  Popular parametric and semiparametric hazards regression models for clustered
survival data are inappropriate and inadequate when the unknown effects of
different covariates and clustering are complex. This calls for a flexible
modeling framework to yield efficient survival prediction. Moreover, for some
survival studies involving time to occurrence of some asymptomatic events,
survival times are typically interval censored between consecutive clinical
inspections. In this article, we propose a robust semiparametric model for
clustered interval-censored survival data under a paradigm of Bayesian ensemble
learning, called Soft Bayesian Additive Regression Trees or SBART (Linero and
Yang, 2018), which combines multiple sparse (soft) decision trees to attain
excellent predictive accuracy. We develop a novel semiparametric hazards
regression model by modeling the hazard function as a product of a parametric
baseline hazard function and a nonparametric component that uses SBART to
incorporate clustering, unknown functional forms of the main effects, and
interaction effects of various covariates. In addition to being applicable for
left-censored, right-censored, and interval-censored survival data, our
methodology is implemented using a data augmentation scheme which allows for
existing Bayesian backfitting algorithms to be used. We illustrate the
practical implementation and advantages of our method via simulation studies
and an analysis of a prostate cancer surgery study where dependence on the
experience and skill level of the physicians leads to clustering of survival
times. We conclude by discussing our method's applicability in studies
involving high dimensional data with complex underlying associations.
