Refining the Martin-Hopkins method for estimating low-density lipoprotein cholesterol levels: Median versus optimal TG/VLDL-C ratio

Abstract

Background: Low-density lipoprotein cholesterol (LDL-C), a major modifiable risk factor for cardiovascular diseases, is typically calculated using the Friedewald formula when triglyceride (TG) levels are below 400 mg/dL. Recent studies have demonstrated the superior accuracy of the Martin-Hopkins method across diverse populations. While this method estimates very-low-density lipoprotein cholesterol (VLDL-C) using strata-specific median TG/VLDL-C ratios, its reliance on median statistics raises questions about whether these ratios are truly optimal.

Objectives and methods: This study evaluated the performance of the Martin-Hopkins method compared to the Friedewald formula, focusing on its potential for improvement by applying optimal TG/VLDL-C ratios. Using data from 18,322 individuals in the Korea National Health and Nutrition Examination Survey (KNHANES), we derived strata-specific optimal TG/VLDL-C ratios designed to maximize concordance with directly measured LDL-C values, based on LDL-C categories defined by clinical guidelines. We compared the performance of four LDL-C estimation models: the Friedewald formula (LDL-CF), the original Martin-Hopkins method (LDL-CM-N), and two alternative models that applied TG/VLDL-C ratios derived from our data-one using median values (LDL-CKM-N) and the other using optimal values tailored to each stratum (LDL-CKO-N).

Results: The Martin-Hopkins method showed significantly higher concordance than the Friedewald formula for TG levels < 400 mg/dL (79.6% for LDL-CF vs. 83.2% for LDL-CM-180, p < 0.001). Concordance improved by less than 2% for TG levels < 150 mg/dL (83.3% vs. 84.9%), but by approximately 10% for TG levels of 150-399 mg/dL (68.8% vs. 78.0%). The largest discrepancy was observed in classifying LDL-C levels < 70 mg/dL among individuals with TG levels of 150-399 mg/dL (47.5% for LDL-CF vs. 90.3% for LDL-CM-180). However, the overall concordance differed only modestly between the 10-cell and 180-cell Martin-Hopkins equations (82.8% for LDL-CM-10 vs. 83.2% for LDL-CM-180, a difference of 0.4%), indicating only a marginal benefit despite the substantial increase in the number of strata. Using optimal TG/VLDL-C ratios increased overall concordance compared to median ratios within the same stratification, with LDL-CKO-N estimates outperforming their LDL-CKM-N counterparts. However, this improvement was not statistically significant in LDL-C estimates derived from TG-only stratification.

Conclusions: Applying optimal TG/VLDL-C ratios within the Martin-Hopkins method improves accuracy compared to median ratios, particularly when stratifications incorporate both TG and non-high-density lipoprotein cholesterol (non-HDL-C) levels. This enhancement can be achieved without increasing the number of strata, offering a practical pathway to refine LDL-C estimation while avoiding excessive stratification. Our findings suggest that while median statistics may be sufficient for TG-only stratifications, they do not fully capture optimal TG/VLDL-C ratios for combined TG and non-HDL-C stratifications.

Fig 1. Optimal TG/VLDL-C ratios across six TG strata.

Panels (A–F) depict the concordance (green line), under-classification (orange line), and over-classification (gray line) rates based on the NCEP–ATP III guideline classification as a function of TG/VLDL-C ratio across six TG strata. In each panel, the vertical green line represents the TG/VLDL-C ratio that achieved the highest concordance (i.e., the optimal value). Dashed black lines indicate the fixed ratio of 5 used in the Friedewald formula. Abbreviations: TG/VLDL-C ratio: ratio of triglycerides to very-low-density lipoprotein cholesterol; TG: triglyceride; NCEP–ATP III: National Cholesterol Education Program Adult Treatment Panel III.

Fig 2. Median and optimal TG/VLDL-C ratios by TG and non–HDL-C strata (28-cell).

The left and right panels display the median and optimal TG/VLDL-C ratios, respectively. Color bands represent the TG/VLDL-C ratio ranges as follows: blue (< 4.0), light blue (4.0–4.9), green (5.0–5.9), yellow (6.0–6.9), and red (≥ 7.0). Abbreviations: TG/VLDL-C ratio: ratio of triglycerides to very-low-density lipoprotein cholesterol; TG: triglyceride; non–HDL-C: non–high-density lipoprotein cholesterol.

Fig 3. Comparison of concordance rates between Friedewald and Martin–Hopkins LDL-C estimates by TG levels: < 150 mg/dL and 150–399 mg/dL, based on NCEP–ATP III guideline.

Panel (A) shows results for individuals with TG levels < 150 mg/dL, and Panel (B) for those with TG levels of 150–399 mg/dL. Bars represent concordance rates ± 95% confidence intervals for each LDL-C estimate. From left to right, bars correspond to the following LDL-C estimates: LDL-C_F, LDL-C_M-180, LDL-C_KO-6, LDL-C_KO-12, and LDL-C_KO-28. * Bars labeled with the same letters indicate no statistically significant difference in concordance between LDL-C estimates (α = 0.05), based on pairwise comparisons using McNemar’s exact test for correlated proportions (see S9 and S10 Tables). The 95% confidence intervals for concordance rates were calculated using the Clopper–Pearson exact method. Abbreviations: NCEP–ATP III: National Cholesterol Education Program Adult Treatment Panel III; TG: triglyceride; LDL-C: low-density lipoprotein cholesterol; LDL-C_F: LDL-C calculated using the Friedewald formula; LDL-C_M-180: LDL-C calculated using the original 180-cell Martin–Hopkins equation proposed by Martin et al. [14]; LDL-C_KO-N (LDL-C_KO-6-TG, LDL-C_KO-12, and LDL-C_KO-28): LDL-C calculated using the N-cell tables with the optimal ratios of triglycerides to very-low-density lipoprotein cholesterol (TG/VLDL-C) derived from our dataset.

