Alternatives to hazard ratios for comparing efficacy or safety of therapies in noninferiority studies
*Hajime Uno, Dana-Farber Cancer Institute  LJ Wei, Harvard University 

Keywords: hazard ratio, noninferiority, restricted mean survival time

A noninferiority study is often used to investigate whether a treatment’s efficacy or safety profile is acceptable compared to an alternative therapy regarding the time to a clinical event. The empirical quantification of the treatment difference for such a study is routinely based on the hazard ratio estimate. The hazard ratio, which is not a ratio of risk, may be difficult to interpret clinically. When the proportional hazards (PH) assumption is plausible, due to lack of a benchmark reference value of the hazard function, it is hard to assess if the resulting hazard ratio indicates a clinically meaningful difference between two groups. Moreover, when the PH assumption is violated, the meaning of the hazard ratio estimate is not obvious at all. The precision of the hazard ratio estimate depends primarily on the number of observed events, but not directly on either exposure times or the sample size of the study population. Therefore, if the event rate is low, the study may require an impractically large number of events to ensure that the prespecified noninferiority criterion for the hazard ratio is attainable. We discuss deficiencies of the current approach to design and analysis of a noninferiority study and provide robust alternatives. In particular, for a noninferiority safety study, the patients’ exposure times are more clinically important than the observed number of events. If the study patients’ exposure times are long enough to evaluate safety reliably, these alternative procedures can effectively provide clinically interpretable evidence on safety, even with relatively few observed events. We illustrate these procedures with data from cardiovascular safety studies. These alternative strategies to evaluate safety or efficacy of an intervention lead to more meaningful interpretations of the analysis results than the conventional one via the hazard ratio estimate.