论文标题
分析左截短和右审查的竞争风险数据
Analysis of Left Truncated and Right Censored Competing Risks Data
论文作者
论文摘要
在本文中，根据潜在失败时间模型的假设，对左截短和右审查的竞争风险数据进行了分析。假设有两个竞争的失败原因，尽管大多数结果可以扩展到两个以上的失败原因。假定与失败的竞争原因相对应的生命值遵循具有相同形状参数但标度参数不同的Weibull分布。讨论了模型参数的最大似然估计过程，并使用Bootstrap方法提供了置信区间。当已知常见的形状参数时，可以以显式形式获得比例参数的最大似然估计器，并且当未知形式时，我们提供了一个简单的迭代过程来计算形状参数的最大似然估计器。在形状和比例参数上的一组非常灵活的先验集中，还解决了未知参数的贝叶斯估计值和相关的可信间隔。进行了广泛的蒙特卡洛模拟，以比较不同方法的性能。为说明目的提供了一个数值示例。最后，当假定两种竞争失败的原因是具有不同形状参数的独立Weibull分布时，结果已扩展。
In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibull distributions with the same shape parameter but different scale parameters. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the bootstrap approach. When the common shape parameter is known, the maximum likelihood estimators of the scale parameters can be obtained in explicit forms, and when it is unknown we provide a simple iterative procedure to compute the maximum likelihood estimator of the shape parameter. The Bayes estimates and the associated credible intervals of unknown parameters are also addressed under a very flexible set of priors on the shape and scale parameters. Extensive Monte Carlo simulations are performed to compare the performances of the different methods. A numerical example is provided for illustrative purposes. Finally the results have been extended when the two competing causes of failures are assumed to be independent Weibull distributions with different shape parameters.
