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A Kernel Log-Rank Test of Independence for Right-Censored Data

Fernandez, T; Gretton, A; Rindt, D; Sejdinovic, D; (2021) A Kernel Log-Rank Test of Independence for Right-Censored Data. Journal of the American Statistical Association 10.1080/01621459.2021.1961784. Green open access

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Abstract

We introduce a general nonparametric 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 nonlinear dependence.

Type: Article
Title: A Kernel Log-Rank Test of Independence for Right-Censored Data
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/01621459.2021.1961784
Publisher version: https://doi.org/10.1080/01621459.2021.1961784
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Hilbert space, Independence testing, Log-rank test, Reproducing kernel, Right-censoring, ADJUVANT THERAPY, SURVIVAL-TIME, OMNIBUS TEST, LEVAMISOLE, CARCINOMA
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10139742
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