Random Hazard Forests

Abstract

Clinical data sources such as electronic health records and wearable sensors record patient status repeatedly over follow-up, often at irregular times and on different schedules for different measurements. These data create opportunities for continuously updated, individualized risk prediction. Existing approaches, however, often simplify the temporal structure before modeling it. We introduce Random Hazard Forests (RHF), a survival tree ensemble that learns how a patient's hazard changes in continuous time as new measurements become available. RHF formulates the estimation problem directly through a nonparametric hazard likelihood for predictable covariate processes. An efficient working model guides tree construction, after which flexible time-varying hazards are estimated for each terminal node. Given any predictable covariate path, each tree follows the path through its terminal nodes over time and assembles the corresponding node-level hazards into a trajectory. Averaging these trajectories across trees yields the RHF pathwise hazard estimate. Because routing at each time uses only the covariate state available immediately beforehand, RHF accommodates internal longitudinal covariates without lookahead. Simulations and an intensive care application show that RHF accurately estimates changing risk under irregular and asynchronous covariate updates.