Alternatives to the hazard ratio in summarizing efficacy in time-to-event studies: an example from influenza trials

Estimates of the efficacy of new medicines are key to the investigation of their clinical effectiveness. The most widely recommended approach to summarizing time-to-event data from clinical trials is to use a hazard ratio. When the proportional hazards assumption is questionable, a hazard ratio depends on the length of patient follow-up. Hazard ratios do not directly translate into differences in times to events and therefore can present difficulties in interpretation. This paper describes an area where summary by hazard ratio would seem unsuitable and explores alternative estimates of efficacy. In particular, the difference in median time to event between treatments can provide a useful and consistent measure of efficacy. Methods of calculating confidence intervals for differences in medians for censored time-to-event will be described. Accelerated failure time models provide a useful alternative approach to proportional hazards modelling. Estimates of the ratio of the median time to event between treatments are directly available from these models. One of the reasons given for summarizing time-to-event studies by a hazard ratio is to facilitate meta-analyses. The bootstrap estimate of standard error for difference in median in each trial can provide a method for combining results based on summary statistics.