Clinical background
LDL cholesterol is the primary target of lipid-lowering treatment in virtually all current guidelines, and the thresholds for starting treatment and for goal attainment are expressed in mg/dL or mmol/L of LDL cholesterol. The gold standard against which these thresholds were originally validated is ultracentrifugation (beta quantification), a method too expensive and slow for routine use. The Friedewald equation offers an estimate of LDL cholesterol from three variables that form part of a standard lipid profile and requires no additional assay. It is precisely this simplicity that has made the equation the dominant method worldwide for over fifty years.
The decision the equation serves is whether a patient is reaching their LDL target, and whether uptitration of a statin or the addition of ezetimibe or a PCSK9 inhibitor is warranted. The problem is that the equation is least accurate exactly where the decision is hardest: in patients with low LDL cholesterol and raised triglycerides, that is, the highest-risk patients who are treated most aggressively.
Calculating LDL cholesterol with the Friedewald equation
The equation is based on total cholesterol being the sum of LDL cholesterol, HDL cholesterol and VLDL cholesterol. VLDL cholesterol is in turn estimated from triglycerides with a fixed ratio of 5:1 (mg/dL), based on the fact that VLDL particles carry on average one-fifth of their mass as cholesterol:
In mmol/L the factor becomes 2.2 instead of 5, because the unit conversion between mmol/L and mg/dL differs for triglycerides and for cholesterol:
The derivation cohort consisted of patients at the National Institutes of Health in Bethesda and was published in 1972 by Friedewald, Levy and Fredrickson [1]. The cohort comprised patients with various forms of dyslipidaemia in whom LDL cholesterol was measured by preparative ultracentrifugation. The equation was validated against beta quantification in fasting individuals with triglycerides below 400 mg/dL (4.5 mmol/L). Either fasting or non-fasting samples were originally accepted, but the equation presupposes that the triglycerides are not so high that the fixed 5:1 ratio breaks down.
Interpretation in practice
The Friedewald equation is not a risk instrument with bands leading to different actions, but an estimate of a laboratory variable. Its interpretive value lies in how well the estimate agrees with directly measured LDL cholesterol, and hence how far a given value can be relied upon in treatment decisions.
| Situation | Interpretation | Management |
|---|---|---|
| Triglycerides <150 mg/dL (<1.7 mmol/L) and LDL-C >70 mg/dL (>1.8 mmol/L) | The estimate is generally reliable | The calculated value can be used for treatment decisions |
| Triglycerides 150–199 mg/dL (1.7–2.2 mmol/L) and estimated LDL-C <70 mg/dL (<1.8 mmol/L) | Underestimation likely; the median deviation from directly measured LDL-C is approximately 9 mg/dL | Consider direct LDL-C measurement in the highest-risk patients |
| Triglycerides 200–399 mg/dL (2.3–4.5 mmol/L) and estimated LDL-C <70 mg/dL | Substantial underestimation; median deviation approximately 18 mg/dL, and up to 59% of patients with an estimated LDL-C <70 in fact have ≥70 mg/dL | Use non-HDL cholesterol or direct LDL-C measurement |
| Triglycerides ≥400 mg/dL (≥4.5 mmol/L) | The equation is not validated and should not be used | The laboratory usually does not issue a value; request direct measurement or use non-HDL cholesterol |
Non-HDL cholesterol (total cholesterol minus HDL cholesterol) is unaffected by triglycerides and is a robust alternative target in hypertriglyceridaemia. It requires no additional assay and captures all atherogenic cholesterol carried by LDL and VLDL.
Validation and performance
The Friedewald equation has been validated in several large cohorts against LDL cholesterol measured by ultracentrifugation. The most comprehensive external evaluation was carried out by Martin and colleagues in the Very Large Database of Lipids, which comprised 1,310,440 American adults with lipid profiles measured by vertical ultracentrifugation between 2009 and 2011 [2]. The lipid distribution matched NHANES and hence the US population. The study showed that the Friedewald equation systematically underestimates LDL cholesterol, and that the error is greatest at low LDL levels with concurrently raised triglycerides. Among patients with a Friedewald-estimated LDL-C below 70 mg/dL, 23% had a directly measured value of 70 mg/dL or higher. When the triglycerides were simultaneously between 150 and 199 mg/dL the proportion rose to 39%, and at triglycerides of 200 to 399 mg/dL the figure was 59% [2].
In a later study from the same database, the Friedewald equation was compared with the Martin/Hopkins equation and the Sampson equation in 111,939 patients with triglycerides of 400 to 799 mg/dL [3]. The Friedewald equation classified only 19.3% of patients into the correct guideline category, compared with 62.1% for extended Martin/Hopkins and 40.4% for Sampson. For patients with an LDL-C below 70 mg/dL, the accuracy of Friedewald was a low 5.1%, and for LDL-C below 40 mg/dL, 92.5% of patients had a deviation of at least 30 mg/dL from the directly measured value [3].
The Sampson equation, derived from 8,656 patients at the NIH between 1976 and 1999, performed considerably better than the Friedewald equation in external validations [4]. Against beta quantification, Sampson had an RMSE of 15.2 mg/dL and an R² of 0.965, compared with an RMSE of 32 mg/dL and an R² of 0.881 for Friedewald. In hypertriglyceridaemia the mean absolute deviation was 24.9 mg/dL for Sampson versus 56.4 mg/dL for Friedewald. The Sampson equation is moreover validated for triglycerides up to 800 mg/dL and gave 35% fewer misclassifications than Friedewald in this range [4].
Limitations
The fixed 5:1 ratio between triglycerides and VLDL cholesterol is the core weakness of the equation. In reality the ratio varies with the triglyceride level, the LDL level and the metabolic profile. At high triglycerides the VLDL particles become richer in triglyceride per unit of cholesterol, so the ratio exceeds 5:1 and the equation therefore underestimates VLDL cholesterol and overestimates LDL cholesterol. At very low LDL levels the absolute error is small but the relative error large, which has consequences for classification around treatment thresholds.
The equation does not apply to non-fasting samples with meal-induced rises in triglycerides, and it does not apply at all at triglycerides ≥400 mg/dL (≥4.5 mmol/L). In type III hyperlipoproteinaemia (dysbetalipoproteinaemia) the VLDL composition is abnormal and the ratio wholly invalid, so the equation gives incorrect values irrespective of the triglyceride level.
The commonest error in clinical practice is to rely blindly on a Friedewald-estimated LDL value below 70 mg/dL in a highest-risk patient with moderately raised triglycerides, and thereby withhold intensified treatment that is in fact indicated. Another common error is to use the equation at triglycerides above 400 mg/dL when the laboratory does not automatically suppress the result.
References
- Friedewald WT, Levy RI, Fredrickson DS. Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge. Clin Chem. 1972;18(6):499–502. PMID: 4337382
- Martin SS, Blaha MJ, Elshazly MB et al. Friedewald-estimated versus directly measured low-density lipoprotein cholesterol and treatment implications. J Am Coll Cardiol. 2013;62(8):732–739. PMID: 23524048
- 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
- Sampson M, Ling C, Sun Q et al. A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia. JAMA Cardiol. 2020;5(5):540–548. PMID: 32101259
