Harlan Campbell - MSc Defence

Comparing Treatments when Survival Curves Cross Unexpectedly

When 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– how should one determine if there is significant evidence to suggest that a treatment yields better long-term survival? Although many options exist, proposed as alternatives to the Cox PH model, does the potential bias introduced by the sequential model fitting procedure merit concern and if so require correction? We investigate this question by means of simulation study. Furthermore, we draw attention to the considerable drawbacks, with regards to power, of a simple resampling technique, the permutation adjustment. Finally, we consider the recently proposed two-stage testing strategy of Qiu & Sheng (2008) and a new procedure based on premutation-adjusted bootstrap model averaging as attractive recourses.