Consequences on the two-stage approach: comparing treatments when survival curves may cross

For testing the efficacy of a treatment in a clinical trial (e.g. treatment vs. control), the Cox proportional hazards model is the well-accepted, conventional tool. When using this model, one must confirm that the required proportional hazards (PH) assumption holds true. If the PH assumption fails to hold, it may occur that upon examining a Kaplan-Meier (KM) plot, the survival curves appear to cross, suggesting long-term survival is higher among one group of patients. In this situation –given that the PH assumption does not hold, and given that the KM survival curves are observed to cross– there are options available, proposed as alternatives to the Cox PH model, which are used to test that a treatment yields better longterm survival. An important question which arises is whether the potential bias introduced by such a sequential model fitting procedure merits concern and, if so, what are effective mechanisms for correction. We investigate by means of simulation study and draw attention to the considerable drawbacks, with regards to power, of a simple resampling technique, the permutation adjustment, a natural recourse for addressing such challenges. Finally, we consider the recently proposed two-stage testing strategy of Qiu & Sheng (2008) and a new procedure based on permutation-adjusted bootstrap model averaging, as attractive alternatives.