Functional regression analysis using an F test for longitudinal data with large numbers of repeated measures

Longitudinal data sets from certain fields of biomedical research often consist of several variables repeatedly measured on each subject yielding a large number of observations. This characteristic complicates the use of traditional longitudinal modelling strategies, which were primarily developed for studies with a relatively small number of repeated measures per subject. An innovative way to model such 'wide' 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. Shen and Faraway 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. A smoking cessation study for methadone-maintained tobacco smokers is analysed 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 mixed-effects linear regression model. A simulation study is also conducted under the condition of the smoking data to investigate the statistical power for the F test, Wilks' likelihood ratio test, and the linear mixed-effects model using AIC.