A kernel log-rank test of independence for right-censored data

TL;DR

This paper proposes a new non-parametric independence test for right-censored survival data using kernel methods, which effectively detects complex dependencies and outperforms existing approaches.

Contribution

It introduces a kernel-based independence test combining log-rank tests and RKHS embeddings, with proven asymptotic properties and a practical Wild Bootstrap threshold.

Findings

Test performs better than existing methods in simulations

Effective at detecting complex non-linear dependencies

Computationally straightforward with consistent bootstrap threshold

Abstract

We introduce a general non-parametric independence test between right-censored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the Hilbert-Schmidt Independence Criterion (HSIC) test-statistic. We study the asymptotic properties of the test, finding sufficient conditions to ensure our test correctly rejects the null hypothesis under any alternative. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild Bootstrap procedure. Extensive investigations on both simulated and real data suggest that our testing procedure generally performs better than competing approaches in detecting complex non-linear dependence.