Abstract
The motivation behind this talk are outcomes in randomized clinical time-to-event trials where neither Kaplan-Meier-type methodology nor competing risks suffice. In a study on stem cell transplanted leukemia patients, we will aim at demonstrating superiority w.r.t the outcome probability "alive w/o immunosuppressive therapy". In a treatment trial for severe infectious diseases, we will aim at demonstrating non-inferiority w.r.t the outcome probability "cured and alive" on the entire follow-up period. Both of these outcome probabilities are non-monotone, and the first outcome is complicated by immunosuppressive therapy being switched on and off a random number of times. To this end, we will suggest ("wild" or "weird") bootstrapping on the multivariate hazard scale which will be subsequently translated onto probabilities. Comparison of treatment groups will be based on time-simultaneous confidence bands. Unlike the standard bootstrap which draws with replacement from the data, we will not require an i.i.d. data structure, but only general martingale properties. Examples of deviations from an i.i.d. setting are event driven trials in oncology or nested case-control studies. We will also outline how a third bootstrap approach can be used for planning, e.g., of sample size based on published data only. Our underlying approach will be time-inhomogeneous Markov multistate models, and time permitting, we will also discuss non-Markov models.