Mixed-Eff ects Smoothing Splines in Modeling Subject-Speci fic Trajectories of Cardiovascular Disease Risk Factors

Abstract

In this thesis, spline methods for modeling longitudinal non-linear risk factor trajectories of cardiovascular diseases (CVDs) are reviewed. These methods are applied to data from the International Childhood Cardiovascular Cohort (i3C) consortium, a large collaboration of longitudinal studies on CVD risk factors. Three risk factors are considered in this work, body mass index (BMI), systolic blood pressure and the level of total cholesterol.

Anthropometric measurements tend to behave in a non-linear manner over time, and thus methods for modeling longitudinal non-linear data are needed. In particular, this thesis covers different types of spline functions, including natural cubic regression splines, interpolating splines and smoothing splines.

To account for non-linear individual-specific risk factor profiles, the spline methods can be extended to a mixed-effects framework. Mixed-effects smoothing splines are presented in more detail and applied to simulated data as well as to empirical i3C data to model risk factor profiles.

The use of mixed-effects smoothing splines is demonstrated by using area under curve (AUC) values, based on estimates of individual-specific risk factor profiles in childhood and adolescence, as explanatory variables in the Cox proportional hazards model for CVD. The AUC is used as a proxy for the cumulative burden by the respective risk factor. The cumulative burden of BMI and total cholesterol was found to be associated with the hazard of CVD in adulthood.

In conclusion, the mixed-effects smoothing splines offer a flexible approach to model subject-specific risk factor profiles. They are especially beneficial in case of unbalanced data with missing observations.