# Non‐Markov Nonparametric Estimation of Complex Multistate Outcomes After Hematopoietic Stem Cell Transplantation

## TL;DR

The paper introduces a new statistical method to estimate complex health outcomes after stem cell transplants, using a technique that handles recurring events more accurately.

## Contribution

A novel wild bootstrap procedure is proposed for estimating probabilities in non-Markov multistate models with recurrent events.

## Key findings

- The wild bootstrap procedure for linear combinations of Kaplan–Meier estimators is adaptable to various multistate models.
- Confidence bands for chronic GvHD- and relapse-free survival were successfully generated using the proposed method.
- Simulations showed that the wild bootstrap provides better coverage probabilities compared to Efron's bootstrap.

## Abstract

Often probabilities of nonstandard time‐to‐event endpoints are of interest, which are more complex than overall survival. One such probability is chronic graft‐versus‐host disease (GvHD‐) and relapse‐free survival, the probability of being alive, in remission, and not suffering from chronic GvHD after stem cell transplantation, with chronic GvHD being a recurrent event. Because the probabilities for endpoints with recurrent events may not fall monotonically, one should not use the Kaplan–Meier estimator for estimation, but the Aalen–Johansen estimator. The Aalen–Johansen is a consistent estimator even in non‐Markov scenarios if state occupation probabilities are being estimated and censoring is random. In some multistate models, it is also possible to use linear combinations of Kaplan–Meier estimators, which do not depend on the Markov assumption but can estimate probabilities to be out of bounds. For these linear combinations, we propose a wild bootstrap procedure for inference and compare it with the wild bootstrap for the Aalen–Johansen estimator in non‐Markov scenarios. In the proposed procedure, the limiting distribution of the Nelson–Aalen estimator is approximated using the wild bootstrap and transformed via the functional delta method. This approach is adaptable to different multistate models. Using real data, confidence bands are generated using the wild bootstrap for chronic GvHD‐ and relapse‐free survival. Additionally, coverage probabilities of confidence intervals and confidence bands generated by Efron's bootstrap and the wild bootstrap are examined with simulations.