Clinical background
LDL cholesterol is the primary treatment target in both European and American guidelines for cardiovascular prevention. In routine practice, LDL-C is usually calculated indirectly from a standard lipid panel, since direct measurement by ultracentrifugation is resource-intensive and not widely available. The Friedewald equation, derived in 1972 in 448 patients, has long been the first choice. It rests on the assumption that the ratio of triglycerides to VLDL cholesterol (TG:VLDL-C) is a constant 5:1. This assumption breaks down in two clinically important situations: when triglycerides are raised and when LDL-C is low, particularly below 70 mg/dL (1.8 mmol/L). In both cases the Friedewald equation tends to underestimate LDL-C, which can lead to undertreatment of high-risk patients who are at or below current treatment targets.
The Martin equation was developed precisely to address these weaknesses. By replacing the fixed divisor of 5 with an adjustable, stratum-specific factor that varies with the triglyceride and non-HDL-C level, the equation captures the actual variance in the TG:VLDL-C ratio and gives a more accurate estimate, particularly in the low range in which modern treatment targets lie.
Calculating the Martin equation
The Martin equation calculates LDL-C as:
where non-HDL-C = total cholesterol − HDL cholesterol, and the adjustable factor is the stratum-specific median TG:VLDL-C ratio taken from a table of 180 cells. The table is divided by triglyceride level (30 strata) and non-HDL-C level (6 strata). In practice, the calculator looks up the patient's combination of triglycerides and non-HDL-C in the table and uses the corresponding median ratio as the divisor instead of Friedewald's fixed 5.
The derivation cohort consisted of 1,350,908 consecutive lipid panels from the Very Large Database of Lipids (VLDbL), collected from 2009 to 2011 at Atherotech Diagnostics Laboratory in the USA [1]. The samples came from children, adolescents and adults, and the lipid distribution matched population-based NHANES data. Cholesterol concentrations were measured directly by vertical density gradient ultracentrifugation (Vertical Auto Profile) and triglycerides directly on an Abbott ARCHITECT C-8000. The cohort was randomly split 2:1 into a derivation dataset (n = 900,605) and a validation dataset (n = 450,303).
In the derivation dataset the median TG:VLDL-C ratio was 5.2 (IQR 4.5 to 6.0), that is, higher than Friedewald's assumed 5.0. Triglycerides and non-HDL-C explained 65% of the variance in the ratio. Adding age and sex did not appreciably improve the model (<0.01 improvement), and these variables are therefore not included. The 180-cell table was chosen because larger tables gave no more than 0.1% higher concordance.
Interpretation in practice
The Martin equation gives an estimate of LDL-C in the same unit and on the same scale as Friedewald. It should be interpreted against the treatment targets of the applicable guideline, not against a separate interpretive scale. The point of the equation is not that it sets new thresholds, but that it reduces the risk of a patient being wrongly classified as at target when the LDL-C is in fact above the threshold.
The clinical gain is greatest in two situations:
| Situation | What the Martin equation changes | Guidance |
|---|---|---|
| LDL-C <70 mg/dL and TG 150 to 399 mg/dL | Friedewald tends to underestimate LDL-C substantially; the Martin equation gives a higher and more accurate estimate | If the estimated value lies just below target, consider confirming with a direct LDL-C measurement before deciding not to intensify treatment |
| TG 400 to 799 mg/dL | The Friedewald equation is not validated; an extended version of the Martin equation can be used, but with substantial residual uncertainty | Use a direct LDL-C measurement where available; otherwise interpret the estimate with caution and follow up |
At triglycerides below 150 mg/dL and LDL-C above 100 mg/dL the difference between the Martin equation and Friedewald is small and rarely clinically decisive.
Validation and performance
In the internal validation dataset (n = 450,303, TG <400 mg/dL) the overall concordance with directly measured LDL-C in guideline classification was 91.7% (95% CI 91.6 to 91.8) for the Martin equation versus 85.4% (95% CI 85.3 to 85.5) for Friedewald [1]. The improvement was most marked at LDL-C below 70 mg/dL. Among patients with an estimated LDL-C below 70 mg/dL and triglycerides of 200 to 399 mg/dL, the directly measured LDL-C was also below 70 mg/dL in 84.0% with the Martin equation versus 40.3% with Friedewald.
