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

Date Published: March 7, 2019

Publisher: Public Library of Science

Author(s): Charles M. Rowland, Dov Shiffman, Michael Caulfield, Veronica Garcia, Olle Melander, Trevor Hastie, Tatsuo Shimosawa.


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.

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.

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.

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.

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.

Partial Text

Functional data can be represented by functions that describe curves or surfaces of a low-dimensional index[1]. Examples of functional data are measurements collected over time, across locations, or, as in the present analysis, across a vector of particle diameters. Functional data analysis exploits these data attributes by imposing structure: for example, smoothness on regression coefficients, as a function of the same index[2]. Regression modelling of functional data has been, and continues to be, an active area of methodological development and has been used in a variety of applications[3, 4]. A previous publication provided several examples of functional data analysis within the field of medical science in order to increase awareness of the challenges and possibilities involved, and to encourage scientists to explore the robustness of functional approaches in additional applications[5]. While some aspects of functional data analysis may be common across a wide range of applications, it is likely that each application will also have unique challenges worthy of exploration. The current paper explores a functional data analysis approach to assess the association between size-fractionated lipoprotein particles and cardiovascular disease (CVD).

A high resolution size distribution of lipoprotein particles can be measured by ion-mobility and other methods. However, lipoprotein measurements are typically reported as particle concentration in a small number of large regions with broad size range. In this study, we developed and assessed methods that can assess the association of the entire lipoprotein size spectrum as a single score. This approach has the advantage that it does not arbitrarily discard or collapse information generated by ion mobility measurement of lipoprotein size distribution. In principle, this approach can also be applied to other methods that analyze lipoprotein size or density in a continuous manner.




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