ABSTRACT Competing risks arise when an individual is exposed to the several causes of failure. In this case, the recorded data includes two components, the failure times and the cause of failure indicators. Such data may suffer from censoring in the former part and missingness in the latter part. Prior researches have ignored the missing mechanism when analysing such data which might lead to invalid statistical inferences. Since the ignorability assumption is unverifiable from the available data, the sensitivity analysis is recommended. In this paper, the Bayesian index of local sensitivity to non-ignorability (ISNI) is derived to quantify the sensitivity of Bayesian estimators to the ignorability assumption for hybrid censored incomplete competing risks data when the lifetimes follow exponential, Weibull, and generalized exponential distributions. Also, some simulation studies are conducted to evaluate the performance of the proposed Bayesian ISNI in different missing and competing risks scenarios. Finally, a real-world example is analysed for illustrative purposes.

中文翻译：

---

混合删失竞争风险数据不可忽视的失败原因的贝叶斯敏感性分析

摘要 当个人暴露于多种失败原因时，就会产生竞争风险。在这种情况下，记录的数据包括两个组成部分，故障次数和故障原因指标。此类数据可能会受到前一部分删失和后一部分缺失的影响。先前的研究在分析此类数据时忽略了缺失机制，这可能导致无效的统计推断。由于可忽略性假设无法从可用数据中得到验证，因此建议进行敏感性分析。在本文中，当生命周期遵循指数分布、威布尔分布和广义指数分布时，贝叶斯对不可忽略性的局部敏感性指数 (ISNI) 被推导出来量化贝叶斯估计量对混合删失不完全竞争风险数据的可忽略性假设的敏感性。此外，还进行了一些模拟研究，以评估所提出的贝叶斯 ISNI 在不同的缺失和竞争风险场景中的性能。最后，为了说明目的，分析了一个真实世界的例子。