  Studies to compare the survival of two or more groups using time-to-event
data are of high importance in medical research. The gold standard is the
log-rank test, which is optimal under proportional hazards. As the latter is no
simple regularity assumption, we are interested in evaluating the power of
various statistical tests under different settings including proportional and
non-proportional hazards with a special emphasize on crossing hazards. This
challenge has been going on for many years now and multiple methods have
already been investigated in extensive simulation studies. However, in recent
years new omnibus tests and methods based on the restricted mean survival time
appeared that have been strongly recommended in biometric literature. Thus, to
give updated recommendations, we perform a vast simulation study to compare
tests that showed high power in previous studies with these more recent
approaches. We thereby analyze various simulation settings with varying
survival and censoring distributions, unequal censoring between groups, small
sample sizes and unbalanced group sizes. Overall, omnibus tests are more robust
in terms of power against deviations from the proportional hazards assumption.
