We propose a new class of metrics, called the survival independence divergence (SID), to test dependence between a right-censored outcome and covariates. A key technique for deriving the SIDs is to use a counting process strategy, which equivalently transforms the intractable independence test due to the presence of censoring into a test problem for complete observations. The SIDs are equal to zero if and only if the right-censored response and covariates are independent, and they are capable of detecting various types of nonlinear dependence. We propose empirical estimates of the SIDs and establish their asymptotic properties. We further develop a wild bootstrap method to estimate the critical values and show the consistency of the bootstrap tests. The numerical studies demonstrate that our SID-based tests are highly competitive with existing methods in a wide range of settings.

翻译：本文提出了一类称为生存独立性散度（SID）的新度量指标，用于检验右删失结果与协变量之间的依赖性。推导SID的关键技术是采用计数过程策略，该策略将因删失存在而难以处理的独立性检验问题等价转化为针对完全观测的检验问题。当且仅当右删失响应变量与协变量独立时，SID为零，且该方法能够检测多种类型的非线性依赖关系。我们提出了SID的经验估计量并建立了其渐近性质。进一步开发了wild bootstrap方法来估计临界值，并证明了bootstrap检验的一致性。数值研究表明，基于SID的检验方法在多种设定下均与现有方法相比具有高度竞争力。