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A Wild Bootstrap Approach for the Aalen–Johansen Estimator
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COMBACTE-MAGNET recently published an article from its WP3B study. WP3B provides mathematical modelling in order to describe the burden of P. aeruginosa infections among intensive-care unit (ICU) patients.

Abstract: 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.