Survival tree averaging by functional martingale-based residuals

Abstract

A large literature has been established for random survival forest (RSF), a popular tool developed to analyze right-censored failure time data, under various situations. However, its prediction performance may not be optimal sometimes. To address this issue, we propose two optimal model averaging methods based on martingale residual processes. In particular, an in-of-bag and out-of-bag (IBOB) data process is defined, and two new IBOB functionals criteria are derived for the selection of weights. Furthermore, for their implementation, a greedy algorithm is presented, and the asymptotic optimality of the proposed model averaging approaches is established along with the convergence of the greedy averaging algorithms. Finally, an extensive simulation study is conducted, which indicates that the proposed methods work well, and an illustration is provided.