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.

中文翻译：

---

使用软贝叶斯加性回归树 (SBART) 对聚类区间删失生存数据进行半参数分析

当不同协变量和聚类的未知影响很复杂时，用于聚类生存数据的流行参数和半参数风险回归模型是不合适和不充分的。这需要一个灵活的建模框架来产生有效的生存预测。此外，对于一些涉及到一些无症状事件发生时间的生存研究，生存时间通常是连续临床检查之间的间隔截尾。在本文中，我们提出了一种在贝叶斯集成学习范式下用于聚类间隔删失生存数据的鲁棒半参数模型，称为软贝叶斯加性回归树或 SBART（Linero 和 Yang，2018），它结合了多个稀疏（软）决策树以获得出色的预测准确性。我们通过将风险函数建模为参数基线风险函数和使用 SBART 的非参数组件的乘积来开发一种新的半参数风险回归模型，该模型包含聚类、主效应的未知函数形式以及各种协变量的交互作用。除了适用于左删失、右删失和区间删失生存数据外，我们的方法还使用数据增强方案实现，该方案允许使用现有的贝叶斯反拟合算法。我们通过模拟研究和前列腺癌手术研究的分析来说明我们方法的实际实施和优势，其中对医生的经验和技能水平的依赖导致生存时间的聚集。我们通过讨论我们的方法得出结论