Optimal Designs for Longitudinal Studies via Functional Data Analysis

• Activity Number: 328
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Hans-Georg G. Mueller* and Hao Ji
• Companies: UC Davis and UC Davis
• Keywords: Functional Data Analysis ; Functional Principal Component ; Prediction ; Sparse Design ; Gaussian Process ; Longitudinal Study

Abstract

How to optimally collect longitudinal data when the resources for data collection per subject are limited is of interest for designing longitudinal studies. For situations where one has underlying Gaussian processes with prior information about the time-dynamic structure from a pilot study, we discuss optimal designs that are characterized by a few fixed time points where longitudinal predictor variables are to be measured. The proposed optimal designs are constructed for two specific settings, (a) Designs to recover the underlying smooth but unknown random trajectory curve for each subject, aiming to minimize squared prediction error; (b) Designs such that prediction errors for functional linear regression with functional/longitudinal predictors and scalar responses are minimized. Estimates of the proposed optimal longitudinal designs are shown to be consistent as the sample size of the pilot study increases. The proposed designs are illustrated with simulations and data from the Baltimore Longitudinal Study of Aging.