Regression Trees for Longitudinal Data

Abstract: While studying response trajectory, often the population of interest may be diverse enough to exist distinct subgroups within it and the longitudinal change in response may not be uniform in these subgroups. That is, the timeslope and/or influence of covariates in longitudinal profile may vary among these different subgroups. For example, Raudenbush (2001) used depression as an example to argue that it is incorrect to assume that all the people in a given population would be experiencing either increasing or decreasing levels of depression. In such cases, traditional linear mixed effects model (assuming common parametric form for covariates and time) is not directly applicable for the entire population as a group-averaged trajectory can mask important subgroup differences. Our aim is to identify and characterize longitudinally homogeneous subgroups based on the combination of baseline covariates in the most parsimonious way. This goal can be achieved via constructing regression tree for longitudinal data using baseline covariates as partitioning variables. We have proposed LongCART algorithm to construct regression tree for the longitudinal data. In each node, the proposed LongCART algorithm determines the need for further splitting (i.e. whether parameter(s) of longitudinal profile is influenced by any baseline attributes) via parameter instability tests and thus the decision of further splitting is type-I error controlled. We have obtained the asymptotic results for the proposed instability test and examined finite sample behavior of the whole algorithm through simulation studies. Finally, we have applied the LongCART algorithm to study the longitudinal changes in choline level among HIV patients.