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Functional Regression Analysis using an F Test for Longitudinal Data with Large Numbers of Repeated Measures

  • Author(s): Yang, Xiaowei
  • Shen, Qing
  • Xu, Hongquan
  • Shoptaw, Steven
  • et al.
Abstract

Longitudinal data sets from certain fields of biomedical research often consist of several variables repeatedly measured on each subject yielding large number of observations. This characteristic complicates the use of standard longitudinal modeling strategies, such as random effects models and marginal models, where rigorous assumptions on intra- subject correlation structure are required. An innovative way to model the data is to apply functional regression analysis, an emerging statistical approach in which observations of the same subject are viewed as a sample from a functional space. No assumptions are needed for the intra-subject correlation structure. Shen and Faraway (Satistica Sinica 2004; 1239-1257) introduced an F test for linear models with functional responses. This paper illustrates how to apply this F test and functional regression analysis to the setting of longitudinal data where intra-subject repeated measures are viewed as discrete samples from an underlying curve with continuous function forms. A smoking cessation study for methadone-maintained tobacco smokers is analyzed for demonstration. In estimating the treatment effects, the functional regression analysis provides meaningful clinical interpretations, and the functional F test provides consistent results supported by a random-effects linear regression model.

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