Buckley-James boosting model based on extreme learning machine and random survival forests.

Buckley-James (BJ) model is a typical semiparametric accelerated failure time model, which is closely related to the ordinary least squares method and easy to be constructed. However, traditional BJ model built on linearity assumption only captures simple linear relationships, while it has difficulty in processing nonlinear problems. To overcome this difficulty, in this paper, we develop a novel regression model for right-censored survival data within the learning framework of BJ model, basing on random survival forests (RSF), extreme learning machine (ELM), and L boosting algorithm. The proposed method, referred to as ELM-based BJ boosting model, employs RSF for covariates imputation first, then develops a new ensemble of ELMs-ELM-based boosting algorithm for regression by ensemble scheme of L boosting, and finally, uses the output function of the proposed ELM-based boosting model to replace the linear combination of covariates in BJ model. Due to fitting the logarithm of survival time with covariates by the nonparametric ELM-based boosting method instead of the least square method, the ELM-based BJ boosting model can capture both linear covariate effects and nonlinear covariate effects. In both simulation studies and real data applications, in terms of concordance index and integrated Brier sore, the proposed ELM-based BJ boosting model can outperform traditional BJ model, two kinds of BJ boosting models proposed by Wang et al., RSF, and Cox proportional hazards model.