The Wild Bootstrap for Multivariate Nelson-Aalen Estimators

TL;DR

This paper extends the wild bootstrap method to multivariate Nelson-Aalen estimators within Aalen's model, enabling more accurate inference in complex multistate survival analysis with practical applications and simulation validation.

Contribution

It introduces a rigorous extension of the wild bootstrap for multivariate Nelson-Aalen estimators under Aalen's model, applicable to multistate models with censored data.

Findings

Valid confidence bands and tests for hazard ratios.

Improved finite sample performance demonstrated in simulations.

Application to ICU ventilation data shows practical utility.

Abstract

We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson-Aalen estimator under Aalen's multiplicative intensity model. Aalen's model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study.