Regression Trees in a Longitudinal Data Setting and Their Application in a Metabolite Expression Neuroimaging Study

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Madan Kundu*+ and Jaroslaw Harezlak
• Companies: IU School of Medicine and Indiana Univ Fairbanks School of Public Health
• Keywords: Regression trees ; instability test ; longitudinal data ; score process ; Brownian Bridge

Abstract

Longitudinal data methods developed by Laird and Ware (1982) are extremely useful. They implicitly assume that a mean longitudinal model conditional on baseline covariates is applicable to the entire population. However in a heterogeneous population the variation in longitudinal trajectories can be hard to explain. This is usually the case in observational studies with many possible predictors. In such cases, a group-averaged trajectory can mask important subgroup differences. Our aim is to identify and characterize subgroups with differential longitudinal behavior based on the combination of baseline covariates. We apply the regression tree method (Breiman et al., 1984) to find the subgroups by repetitive evaluation of goodness of fit criterion at all splits of the partitioning variables. This results in a problem of multiple testing though. We avoid this problem by performing a single test to identify the instability of the parameter(s) in the longitudinal model. We offer a tree construction algorithm and obtain asymptotic results. Numerical results are explored through simulation studies. We apply our method to study changes in brain metabolite levels of HIV infected patients.