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：本文以贝叶斯新视角重新探讨了通过非参数转换模型（NTM）进行预测这一经典问题。尽管NTM在生存分析中具有稳健的预测能力而备受关注，但模型不可识别性使其估计颇具挑战。受后验预测分布唯一性的启发，我们在贝叶斯范式下借助上述NTM实现了高效预测。我们的策略是为非参数成分赋予弱信息先验，而非像现有文献那样通过添加复杂约束来识别模型。这一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，将无限维参数空间压缩至正象限（考虑到失效时间的非负性）；ii) 为重构后的变换函数构建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，我们提出了一种便捷精确的估计方法，通过后验修正对服从通用单位范数约束的可识别参数分量进行推断，从而有效估计相对风险。仿真实验与实际数据集应用表明，本文方法具有鲁棒性且优于对比方法。R软件包BuLTM可预测生存曲线、估计相对风险并支持后验检验。