Flexible tree-structured regression models for discrete event times

Abstract

Discrete hazard models are widely applied for the analysis of time-to-event outcomes that are intrinsically discrete or grouped versions of continuous event times. Commonly, one assumes that the effect of explanatory variables on the hazard can be described by a linear predictor function. This, however, may be not appropriate when non-linear effects or interactions between the explanatory variables occur in the data. To address this issue, we propose a novel class of discrete hazard models that utilizes recursive partitioning techniques and allows to include the effects of explanatory variables in a flexible data-driven way. We introduce a tree-building algorithm that inherently performs variable selection and facilitates the inclusion of non-linear effects and interactions, while the favorable additive form of the predictor function is kept. In a simulation study, the proposed class of models is shown to be competitive with alternative approaches, including a penalized parametric model and Bayesian additive regression trees, in terms of predictive performance and the ability to detect informative variables. The modeling approach is illustrated by two real-world applications analyzing data of patients with odontogenic infection and lymphatic filariasis.