Fig 4. Bland–Altman plots comparing estimated LDL-C values with directly measured LDL-C.

Each panel displays the bias (i.e., the difference between LDL-C_E and LDL-C_D) plotted against the mean of LDL-C_E and LDL-C_D. The black dashed line represents the mean bias, while the orange and red dashed lines indicate the upper and lower 95% limits of agreement (mean ± 1.96 SD), respectively. Panels (A), (B), and (C) correspond to LDL-C_F, LDL-C_M-180, and LDL-C_KO-28, respectively. These plots illustrate differences in bias magnitude and variability, reflecting the level of agreement between each LDL-C_E and LDL-C_D. Green dots indicate individuals with TG levels of 300–399 mg/dL. Abbreviations: LDL-C: low-density lipoprotein cholesterol; TG: triglyceride; LDL-C_E: estimated LDL-C; LDL-C_D: LDL-C directly measured using a homogeneous enzymatic assay; LDL-C_F: LDL-C calculated using the Friedewald formula; LDL-C_M-180: LDL-C calculated using the original 180-cell Martin–Hopkins equation proposed by Martin et al. [14]; LDL-C_KO-28: LDL-C calculated using the 28-cell table (Fig 2) with the optimal ratios of triglycerides to very-low-density lipoprotein cholesterol (TG/VLDL-C) derived from our dataset; SD: standard deviation.

Fig 5. Concordance in the NCEP–ATP III guideline classification: Friedewald vs. Martin–Hopkins LDL-C estimates.

The figure compares concordance rates for LDL-C estimates stratified by TG levels: < 150 mg/dL (A) and 150–399 mg/dL (B). The LDL-C estimates include LDL-C_F (gray), LDL-C_M-180 (dark blue), and LDL-C_KO-28 (blue). The bars indicate concordance rates for each estimated LDL-C category according to the NCEP–ATP III guideline classification, illustrating differences in concordance across the methods. Abbreviations: NCEP–ATP III: National Cholesterol Education Program Adult Treatment Panel III; LDL-C: low-density lipoprotein cholesterol; TG: triglyceride; LDL-C_F: LDL-C calculated using the Friedewald formula; LDL-C_M-180: LDL-C calculated using the original 180-cell Martin–Hopkins equation proposed by Martin et al. [14]; LDL-C_KO-28: LDL-C calculated using the 28-cell table (Fig 2) with the optimal ratios of triglycerides to very-low-density lipoprotein cholesterol (TG/VLDL-C) derived from our dataset.

Fig 6. Discordance rates in LDL-C classification according to the NCEP–ATP III guideline: Friedewald vs. Martin–Hopkins LDL-C estimates.

This figure illustrates differences in discordance rates between two LDL-C estimates calculated using the Friedewald formula (LDL-C_F) and the optimized 28-cell Martin–Hopkins method (LDL-C_KO-28). Discordance is divided into under-classification (black bars) and over-classification (gray bars), and is stratified by either TG levels or estimated LDL-C categories. Panels (A) and (B) show discordance rates by TG levels for LDL-C_F and LDL-C_KO-28, respectively. Panels (C) and (D) display discordance by LDL-C categories in individuals with TG levels < 150 mg/dL. Panels (E) and (F) present corresponding results for individuals with TG levels of 150–399 mg/dL. This arrangement allows direct visual comparison between the two LDL-C estimates across different lipid profiles. Abbreviations: NCEP–ATP III: National Cholesterol Education Program Adult Treatment Panel III; TG: triglyceride; LDL-C: low-density lipoprotein cholesterol; LDL-C_F: LDL-C calculated using the Friedewald formula; LDL-C_KO-28: LDL-C calculated using the 28-cell table (Fig 2) with the optimal ratios of triglycerides to very-low-density lipoprotein cholesterol (TG/VLDL-C) derived from our dataset.

Fig 7. Correct and incorrect reclassification using LDL-C_M-180 and LDL-C_KO-28 compared with LDL-C_F. Reclassification was defined as a shift in the NCEP–ATP III guideline-based treatment category initially assigned by LDL-C_F when using either LDL-C_M-180 or LDL-C_KO-28.

The correctness of reclassification was evaluated against directly measured LDL-C, and each panel illustrates the proportions of correct (blue) and incorrect (gray) reclassifications. Panels (A) and (B) show reclassification by triglyceride levels (< 50, 50–99, 100–149, 150–199, 200–299, and 300–399 mg/dL) using LDL-C_M-180 and LDL-C_KO-28, respectively. Panels (C) and (D) show reclassification by LDL-C_F treatment categories among individuals with TG levels <150 mg/dL, using LDL-C_M-180 and LDL-C_KO-28, respectively. Panels (E) and (F) present the same comparisons for individuals with TG levels of 150–399 mg/dL. Abbreviations: NCEP–ATP III: National Cholesterol Education Program Adult Treatment Panel III; LDL-C: low-density lipoprotein cholesterol; LDL-C_F: LDL-C calculated using the Friedewald formula; LDL-C_M-180: LDL-C calculated using the original 180-cell Martin–Hopkins equation proposed by Martin et al. [14]; LDL-C_KO-28: LDL-C calculated using the 28-cell table (Fig 2) with the optimal ratios of triglycerides to very-low-density lipoprotein cholesterol (TG/VLDL-C) derived from our dataset.