We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use optimal transport to transform the censored dataset into an uncensored one, while preserving the relevant dependencies. We then apply a permutation test using the kernel-based dependence measure as a statistic to the transformed dataset. The type 1 error is proven to be correct in the case where censoring is independent of the covariate. Experiments indicate that optHSIC has power against a much wider class of alternatives than Cox proportional hazards regression and that it has the correct type 1 control even in the challenging cases where censoring strongly depends on the covariate.

中文翻译：

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协变量和右删失寿命之间独立性的基于内核和最优传输的测试

我们提出了一种独立性的非参数检验，称为 optHSIC，介于协变量和右删失寿命之间。因为审查的存在给应用标准的基于排列的测试方法带来了挑战，我们使用最佳传输将审查的数据集转换为未经审查的数据集，同时保留相关的依赖关系。然后，我们使用基于内核的依赖度量作为对转换后的数据集的统计量应用排列测试。在审查与协变量无关的情况下，类型 1 错误被证明是正确的。实验表明，与 Cox 比例风险回归相比，optHSIC 具有更广泛的替代方案类别，并且即使在审查强烈依赖于协变量的具有挑战性的情况下，它也具有正确的类型 1 控制。