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Popular parametric and semiparametric hazards regression models for clusteredsurvival data are inappropriate and inadequate when the unknown effects ofdifferent covariates and clustering are complex. This calls for a flexiblemodeling framework to yield efficient survival prediction. Moreover, for somesurvival studies involving time to occurrence of some asymptomatic events,survival times are typically interval censored between consecutive clinicalinspections. In this article, we propose a robust semiparametric model forclustered interval-censored survival data under a paradigm of Bayesian ensemblelearning, called Soft Bayesian Additive Regression Trees or SBART (Linero andYang, 2018), which combines multiple sparse (soft) decision trees to attainexcellent predictive accuracy. We develop a novel semiparametric hazardsregression model by modeling the hazard function as a product of a parametricbaseline hazard function and a nonparametric component that uses SBART toincorporate clustering, unknown functional forms of the main effects, andinteraction effects of various covariates. In addition to being applicable forleft-censored, right-censored, and interval-censored survival data, ourmethodology is implemented using a data augmentation scheme which allows forexisting Bayesian backfitting algorithms to be used. We illustrate thepractical implementation and advantages of our method via simulation studiesand an analysis of a prostate cancer surgery study where dependence on theexperience and skill level of the physicians leads to clustering of survivaltimes. We conclude by discussing our method's applicability in studiesinvolving high dimensional data with complex underlying associations.

Semiparametric analysis of clustered interval-censored survival data using Soft Bayesian Additive Regression Trees (SBART)