A wild bootstrap approach for the Aalen–Johansen estimator

We suggest a wild bootstrap resampling technique for nonparametric inference on transition probabilities in a general time‐inhomogeneous Markov multistate model. We first approximate the limiting distribution of the Nelson–Aalen estimator by repeatedly generating standard normal wild bootstrap variates, while the data is kept fixed. Next, a transformation using a functional delta method argument is applied. The approach is conceptually easier than direct resampling for the transition probabilities. It is used to investigate a non‐standard time‐to‐event outcome, currently being alive without immunosuppressive treatment, with data from a recent study of prophylactic treatment in allogeneic transplanted leukemia patients. Due to non‐monotonic outcome probabilities in time, neither standard survival nor competing risks techniques apply, which highlights the need for the present methodology. Finite sample performance of time‐simultaneous confidence bands for the outcome probabilities is assessed in an extensive simulation study motivated by the clinical trial data. Example code is provided in the web‐based Supplementary Materials.