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

Author

Listed:
  • Rindt David
  • Sejdinovic Dino
  • Steinsaltz David

    (Department of Statistics, University of Oxford, Oxford, UK)

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.

Suggested Citation

  • Rindt David & Sejdinovic Dino & Steinsaltz David, 2021. "A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes," The International Journal of Biostatistics, De Gruyter, vol. 17(2), pages 331-348, November.
    • Handle: RePEc:bpj:ijbist:v:17:y:2021:i:2:p:331-348:n:2
    DOI: 10.1515/ijb-2020-0022
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