  What can be considered an appropriate statistical method for the primary
analysis of a randomized clinical trial (RCT) with a time-to-event endpoint
when we anticipate non-proportional hazards owing to a delayed effect? This
question has been the subject of much recent debate. The standard approach is a
log-rank test and/or a Cox proportional hazards model. Alternative methods have
been explored in the statistical literature, such as weighted log-rank tests
and tests based on the Restricted Mean Survival Time (RMST). While weighted
log-rank tests can achieve high power compared to the standard log-rank test,
some choices of weights may lead to type-I error inflation under particular
conditions. In addition, they are not linked to an unambiguous estimand.
Arguably, therefore, they are difficult to intepret. Test statistics based on
the RMST, on the other hand, allow one to investigate the average difference
between two survival curves up to a pre-specified time point $\tau$ -- an
unambiguous estimand. However, by emphasizing differences prior to $\tau$, such
test statistics may not fully capture the benefit of a new treatment in terms
of long-term survival. In this article, we introduce a graphical approach for
direct comparison of weighted log-rank tests and tests based on the RMST. This
new perspective allows a more informed choice of the analysis method, going
beyond power and type I error comparison.
