Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data

TL;DR

This paper introduces new kernelized Stein discrepancy tests tailored for censored time-to-event data, improving goodness-of-fit testing in survival analysis by addressing challenges posed by censoring.

Contribution

It proposes a collection of novel kernelized Stein discrepancy tests specifically designed for censored data, with theoretical analysis and empirical validation showing superior performance.

Findings

Proposed tests outperform existing goodness-of-fit tests.

Theoretical properties of the tests are established.

Empirical results demonstrate improved accuracy in censored data scenarios.

Abstract

Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest such as death from a particular disease or failure of a component in a mechanical system. This type of data is unique due to the presence of censoring, a type of missing data that occurs when we do not observe the actual time of the event of interest but, instead, we have access to an approximation for it given by random interval in which the observation is known to belong. Most traditional methods are not designed to deal with censoring, and thus we need to adapt them to censored time-to-event data. In this paper, we focus on non-parametric goodness-of-fit testing procedures based on combining the Stein's method and kernelized discrepancies. While for uncensored data, there is a natural way of implementing a kernelized Stein discrepancy test, for censored data there are several options, each of them with different advantages and disadvantages. In this paper, we propose a collection of kernelized Stein discrepancy tests for time-to-event data, and we study each of them theoretically and empirically; our experimental results show that our proposed methods perform better than existing tests, including previous tests based on a kernelized maximum mean discrepancy.