In this paper, we discuss the estimation problem of the competing risks model when the exact cause of failure for some units may not be completely observed. The failure times of the components are assumed to follow Weibull distributions with different shape and scale parameters according to each competing risk. In the applied competing risks analysis, it is common to have failed units during life testing which do not have a certain cause of failure. Actually, the cause is not completely missed but is only known to belong to a certain subset of all possible causes. This case is known as masking. We propose to analyse these data assuming an underling masking mechanism as apart of data model, to allow the potential dependency of the masking probability on the unknown cause of failure and/or the observed failure time, applying an appropriate Generalized Linear Model. The parameters of the joint competing risks and masking mechanism model are estimated using the maximum likelihood approach. Also, several simulation studies are conducted to access the effect of different masking rates, mechanisms and sample sizes on the parameter estimation of Weibull competing risks data with different sets of shape and scale parameters. Finally, a real data example is analysed to illustrate the application of the proposed methods.

中文翻译：

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具有原因和时间相关掩蔽机制的掩蔽竞争风险数据分析

在本文中，我们讨论了当可能无法完全观察到某些单元的确切故障原因时竞争风险模型的估计问题。根据每个竞争风险，假设组件的故障时间遵循具有不同形状和尺度参数的威布尔分布。在应用的竞争风险分析中，在寿命测试期间出现故障单元并没有特定的故障原因是很常见的。实际上，原因并没有完全被忽略，而只是知道属于所有可能原因的某个子集。这种情况称为掩蔽。我们建议假设底层屏蔽机制作为数据模型的一部分来分析这些数据，以允许屏蔽概率对未知故障原因和/或观察到的故障时间的潜在依赖性，应用适当的广义线性模型。使用最大似然法估计联合竞争风险和掩蔽机制模型的参数。此外，还进行了多项模拟研究，以了解不同掩蔽率、机制和样本大小对具有不同形状和尺度参数集的威布尔竞争风险数据的参数估计的影响。最后，通过一个真实的数据例子来说明所提出方法的应用。具有不同形状和尺度参数集的 Weibull 竞争风险数据参数估计的机制和样本大小。最后，通过一个真实的数据例子来说明所提出方法的应用。具有不同形状和尺度参数集的 Weibull 竞争风险数据参数估计的机制和样本大小。最后，通过一个真实的数据例子来说明所提出方法的应用。