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

Rindt David (), Sejdinovic Dino () and Steinsaltz David ()
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Rindt David: Department of Statistics, University of Oxford, Oxford, UK
Sejdinovic Dino: Department of Statistics, University of Oxford, Oxford, UK
Steinsaltz David: Department of Statistics, University of Oxford, Oxford, UK

The International Journal of Biostatistics, 2021, vol. 17, issue 2, 331-348

Abstract: 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.

Keywords: independence testing; kernel methods; reproducing kernel Hilbert spaces; survival analysis (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/ijb-2020-0022

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