Association of cardiovascular events and lipoprotein particle size: Development of a risk score based on functional data analysis

Background: Functional data is data represented by functions (curves or surfaces of a low-dimensional index). Functional data often arise when measurements are collected over time or across locations. In the field of medicine, plasma lipoprotein particles can be quantified according to particle diameter by ion mobility. Goal: We wanted to evaluate the utility of functional analysis for assessing the association of plasma lipoprotein size distribution with cardiovascular disease after adjustment for established risk factors including standard lipids. Methods: We developed a model to predict risk of cardiovascular disease among participants in a case-cohort study of the Malmö Prevention Project. We used a linear model with 311 coefficients, corresponding to measures of lipoprotein mass at each of 311 diameters, and assumed these coefficients varied smoothly along the diameter index. The smooth function was represented as an expansion of natural cubic splines where the smoothness parameter was chosen by assessment of a series of nested splines. Cox proportional hazards models of time to a first cardiovascular disease event were used to estimate the smooth coefficient function among a training set consisting of one half of the participants. The resulting model was used to calculate a functional risk score for the remaining half of the participants (test set) and its association with events was assessed in Cox models that adjusted for traditional cardiovascular risk factors. Results: In the test set, participants with a functional risk score in the highest quartile were found to be at increased risk of cardiovascular events compared with the lowest quartile (Hazard ratio = 1.34; 95% Confidence Interval: 1.05 to 1.70) after adjustment for established risk factors. Conclusion: In an independent test set of Malmö Prevention Project participants, the functional risk score was found to be associated with cardiovascular events after adjustment for traditional risk factors including standard lipids.