Developing and evaluation of a novel machine learning-derived formula for LDL-C estimation

Abstract Objectives The Friedewald, Martin, and Sampson equations are widely used for calculating low-density lipoprotein cholesterol (LDL-C). We aimed to develop a new machine-learning-based formula to address errors and uncertainties associated with these equations. Methods We collected LDL-C, total cholesterol, triglyceride (TG), and high-density lipoprotein cholesterol measurements from 2,270 patients using the Abbott Architect c16000 analyzer for the training dataset. Three independent test datasets were generated using the homogeneous enzymatic method: 40,941 results from Architect c16000, 42,520 from Beckman Coulter AU5800, and 5,813 from Cobas c501 analyzers. Equations were developed using machine learning and symbolic regression in Python. Results The novel equation (mg/dL): (Y-LDL-C)=TC – HDL_C – (√TG) xTC/100. The formula demonstrated better performance across all datasets with the lowest root mean square error (9.9, 8.1, 16.0), mean absolute error (6.8, 5.9, 12.8), and mean absolute percentage error (5.2, 4.6, 9.9 %), along with the highest R 2 values (0.94, 0.95, 0.84) and accuracy rates (95.7, 95.3, 71.1 %). For samples with TG<400 mg/dL(<4.516 mmol/L), analytical accuracy was 96.3, 95.4, and 71.5 %, with minimal clinical error rates (0.6, 0.6, 3.5 %). Even with TG>400 mg/dL(>4.516 mmol/L), accuracy remained high (72.7, 91.2, 65.3 %) with low clinical error rates (3.9, 1.3, 11.7 %). The novel formula consistently outperformed the Friedewald, Sampson, and extended Martin equations. A key limitation is that the equation was derived using enzymatic LDL-C rather than beta-quantification. Conclusions The novel formula shows improved concordance in LDL-C estimations compared to existing equations, demonstrating better performance across diverse patient populations and laboratory systems.