An external validation was performed in the FOURIER trial, in which 12,742 patients with established atherosclerotic cardiovascular disease were treated with evolocumab in addition to a statin [2]. The reference method was preparative ultracentrifugation. The median deviation from the reference was −2 mg/dL (IQR −4 to 1) for the Martin equation versus −4 mg/dL (IQR −8 to −1) for Friedewald. The proportion of values deviating by more than 5 mg/dL from the reference was 22.9% and 40.1% respectively, and by more than 10 mg/dL: 2.6% and 13.3%. Friedewald thus underestimated systematically, which is clinically relevant because undertreatment is the consequence. Correlation with the reference method was ρ = 0.918 (95% CI 0.916 to 0.919) for the Martin equation versus ρ = 0.867 (95% CI 0.865 to 0.869) for Friedewald.
In a Canadian cohort of 4,150 high-risk patients (diabetes or established cardiovascular disease), the Martin equation gave on average 7.3% higher LDL-C values than Friedewald [3]. Agreement with alternative measures such as non-HDL-C and ApoB was higher for the Martin equation than for Friedewald when triglycerides were raised, but neither equation performed satisfactorily at high triglyceride levels.
An extended version of the Martin equation has been tested for triglycerides of 400 to 799 mg/dL in 111,939 patients from the VLDbL database [4]. Overall classification accuracy was 62.1% for the Martin equation versus 19.3% for Friedewald and 40.4% for the Sampson equation. For LDL-C below 70 mg/dL the corresponding figures were 67.3%, 5.1% and 26.4%. Although the Martin equation was clearly superior, substantial error remained, and the authors recommend caution whichever method is used in this triglyceride range.
Limitations
The Martin equation is not validated for triglycerides above 800 to 1000 mg/dL. At such levels the VLDL-C estimate is too uncertain, and direct LDL-C measurement should be used. In type III dysbetalipoproteinaemia (remnant accumulation) the TG:VLDL-C ratio is systematically raised and no estimating equation is reliable; direct measurement or calculation of remnant cholesterol is required here.
The equation is based on an American cohort with lipid distributions matching NHANES. Populations with atypical lipid metabolism, for example in severe familial hypercholesterolaemia or combined hyperlipidaemia, may have TG:VLDL-C ratios that differ from those on which the table is based. A study of patients with familial combined hyperlipidaemia found that the Martin equation did indeed perform better than Friedewald, but with substantial residual error in this specific population.
The 180-cell table requires a look-up, which makes manual calculation impractical. In routine practice the equation must be implemented in the laboratory system or in a calculator. This is not a methodological problem, but a practical prerequisite for its use.
The equation estimates LDL-C and says nothing about LDL particle number or LDL particle size. In atherogenic dyslipidaemia (low HDL-C, raised triglycerides, small dense LDL particles), LDL-C may underestimate the atherogenic burden, whichever estimating equation is used. In these cases ApoB is a more accurate measure.
Place in current practice
Laboratories use the Friedewald equation, the Martin equation or direct LDL-C measurement to varying degrees. The European Atherosclerosis Society (EAS) and the European Society of Cardiology (ESC) recommend in their guidelines that the Martin equation be preferred to Friedewald when LDL-C is estimated, particularly at low LDL-C levels and with raised triglycerides. The 2019 EAS consensus statement also emphasises that the Martin equation is reliable in the non-fasting state, unlike what previously applied to the Friedewald equation. Clinicians who still use the Friedewald equation with low treatment targets should be aware of the risk of systematic underestimation.
References
- Martin SS, Blaha MJ, Elshazly MB, et al. Comparison of a novel method vs the Friedewald equation for estimating low-density lipoprotein cholesterol levels from the standard lipid profile. JAMA 2013;310(19):2061-8. PMID: 24240933
- Martin SS, Giugliano RP, Murphy SA, 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(7):749-53. PMID: 29898218
- Cartier LJ, St-Coeur S, Robin A, et al. Impact of the Martin/Hopkins modified equation for estimating LDL-C on lipid target attainment in a high risk patient population. Clin Biochem 2020;76:35-7. PMID: 31843663
- Sajja A, Park J, Sathiyakumar V, et al. Comparison of methods to estimate low-density lipoprotein cholesterol in patients with high triglyceride levels. JAMA Netw Open 2021;4(10):e2128817. PMID: 34709388
