We propose Bayesian case influence diagnostics for complex survival models. We develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the Kullback-Leibler divergence (K-L divergence). We present a simplified expression for computing the K-L divergence between the posterior with the full data and the posterior based on single case deletion, as well as investigate its relationships to the conditional predictive ordinate. All the computations for the proposed diagnostic measures can be easily done using Markov chain Monte Carlo samples from the full data posterior distribution. We consider the Cox model with a gamma process prior on the cumulative baseline hazard. We also present a theoretical relationship between our case-deletion diagnostics and diagnostics based on Cox's partial likelihood. A simulated data example and two real data examples are given to demonstrate the methodology.

译文

我们提出了复杂生存模型的贝叶斯案例影响诊断。我们基于Kullback-Leibler散度 (k-l散度) 开发了关节和边缘后验分布的病例缺失影响诊断。我们提供了一个简化的表达式,用于基于单个病例删除来计算具有完整数据的后验与后验之间的k-l差异,并研究其与条件预测坐标的关系。使用来自完整数据后验分布的马尔可夫链蒙特卡洛样本,可以轻松完成建议的诊断措施的所有计算。我们考虑在累积基线风险上具有伽马过程的Cox模型。我们还提出了基于Cox部分可能性的病例删除诊断与诊断之间的理论关系。给出了一个模拟数据示例和两个真实数据示例来演示该方法。

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