指数Weibull族混合固化率模型的随机期望最大化算法
A Stochastic Version of the EM Algorithm for Mixture Cure Rate Model with Exponentiated Weibull Family of Lifetimes
摘要：
缺失值的处理在生存数据的分析中起着重要的作用，特别是以治愈分数为标志的数据。在本文中，我们讨论的性质和实施的随机逼近的期望最大化（EM）算法，以获得极大似然（ML）型估计的情况下，缺失数据自然出现，由于右删失和一部分的个人是免疫的事件感兴趣的。假设非免疫个体的寿命服从一个灵活的三参数指数威布尔（EW）分布族，该分布族同时包含单调（递增和递减）和非单调（单峰和浴盆）风险函数.为了评估SEM算法的性能，在各种参数设置下进行了广泛的仿真研究。使用似然比检验，我们还进行了EW分布族内的模型判别。此外，我们研究了SEM算法的鲁棒性相对于离群值和算法的起始值。随机EM（SEM）算法优于研究良好的期望最大化算法的几种情况下也在给定的上下文中进行了检查。为了进一步证明，一个真实的生存数据皮肤黑色素瘤进行了分析，使用建议的治愈率模型与EW寿命分布和建议的估计技术。通过这些数据，我们说明了适用性的似然比检验拒绝几个众所周知的寿命分布嵌套在更广泛的类EW分布。
英文摘要：
Handling missing values plays an important role in the analysis of survival data, especially, the ones marked by cure fraction. In this paper, we discuss the properties and implementation of stochastic approximations to the expectation-maximization (EM) algorithm to obtain maximum likelihood (ML) type estimates in situations where missing data arise naturally due to right censoring and a proportion of individuals are immune to the event of interest. A flexible family of three parameter exponentiated-Weibull (EW) distributions is assumed to characterize lifetimes of the non-immune individuals as it accommodates both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub) hazard functions. To evaluate the performance of the SEM algorithm, an extensive simulation study is carried out under various parameter settings. Using likelihood ratio test we also carry out model discrimination within the EW family of distributions. Furthermore, we study the robustness of the SEM algorithm with respect to outliers and algorithm starting values. Few scenarios where stochastic EM (SEM) algorithm outperforms the well-studied EM algorithm are also examined in the given context. For further demonstration, a real survival data on cutaneous melanoma is analyzed using the proposed cure rate model with EW lifetime distribution and the proposed estimation technique. Through this data, we illustrate the applicability of the likelihood ratio test towards rejecting several well-known lifetime distributions that are nested within the wider class of EW distributions.
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