Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data
This addresses the need for robust statistical tests in survival analysis and reliability theory, where censoring complicates data analysis, but it is incremental as it adapts existing kernelized Stein discrepancy methods to censored data.
The paper tackles the problem of non-parametric goodness-of-fit testing for time-to-event data with censoring by proposing kernelized Stein discrepancy tests, and it shows that these methods outperform existing tests, including kernelized maximum mean discrepancy tests, in experimental results.
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.