Wild Bootstrap for Counting Process-Based Statistics

TL;DR

This paper develops a unified martingale-based framework for the large sample properties of the wild bootstrap in time-to-event data analysis, covering various models including the Fine-Gray model.

Contribution

It introduces a comprehensive theoretical framework for the wild bootstrap in time-to-event analysis, including new results for the Fine-Gray model with practical demonstrations.

Findings

The wild bootstrap provides reliable inference in time-to-event models.

The framework applies to a wide range of non- and semiparametric methods.

Simulation and real data illustrate the method's effectiveness.

Abstract

The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper consists of two parts: in Part~I, a general framework is developed in which the large sample properties are established in a unified way by using martingale structures. The framework includes most of the well-known non- and semiparametric statistical methods in time-to-event analysis and parametric approaches. In Part II, the Fine-Gray proportional sub-hazards model exemplifies the theory for inference on cumulative incidence functions given the covariates. The model falls within the framework if the data are censoring-complete. A simulation study demonstrates the reliability of the method and an application to a data set about hospital-acquired infections illustrates the statistical procedure.