LDL cholesterol, Sampson equation

Clinical background

LDL cholesterol is the primary target of lipid-lowering treatment in virtually all current guidelines, and the thresholds have fallen progressively. At very low LDL levels, particularly in combination with raised triglycerides, the classical Friedewald equation becomes increasingly unreliable. It rests on a fixed ratio between triglycerides and VLDL cholesterol (5:1), which does not hold in hypertriglyceridaemia, and laboratories often fall back on direct chemical LDL assays when triglycerides exceed 400 mg/dL. These assays are, however, poorly standardised and may give systematically deviating results. The Sampson equation was developed to fill this gap: a calculated LDL estimate that remains usable up to triglyceride levels of 800 mg/dL and that also performs better than Friedewald at low LDL levels, without requiring any assays beyond the standard lipid panel [1].

Calculating LDL cholesterol with the Sampson equation

The equation estimates LDL cholesterol from three variables included in a standard lipid profile: total cholesterol (TC), HDL cholesterol and triglycerides (TG). All values are given in mg/dL. The equation also uses non-HDL cholesterol, calculated as TC minus HDL cholesterol. The full formula is:

$$\text{LDL-C} = \frac{\text{TC}}{0{.}948} - \frac{\text{HDL-C}}{0{.}971} - \left(\frac{\text{TG}}{8{.}56} + \frac{\text{TG} \times \text{non-HDL-C}}{2140} - \frac{\text{TG}^2}{16100}\right) - 9{.}44$$

where $\text{non-HDL-C} = \text{TC} - \text{HDL-C}$.

Unlike Friedewald, which uses a fixed TG:VLDL ratio, the Sampson equation estimates VLDL cholesterol with a multiple regression model incorporating a linear TG term, an interaction term between TG and non-HDL cholesterol, and a quadratic TG term. This allows the equation to capture the non-linear relationship between triglycerides and VLDL cholesterol at high TG levels.

The derivation cohort consisted of 8,656 patients examined at the National Institutes of Health Clinical Center between 1976 and 1999, with a total of 18,715 LDL-C measurements performed by beta quantification as the reference method [1]. The data were randomly split into equally sized training and validation sets. The cohort had an over-representation of patients with dyslipidaemia, including many with very high LDL-C and TG levels, which was a deliberate design choice to ensure that the equation would work precisely in the difficult cases. External validation was performed against both beta quantification (n = 28,891) and direct LDL-C assays (n = 252,888) from several independent data sources [1].

Interpretation in practice

The Sampson equation is not a risk assessment instrument but a calculation method intended to replace or complement the Friedewald equation in the laboratory. The estimated LDL-C value should be interpreted against the same treatment thresholds that apply to directly measured LDL-C, that is, in accordance with current guidelines for cardiovascular prevention.

The clinical benefit arises in two specific situations:

When triglycerides exceed 800 mg/dL the equation should not be used. In that situation direct measurement should be considered, or treatment based on non-HDL cholesterol instead.

Validation and performance

The derivation study reported a slope of 0.964 against beta quantification, an RMSE of 15.2 mg/dL and an R² of 0.9648, which was superior to Friedewald (slope 1.056, RMSE 32 mg/dL, R² 0.8808) and Martin (slope 0.945, RMSE 25.7 mg/dL, R² 0.9022) [1]. For patients with hypertriglyceridaemia the mean absolute difference (MAD) was 24.9 mg/dL for Sampson compared with 56.4 mg/dL for Friedewald and 44.8 mg/dL for Martin. The number of misclassifications at the treatment thresholds of 70, 100 and 190 mg/dL fell by 35% for patients with TG of 400 to 800 mg/dL compared with Friedewald [1].

In the large external validation in the Very Large Database of Lipids (VLDbL), with 5,051,467 patients and ultracentrifugation (VAP) as the reference, the Sampson equation classified LDL-C into the correct treatment category in 86.3% of cases, compared with 89.6% for Martin/Hopkins and 83.2% for Friedewald [2]. The median error was 1.7 mg/dL for Sampson, 0.3 mg/dL for Martin/Hopkins and higher for Friedewald. For patients with TG of 150 to 399 mg/dL the accuracy of Sampson was 79.3% versus 83.5% for Martin/Hopkins and 67.8% for Friedewald [2].

