Development and Validation of a Simplified Martin-Hopkins LDL-C Equation Using Machine Learning

Introduction

Low-density lipoprotein cholesterol (LDL-C) is a critical biomarker widely used to assess cardiovascular risk and guide lipid-lowering therapies. The Martin-Hopkins equation has been extensively validated and adopted clinically for estimating LDL-C from standard lipid panels, improving accuracy beyond the traditional Friedewald formula. However, despite its effectiveness, the Martin-Hopkins method’s complexity can limit its routine clinical adoption. This study aimed to develop a simplified machine learning-based LDL-C estimation equation, leveraging multivariate adaptive regression splines (MARS), and to validate its performance against established formulas including Friedewald, Sampson, Modified Sampson, and the original Martin-Hopkins equations.

Background

Accurate LDL-C measurement is essential because elevated LDL-C is a major modifiable risk factor for atherosclerotic cardiovascular disease (ASCVD). While direct LDL-C measurement through ultracentrifugation or other preparative methods remains the gold standard, these methods are expensive and not routinely available at all clinical laboratories. Consequently, LDL-C is often estimated using equations based on total cholesterol, high-density lipoprotein cholesterol (HDL-C), triglycerides, and other lipid parameters. The Friedewald formula has been the standard for decades but is less accurate in patients with high triglycerides or low LDL-C levels. The Martin-Hopkins equation improves this by using an adjustable factor for triglycerides, providing better individualized LDL-C estimates, yet it is computationally more involved.

Study Design and Methods

This investigation utilized data from the Very Large Database of Lipids (VLDL), which contains cross-sectional lipid profiles representative of both adult and pediatric populations. Lipid measurements were performed using Vertical Auto Profile (VAP) ultracentrifugation from October 2015 through June 2019. Patients with complete lipid panels were randomly assigned to either a training set (over 3 million patients) used to develop the model, or a test set (over 1.6 million patients) used for internal validation. Further external validation employed datasets from the Mayo Clinic laboratory, representing a broad range of LDL-C concentrations, and the FOURIER clinical trial consisting of patients treated with the PCSK9 inhibitor evolocumab, notable for very low LDL-C levels.

LDL-C estimates from five equations were compared: Friedewald (LDL-C-F), Sampson (LDL-C-S), Modified Sampson (LDL-C-MS), Martin-Hopkins (LDL-C-MH), and the newly developed machine learning-based MARS equation (LDL-C-MH-MARS). Outcomes focused on accuracy metrics including median bias, interquartile range, root mean square error (RMSE), and classification concordance across guideline-based LDL-C categories.

Results

The dataset included nearly 5 million patients with a mean age of 56 years and balanced sex distribution. The LDL-C-MH-MARS model demonstrated exceptional accuracy, with a median bias of -0.1 mg/dL and a very narrow interquartile range (-2.1 to 1.8 mg/dL), closely matching the performance of the original Martin-Hopkins equation. The difference between the new machine learning model and original equation was minimal (median difference -0.5 mg/dL), reinforcing equivalence.

The RMSE values favored the MARS and original Martin-Hopkins equations (4.7 and 4.9 mg/dL respectively), outperforming the Sampson (5.8 mg/dL), Modified Sampson (6.0 mg/dL), and Friedewald formulas (7.2 mg/dL). Clinical categorization agreement was highest for LDL-C-MH-MARS (89.7%) and LDL-C-MH (89.6%), compared with lower rates for the other formulas.

A critical clinical benefit was observed in patients with triglyceride levels between 200-399 mg/dL and LDL-C below 70 mg/dL. Here, underestimation rates were lowest with LDL-C-MH-MARS (16%) and LDL-C-MH (17%) compared to Friedewald (60%). External validations confirmed these trends, including in populations with very low LDL-C receiving evolocumab.

Discussion

The newly developed LDL-C-MH-MARS equation effectively balances accuracy and usability, consolidating the prior complex set of Martin-Hopkins factors into a streamlined, single-formula approach facilitated by machine learning. By achieving equivalent performance to the gold standard method while simplifying calculation, the new model could increase clinical adoption and integration into laboratory reporting systems.

This innovation also emphasizes the utility of machine learning techniques in refining and optimizing biochemical estimations derived from routine clinical data, moving towards personalized medicine that can adapt to diverse patient profiles.

Clinical Implications

Accurate LDL-C estimation is imperative for identifying patients at heightened cardiovascular risk and making appropriate therapy decisions, particularly in challenging cases with atypical lipid profiles or triglyceride elevations. The LDL-C-MH-MARS model can reliably replace more cumbersome methods, facilitating rapid and precise LDL-C reporting that supports timely intervention.

Integration of this equation into laboratory information systems and calculation tools could allow for wider use in clinical practice without additional testing burden or cost.

Limitations and Future Directions

While the model was validated in exceptionally large and diverse populations, real-world implementation studies are warranted to assess operational impact and ease of use in varied laboratory settings. Further research could also explore the applicability to pediatric subgroups, different ethnic groups, and evolving lipid-lowering therapies.

Conclusion

The study successfully developed and externally validated a simplified LDL-C estimation formula using machine learning that matches the accuracy of the original Martin-Hopkins equation. This advancement holds promise to enhance routine cardiovascular risk stratification and clinical decision-making by providing a more accessible yet reliable lipid measurement tool.

Reference:

Park J, Fan L, Marzinke MA, Sokoll LJ, Muthukumar A, Murphy SA, Sabatine MS, Gurudu R, Meeusen JW, Martin SS. Development and Validation of a Simplified Martin-Hopkins LDL-C Equation Using Machine Learning. JAMA Cardiol. 2026 Jul 15:e262314. doi: 10.1001/jamacardio.2026.2314. Epub ahead of print. PMID: 42455545; PMCID: PMC13373734.