore, underestimation should be avoided as much as possible. As the Bland–Altman plot in Figure 5 shows, among the 21,168 paired LDL_F and LDL_NIH equation LDLC levels, several results underestimated the direct-LDLC levels by more than 5 mol/L, and LDL_nonHDL and LDL_TC did not. Combining the NIH LDLC equation and our novel LDLC equation may improve accuracy while avoiding underestimation to avoid undertreatment of high LDLC levels.¹¹ In clinical practice, the method with a relatively overestimated LDLC equation should be selected as the first method, and the direct LDLC method should be used after it exceeds the standard.

When LDLC cannot be calculated from the LDLC equations, a direct-LDLC test is used. We can calculate LDLC through a laboratory information system based on a lipid panel. Our lab automatically performs a direct-LDLC analysis when TGs are high, or a doctor may request direct-LDLC measurement if you have a history of high LDLC calculated from the LDLC-equation or high TG. When the calculated LDLC level is high or the TG level is high, a reflex direct-LDLC test is automatically performed by a full duplex system consisting of a laboratory information system and biochemical analyser.¹²

There is a limitation in this study. The reference method of LDLC is direct-LDL (direct clearance method).

The results of the present study indicate that our novel LDLC equations may be superior to the LDL_NIH equation. To the best of our knowledge, this study is the first to establish LDLC equations by using ROC curve analysis. The novel LDLC equation may be suitable for other labs. However, because of different detection systems and different subjects, the novel LDLC equation may be slightly differ across all clinics.

In summary, LDLC calculated by the novel LDLC equation exhibited superiority over the NIH equation in terms of their correlations with direct LDLC, and this was concordant with the direct LDLC levels at the LDLC cut-offs. The LDL_NIH equation and our novel equations can be utilized to calculate LDLC and replace the Friedewald equation. Combining the NIH LDLC equation and our novel LDLC equation may improve accuracy and avoid the underestimation of high LDLC levels. Our study demonstrated that the strategy in this study is worth promoting.