A decision tree analysis for longitudinal measurement data and its applications

Longitudinal data are encountered in many fields, but its statistical analysis is often complex and not always easy to interpret. Although various tree-based methods for understanding longitudinal data have been proposed, few approaches clearly distinguish between the main effect of a covariate and its interaction with time, and then recombine them into an interpretable structure. We propose a novel tree-based approach for longitudinal data that evaluates both the effect of a covariate cut-off and its interaction with time, incorporating a weighting mechanism. The proposed method enables the examination of longitudinal data from multiple perspectives, as the resulting tree-structure varies with the assigned weights. Since our method does not treat the time variable as a splitting variable, it allows observation of differences in the longitudinal trajectories of the response variable across terminal nodes. To enhance predictive accuracy beyond that of a single tree and to facilitate interpretation from diverse perspectives, we also propose a method for selecting multiple trees. The performance and characteristics of our method are evaluated through simulation studies and real data applications. We demonstrate that utilizing multiple trees more effectively facilitates the interpretation of complex longitudinal data.