Dormuth, Ina2025-02-072025-02-072024http://hdl.handle.net/2003/4344610.17877/DE290R-25277The comparison of different treatment groups in terms of time to a specific event is paramount in clinical practice. Statistical methods to address such research questions are of fundamental importance. Hence, various tests and effect measures have been proposed to quantify such differences. One fundamental approach combines reporting the hazard ratio as an effect measure and the log-rank test to quantify the derivation. The main reason is that the log-rank test is optimal under proportional hazards. It is the most powerful test to detect differences between treatment arms in such scenarios. However, if we consider other kinds of hazard patterns, the power of the LR potentially drops drastically. At the same time, under non-proportional hazards, the hazard ratio changes over time and does not remain constant, making it challenging to interpret as an overarching measure of effect. Consequently, we need alternative approaches and recommendations on using them in settings where we can not assume proportional hazards. This cumulative thesis is based on five publications dealing with non-proportional hazards. The first work summarizes the current state of two-group comparisons for time-to-event data under non-proportional hazards and compares the methods based on reconstructed real data. The second paper extends the comparison by including additional methods and reevaluating the approaches employing simulation studies. In the third manuscript, we revisit the average hazard ratio and the corresponding test statistic to derive a parametric and simulation-based sample size approach. The fourth manuscript extends the multi-directional weighted log-rank test to multiple testing problems, resulting in a new approach allowing for more than two treatment groups. Finally, the fifth publication incorporates the multi-directional log-rank test into an adaptive design, resulting in a highly flexible approach for situations with little prior knowledge.enSurvival analysisLog-rank testMultiple testingAdaptive designsAverage hazard ratios310PhDThesisMedizinische StatistikStichprobennahmeMultipler TestAdaptiver Test