In this paper we propose a Multiple kernel testing procedure to infer survival data when several factors (e.g. different treatment groups, gender, medical history) and their interaction are of interest simultaneously. Our method is able to deal with complex data and can be seen as an alternative to the omnipresent Cox model when assumptions such as proportionality cannot be justified. Our methodology combines well-known concepts from Survival Analysis, Machine Learning and Multiple Testing: differently weighted log-rank tests, kernel methods and multiple contrast tests. By that, complex hazard alternatives beyond the classical proportional hazard set-up can be detected. Moreover, multiple comparisons are performed by fully exploiting the dependence structure of the single testing procedures to avoid a loss of power. In all, this leads to a flexible and powerful procedure for factorial survival designs whose theoretical validity is proven by martingale arguments and the theory for $V$-statistics. We evaluate the performance of our method in an extensive simulation study and illustrate it by a real data analysis.
翻译:在本文中,我们提出了一个多重内核测试程序,用以在几个因素(如不同的治疗组、性别、医疗史)及其相互作用引起关注时推断生存数据。我们的方法能够同时处理复杂的数据,当相称性等假设无法证明合理时,可以被视为无所不在的考克斯模型的替代物。我们的方法结合了生存分析、机器学习和多重测试等众所周知的概念:不同的加权日志测试、内核方法和多重对比测试。通过这种方法,可以探测出超出传统比例风险设置的复杂危险替代物。此外,通过充分利用单一测试程序的依赖性结构来进行多重比较,以避免丧失权力。这总之,导致对要素生存设计采取灵活而有力的程序,其理论有效性得到马丁格尔论点和美元统计学理论的证明。我们在广泛的模拟研究中评估了我们方法的绩效,并通过真实的数据分析加以说明。