A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes

Journal article

We propose a nonparametric test of independence, termed OPT-HSIC, 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 OPT-HSIC 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.

Authors: Rindt, D; Sejdinovic, D; Steinsaltz, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: De Gruyter
• Journal: International Journal of Biostatistics
• Volume: 17
• Issue: 2
• Pages: 331-348
• Publication date: 2020-12-02
• Acceptance date: 2020-10-28
• DOI: 10.1515/ijb-2020-0022
• ISSN: 1557-4679
• Language: English
• Keywords: stat.TH; math.ST; stat.ML; FFR; 62N03 Survival analysis and censored data