Random Jump Forests

Martin Bladt, Rasmus Frigaard Lemvig

Random jump forests are introduced as a nonparametric tool for estimating conditional cumulative transition rates and occupation probabilities in multi-state models. The main idea is that a single tree partitions the covariate space for all transitions simultaneously, using partially observed trajectories, and with Nelson--Aalen estimators at the terminal nodes. Occupation probabilities are recovered through the product integral without requiring the Markov assumption. Uniform consistency and a functional central limit theorem for the estimators of cumulative rates can be established under the assumption that the covariate vector takes finitely many values, and under suitable splitting conditions. In particular, pointwise confidence intervals and simultaneous bands are available in the Markov case. Simulation studies show a predictive accuracy close to the correctly specified benchmark models and marked improvements when benchmarks are misspecified, with further illustration on four biomedical data sets. In the coverage study, confidence bands attain near-nominal coverage in several settings, with pooling of heterogeneous rates being the main source of possible undercoverage. The…