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

## TL;DR

This paper introduces optHSIC, a nonparametric independence test for censored lifetimes using optimal transport to handle censoring, enabling more flexible detection of dependencies than traditional methods.

## Contribution

The paper presents a novel kernel-based independence test that effectively manages right-censored data through optimal transport, extending the applicability of dependence testing in survival analysis.

## Key findings

- optHSIC controls type 1 error under independent censoring
- It has greater power than Cox regression against various alternatives
- Effective even when censoring depends on covariates

## 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.