This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust prediction capability in survival analysis. Inspired by the uniqueness of the posterior predictive distribution, we achieve efficient prediction via the NTM aforementioned under the Bayesian paradigm. Our strategy is to assign weakly informative priors to nonparametric components rather than identify the model by adding complicated constraints in the existing literature. The Bayesian success pays tribute to i) a subtle cast of NTMs by an exponential transformation for the purpose of compressing spaces of infinite-dimensional parameters to positive quadrants considering non-negativity of the failure time; ii) a newly constructed weakly informative quantile-knots I-splines prior for the recast transformation function together with the Dirichlet process mixture model assigned to the error distribution. In addition, we provide a convenient and precise estimator for the identified parameter component subject to the general unit-norm restriction through posterior modification, enabling effective relative risks. Simulations and applications on real datasets reveal that our method is robust and outperforms the competing methods. An R package BuLTM is available to predict survival curves, estimate relative risks, and facilitate posterior checking.

翻译：本文以新的贝叶斯方法处理基于非参数变换模型(NTM)的经典预测问题。尽管NTM因在生存分析中具有稳健的预测能力而备受关注，但其模型不可识别性使得估计过程极具挑战性。受后验预测分布唯一性的启发，我们通过贝叶斯框架下的NTM实现了高效预测。我们的策略是为非参数分量分配弱信息先验，而非像现有文献那样通过添加复杂约束来识别模型。贝叶斯方法的成功归功于：i) 通过指数变换对NTM进行巧妙重构，将无穷维参数空间压缩至正象限，以适应失效时间的非负性；ii) 为新构建的变换函数设计了基于分位数节点的弱信息I样条先验，并结合狄利克雷过程混合模型对误差分布建模。此外，我们通过后验修正提出了符合一般单位范数约束的识别参数分量的便捷精确估计量，从而实现了有效的相对风险估计。模拟实验与真实数据应用表明，该方法具有稳健性且优于现有竞争方法。本文提供的R包BuLTM可预测生存曲线、估计相对风险并支持后验检验。