Center for Statistics, Hasselt University, Agoralaan Building D, B-3590 Diepenbeek, Belgium.
Biostatistics. 2013 Jul;14(3):433-46. doi: 10.1093/biostatistics/kxs053. Epub 2012 Dec 28.
Frailty models account for the clustering present in event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. In this paper, we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family, we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for the tests. Simulations and data examples illustrate the test's performance.
脆弱性模型可以解释事件时间数据中的聚类现象。具有共享脆弱性的比例风险模型可以表达每个个体的风险。通常，脆弱性假设为单参数伽马分布。在本文中，我们构建了正式的拟合优度检验来检验伽马脆弱性。我们构建了一个新的脆弱性模型类，通过使用某些关于伽马密度的正交多项式展开来扩展伽马脆弱性模型。对于这个扩展的模型族，我们得到了数据的边缘似然的显式表达式。阶选择检验基于在这样一系列扩展模型中找到最佳拟合模型。通过使用自举法来获得检验的 p 值。模拟和数据示例说明了该检验的性能。
