  While well-established methods for time-to-event data are available when the
proportional hazards assumption holds, there is no consensus on the best
approach under non-proportional hazards. A wide range of parametric and
non-parametric methods for testing and estimation in this scenario have been
proposed. In this review we identified EMA marketing authorization procedures
where non-proportional hazards were raised as a potential issue in the
risk-benefit assessment and extract relevant information on trial design and
results reported in the corresponding European Assessment Reports (EPARs)
available in the database at paediatricdata.eu.
  We identified 16 Marketing authorization procedures, reporting results on a
total of 18 trials. Most procedures covered the authorization of treatments
from the oncology domain. For the majority of trials NPH issues were related to
a suspected delayed treatment effect, or different treatment effects in known
subgroups. Issues related to censoring, or treatment switching were also
identified. For most of the trials the primary analysis was performed using
conventional methods assuming proportional hazards, even if NPH was
anticipated. Differential treatment effects were addressed using stratification
and delayed treatment effect considered for sample size planning. Even though,
not considered in the primary analysis, some procedures reported extensive
sensitivity analyses and model diagnostics evaluating the proportional hazards
assumption. For a few procedures methods addressing NPH (e.g.~weighted log-rank
tests) were used in the primary analysis. We extracted estimates of the median
survival, hazard ratios, and time of survival curve separation. In addition, we
digitized the KM curves to reconstruct close to individual patient level data.
Extracted outcomes served as the basis for a simulation study of methods for
time to event analysis under NPH.
