A wild bootstrap approach for the Aalen-Johansen estimator

Area of Science:

• Biostatistics
• Medical Statistics
• Survival Analysis

Background:

• Time-inhomogeneous Markov multistate models are complex for analyzing transition probabilities.
• Standard survival and competing risks methods are insufficient for non-monotonic time-to-event outcomes.

Purpose of the Study:

• To propose a novel wild bootstrap resampling technique for nonparametric inference on transition probabilities.
• To develop a method applicable to general time-inhomogeneous Markov multistate models.
• To address non-standard time-to-event outcomes where traditional methods fail.

Main Methods:

• Approximation of the Nelson-Aalen estimator's limiting distribution using wild bootstrap variates.
• Application of a functional delta method transformation for transition probability inference.
• Validation through an extensive simulation study assessing time-simultaneous confidence bands.

Main Results:

• The wild bootstrap technique provides a conceptually simpler approach to resampling for transition probabilities.
• The method is suitable for analyzing non-monotonic outcome probabilities over time.
• Simulation studies demonstrate the finite sample performance of confidence bands.

Conclusions:

• The proposed wild bootstrap method offers a viable alternative for nonparametric inference in complex Markov models.
• This methodology is crucial for analyzing specific time-to-event outcomes in clinical research, such as in leukemia patient studies.
• The technique facilitates a more accurate understanding of treatment effects in challenging clinical scenarios.