University of California, Davis - Department of Statistics
Both functional and longitudinal data are data recorded over a time period for each subject in the study. However, the approaches to analyze them are intrinsically different, partly due to the difference in the sampling plans. Functional data refer to situations where the entire trajectory is observed for each subject, or when measurements are recorded for each subject at a dense grid of time points. Longitudinal data, however, are often recorded intermittently, leading to varying measurement schedules and numbers of measurements across subjects. In addition, longitudinal data are often sparse and are subject to measurement errors.
Typically, nonparametric approaches are employed to functional data, while parametric approaches have been the norm to analyze longitudinal data. In this talk, we explain the need, at least in the initial data analysis phase, to employ nonparametric methods. We show how to adapt functional principal component analysis to sparse and noisy longitudinal data. Two scenarios will be explored, the first involves no dropouts and the second involves an even-time, such as death, which prevents the collection of the longitudinal data after this event occurs for a subject. This triggers informative dropout and the marginal approaches for the first scenario will induce bias. One way to remove the bias is to model both the event and longitudinal processes simultaneously. Such an approach is termed joint modeling of longitudinal and survival data in the literature. We show how to employ the functional principal component analysis in the joint modeling setting and illustrate the approach through simulations and data example. The EM-algorithm will be used to impute the unobservable random effects and it involves Monte-Carlo integrations. One of the advantages of such an approach is to unveil the individual trajectories of the underlying longitudinal process which provides guidance for further parsimonious modeling. Time permitting, we will show one such application, where the subject specific random effects are multiplicative to the longitudinal data.