At higher triglyceride levels (TG 400 to 799 mg/dL), several studies have shown that the Sampson equation performs less well than expected. In a comparative study of 111,939 patients with TG in this range, the accuracy of Sampson was 40.4%, compared with 62.1% for extended Martin/Hopkins and 19.3% for Friedewald [3]. For patients with an LDL-C below 70 mg/dL the accuracy of Sampson was 26.4%, and for LDL-C below 40 mg/dL only 14.4%. The proportion of patients with an error of 30 mg/dL or more at an LDL-C below 40 mg/dL was 38.7% for Sampson, compared with 2.7% for extended Martin/Hopkins and 92.5% for Friedewald [3]. The authors conclude that, whichever method is chosen, estimated LDL-C should be treated with caution in this triglyceride range.

A study of 88,943 Turkish adults, in which direct LDL-C assays (Roche, Beckman, Siemens) were used as the reference, found that extended Martin/Hopkins was generally the most concordant, but that for patients with TG ≥400 mg/dL the Sampson equation performed best or joint best depending on the assay [4]. At the same time, the Sampson equation underestimated LDL-C as triglycerides rose for the Roche and Beckman assays [4].

A retrospective study of 146,106 patients with established atherosclerotic cardiovascular disease and TG below 400 mg/dL found a discordance of 9% between Friedewald and Sampson at the 70 mg/dL threshold, and of 7% between Sampson and Martin/Hopkins [5]. Among patients with TG ≥150 mg/dL, 27% had a difference of more than 10 mg/dL between Friedewald and Sampson, and 23% between Sampson and Martin/Hopkins. Martin/Hopkins consistently estimated a higher LDL-C than both Friedewald and Sampson, suggesting that Sampson, like Friedewald, may carry a risk of underestimation and undertreatment in high-risk patients [5].

Limitations

The Sampson equation is not validated for triglycerides above 800 mg/dL and should not be used in that range. Even within the validated range (TG 400 to 800 mg/dL) the uncertainty is substantial, particularly at low LDL-C levels, and several independent studies have shown that extended Martin/Hopkins performs better in this range [2, 3].

The derivation cohort from the NIH Clinical Center (1976 to 1999) was selected with an over-representation of patients with severe dyslipidaemia. This strengthened the performance of the equation precisely for these patients in the derivation, but may have exaggerated the advantage over Friedewald in a more normally distributed population. In the large VLDbL cohort, which is representative of the US population, the Sampson equation was indeed better than Friedewald overall, but poorer than Martin/Hopkins [2].

The equation presupposes that all input values (TC, HDL-C, TG) are correctly measured. With non-fasting sampling, triglycerides may be raised without reflecting the patient's baseline metabolism, which affects the estimate. The equation does not correct for Lp(a) cholesterol, which contributes to the measured LDL-C but is not responsive to statin treatment.

An important pitfall is that the Sampson equation, like Friedewald, tends to underestimate LDL-C at low levels with raised triglycerides, although the underestimation is less pronounced than for Friedewald. In patients for whom an accurate LDL-C value is decisive for the treatment decision, particularly with established cardiovascular disease and an LDL-C close to a treatment threshold, direct measurement or the Martin/Hopkins equation should be considered first [2, 5].

References

1. 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):540–8. PMID: 32101259
2. Samuel C, Park J, Sajja A et al. Accuracy of 23 equations for estimating LDL cholesterol in a clinical laboratory database of 5,051,467 patients. Glob Heart. 2023;18(1):36. PMID: 37361322
3. 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
4. Ertürk Zararsız G, Bolat S, Cephe A et al. Validation of Friedewald, Martin-Hopkins and Sampson low-density lipoprotein cholesterol equations. PLoS One. 2022;17(5):e0263860. PMID: 35559957
5. Sajja A, Li HF, Spinelli KJ et al. Discordance between standard equations for determination of LDL cholesterol in patients with atherosclerosis. J Am Coll Cardiol. 2022;79(6):530–541. PMID: 35144744