Tree-Structured Methods for Longitudinal Data

Abstract The thrust of tree techniques is the extraction of meaningful subgroups characterized by common covariate values and homogeneous outcome. For longitudinal data, this homogeneity can pertain to the mean and/or to covariance structure. The regression tree methodology is extended to repeated measures and longitudinal data by modifying the split function so as to accommodate multiple responses. Several split functions are developed based either on deviations around subgroup mean vectors or on two sample statistics measuring subgroup separation. For the methods to be computationally feasible, it is necessary to devise updating algorithms for the split function. This has been done for some commonly used covariance specifications: independence, compound symmetry, and first-order autoregressive models. Data analytic issues, such as handling missing values and time-varying covariates and determining appropriate tree size are discussed. An illustrative example concerning immune function loss in a cohort of human immunodeficiency virus (HIV)-seropositive gay men also is presented.