  Proportional hazards are a common assumption when designing confirmatory
clinical trials in oncology. This assumption not only affects the analysis part
but also the sample size calculation. The presence of delayed effects causes a
change in the hazard ratio while the trial is ongoing since at the beginning we
do not observe any difference between treatment arms and after some unknown
time point, the differences between treatment arms will start to appear. Hence,
the proportional hazards assumption no longer holds and both sample size
calculation and analysis methods to be used should be reconsidered. The
weighted log-rank test allows a weighting for early, middle and late
differences through the Fleming and Harrington class of weights, and is proven
to be more efficient when the proportional hazards assumption does not hold.
The Fleming and Harrington class of weights, along with the estimated delay,
can be incorporated into the sample size calculation in order to maintain the
desired power once the treatment arm differences start to appear. In this
article, we explore the impact of delayed effects in group sequential and
adaptive group sequential designs, and make an empirical evaluation in terms of
power and type-I error rate of the of the weighted log-rank test in a simulated
scenario with fixed values of the Fleming and Harrington class of weights. We
also give some practical recommendations regarding which methodology should be
used in the presence of delayed effects depending on certain characteristics of
the trial.
