  The hazard ratio is routinely used as a summary measure to assess the
treatment effect in clinical trials with time-to-event endpoints. It is
frequently assumed as constant over time although this assumption often does
not hold. When the hazard ratio deviates considerably from being constant, the
average of its plausible values is not a valid measure of the treatment effect,
can be clinically misleading and common sample size formulas are not
appropriate.
  In this paper, we study the hazard ratio along time of a two-component
composite endpoint under the assumption that the hazard ratio for each
component is constant.
  This work considers two measures for quantifying the non-proportionality of
the hazard ratio: the difference $D$ between the maximum and minimum values of
hazard ratio over time and the relative measure $R$ representing the ratio
between the sample sizes for the minimum detectable and the average effects. We
illustrate $D$ and $R$ by means of the ZODIAC trial where the primary endpoint
was progression-free survival.
  We have run a simulation study deriving scenarios for different values of the
hazard ratios, different event rates and different degrees of association
between the components. We illustrate situations that yield non-constant hazard
ratios for the composite endpoints and consider the likely impact on sample
size.
  Results show that the distance between the two component hazard ratios plays
an important role, especially when they are close to 1. Furthermore, even when
the treatment effects for each component are similar, if the two-component
hazards are markedly different, hazard ratio of the composite is often
non-constant.
