Non-constant hazard ratios in randomized controlled trials with composite endpoints

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.