A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes
This work addresses a statistical challenge in survival analysis for researchers dealing with censored data, offering a more robust independence test compared to existing methods like Cox regression.
The authors tackled the problem of testing independence between covariates and right-censored lifetimes by proposing optHSIC, a nonparametric test that uses optimal transport to handle censoring and kernel-based dependence measures. Experiments showed optHSIC has correct type 1 error control and higher power against a wider class of alternatives than Cox regression, with specific gains in challenging censoring scenarios.
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.