Nonparametric independence testing and regression for time-to-event data

Thesis

The main goal of this thesis is to develop statistical methods for non-parametric independence testing and regression between a covariate and a right-censored event-time. First, we study tests of independence that use reproducing kernel Hilbert spaces (RKHSs) to quantify the dependence in a dataset. In particular we study permutation tests with the Hilbert Schmidt independence criterion (HSIC) as the test-statistic. We show such tests are pointswise consistent, which means that, for each fixed alternative hypothesis, the probability the null hypothesis is rejected con-verges to 1 as the sample size converges to infinity. This shows that kernel-based permutation tests of independence are able to detect every type of independence. Second, we propose two nonparametric tests of independence between a covariate and right-censored time. The first of these tests, termed optHSIC, consists of a two-step procedure: first the censored dataset is transformed into an uncensored one using optimal transport, after which a standard permutation test with test statistic HSIC is applied to the uncensored dataset. The second proposed test is the kernel-logrank test. This test uses a supremum of scores over an RKHS as the test-statistic, and uses wild-bootstrap to test for significance. We show that these tests are able to detect a wider range of dependencies between covariates and event-times than existing methods. Lastly, we study scoring rules for right-censored regression models. We show that several often-used scoring rules are not proper, meaning that the true distribution may score worse than inaccurate distributions. Since this does not hold for the right-censored log-likelihood scoring rule, we then propose a method, termed SuMo-net, that uses neural networks to optimize the right-censored log-likelihood. SuMo-net models the cumulative distribution function and the density of a right-censored event-time jointly using partially monotonic neural networks and achieves competitive performance on a range of datasets.

Authors: Rindt, D

• DOI: 10.5287/ora-gjepojpmd
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: time-to-event data; neural networks; statistics; survival analysis; biostatistics
• Subjects: statistics