Testing violations of the exponential assumption in cancer clinical trials with survival endpoints

Personalized cancer therapy requires clinical trials with smaller sample sizes compared to trials involving unselected populations that have not been divided into biomarker subgroups. The use of exponential survival modeling for survival endpoints has the potential of gaining 35% efficiency or saving 28% required sample size (Miller, 1983), making personalized therapy trials more feasible. However, the use of exponential survival has not been fully accepted in cancer research practice due to uncertainty about whether or not the exponential assumption holds. We propose a test for identifying violations of the exponential assumption using a reduced piecewise exponential approach. Compared with an alternative goodness-of-fit test, which suffers from inflation of type I error rate under various censoring mechanisms, the proposed test maintains the correct type I error rate. We conduct power analysis using simulated data based on different types of cancer survival distribution in the SEER registry database, and demonstrate the implementation of this approach in existing cancer clinical trials.