A Marginal Approach to Reduced-Rank Penalized Spline Smoothing with Application to Multilevel Functional Data

• Activity Number: 120
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Huaihou Chen*+ and Yuanjia Wang and Myunghee Cho Paik and H. Alex Choi
• Companies: Columbia University and Columbia University and Columbia University and Columbia University
• Keywords: Penalized spline ; GEE ; Functional data ; Semiparametric models ; Longitudinal data

Abstract

Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects' vital signs were recorded every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of multilevel functional data focus on conditional approaches. However, parameters obtained from the conditional models do not have direct interpretations as population average effects. When population effects are of interest, we may employ marginal regression models. In this work, we propose marginal approaches to fit multilevel functional data through penalized spline GEE. We provide a new variance estimator robust to misspecification of correlation structure. We investigate the large sample properties of the penalized spline GEE with multilevel continuous data. Finally, we apply the methods to the SAH study to evaluate a recent debate on discontinuing the use of Nimodipine in the clinical community.