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Development and Validation of a Simplified Martin-Hopkins LDL-C Equation Using Machine Learning
Jihwan Park1, Leon Fan2, Mark A Marzinke3
1Welch Center for Prevention, Epidemiology and Clinical Research, Johns Hopkins University Bloomberg School of Public Health, Baltimore, Maryland.
Importance:
Although the Martin-Hopkins equation is widely validated and used to estimate low-density lipoprotein cholesterol (LDL-C) for clinical care, a simplified equation could streamline implementation and enable broader adoption.
Objective:
To develop a simplified machine learning-based alternative to the Martin-Hopkins equation using multivariate adaptive regression splines (LDL-C-MH-MARS) and compare its performance with the Friedewald (LDL-C-F), Sampson-National Institutes of Health (LDL-C-S), Modified Sampson (LDL-C-MS), and Martin-Hopkins (LDL-C-MH) equations.
Design, Setting, And Participants:
The Very Large Database of Lipids is a cross-sectional database of clinical lipid measurements from a population-representative convenience sample of adult and pediatric patients. Lipid measurements were performed by Vertical Auto Profile ultracentrifugation between October 1, 2015, and June 30, 2019. The study included patients with complete lipid panel data who were randomly assigned to a training set and a test set. External validation against preparative ultracentrifugation-based LDL-C measurements was performed in reference laboratory datasets from the Mayo Clinic (broad LDL-C concentrations) and the Further Cardiovascular Outcomes Research With Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9) Inhibition in Subjects with Elevated Risk (FOURIER) trial (observations from patients with low LDL-C concentrations while taking evolocumab). Study data were analyzed from January to October 2025.
Exposures:
LDL-C-F, LDL-C-S, LDL-C-MS, LDL-C-MH, and LDL-C-MH-MARS equations.
Main Outcomes And Measures:
Accuracy of estimated vs ultracentrifugation-measured LDL-C concentration based on bias, root mean square error (RMSE), and concordance by guideline-based categories.
Results:
The study included 4 939 528 patients (mean [SD] age, 56 [16] years; 2 635 486 female [53%]) with complete lipid panel data who were randomly assigned to a training set (n = 3 292 889) and a test set (n = 1 646 639). LDL-C-MH-MARS equation demonstrated a very low median (IQR) bias of -0.1 (-2.1 to 1.8) mg/dL (to convert to millimoles per liter, multiply by 0.0259), comparable with LDL-C-MH. The median (IQR) difference between the MARS and original Martin-Hopkins equations (ie, LDL-C-MH-MARS - LDL-C-MH) was -0.5 (-1.2 to 0) mg/dL, further suggesting comparability between the 2 methods. The RMSE was smallest for LDL-C-MH-MARS (4.7 mg/dL) and LDL-C-MH (4.9 mg/dL), followed by LDL-C-S (5.8 mg/dL), LDL-C-MS (6.0 mg/dL), and LDL-C-F (7.2 mg/dL). The proportion of patients correctly classified according to clinical categories was nearly identical for LDL-C-MH-MARS (89.7%) and LDL-C-MH (89.6%) but lower for LDL-C-S (86.3%), LDL-C-MS (84.7%), and LDL-C-F (83.1%). The LDL-C-MH-MARS, LDL-C-MH, LDL-C-MS, LDL-C-S, and LDL-C-F equations underestimated LDL-C concentration in 16%, 17%, 28%, 39%, and 60%, respectively, when classifying LDL-C less than 70 mg/dL in patients with triglyceride concentrations of 200 to 399 mg/dL (to convert to millimoles per liter, multiply by 0.0113). The patterns of results were similar in external validation datasets, with the LDL-C-MH-MARS and LDL-C-MH equations demonstrating the highest accuracy.
Conclusions And Relevance:
Study results suggest that the new machine learning-based LDL-C equation provided results comparable with those of the original Martin-Hopkins method while simplifying implementation to a single equation.
