Safety evaluation is an essential component of clinical trials. To protect study participants, these studies often implement safety stopping rules that will halt the trial if an excessive number of toxicity events occur. Existing safety monitoring methods often treat these events as binary outcomes. A strategy that instead handles these as time-to-event endpoints can offer higher power and a reduced time to signal of excess risk, but must manage additional complexities including censoring and competing risks. We propose the TITE-Safety approach for safety monitoring, which incorporates time-to-event information while handling censored observations and competing risks appropriately. This strategy is applied to develop stopping rules using score tests, Bayesian beta-extended binomial models, and sequential probability ratio tests. The operating characteristics of these methods are studied via simulation for common phase 2 and 3 trial scenarios. Across simulation settings, the proposed techniques offer reductions in expected toxicities of 20% or more compared to binary data methods and maintain the type I error rate near the nominal level across various event time distributions. These methods are demonstrated through a redesign of the safety monitoring scheme for BMT CTN 0601, a single arm, phase 2 trial that evaluated bone marrow transplant as treatment for severe sickle cell disease. Our R package "stoppingrule" offers functions to construct and evaluate these stopping rules, providing valuable tools for trial design to investigators.
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