  Survival time is the primary endpoint of many randomized controlled trials,
and a treatment effect is typically quantified by the hazard ratio under the
assumption of proportional hazards. Awareness is increasing that in many
settings this assumption is a-priori violated, e.g. due to delayed onset of
drug effect. In these cases, interpretation of the hazard ratio estimate is
ambiguous and statistical inference for alternative parameters to quantify a
treatment effect is warranted. We consider differences or ratios of milestone
survival probabilities or quantiles, differences in restricted mean survival
times and an average hazard ratio to be of interest. Typically, more than one
such parameter needs to be reported to assess possible treatment benefits, and
in confirmatory trials the according inferential procedures need to be adjusted
for multiplicity. By using the counting process representation of the mentioned
parameters, we show that their estimates are asymptotically multivariate normal
and we propose according parametric multiple testing procedures and
simultaneous confidence intervals. Also, the logrank test may be included in
the framework. Finite sample type I error rate and power are studied by
simulation. The methods are illustrated with an example from oncology. A
software implementation is provided in the R package nph.
