Abstract
Emergency medical diseases (EMDs) are the leading cause of death worldwide. A time-to-death analysis is needed to accurately identify the risks and describe the pattern of an EMD because the mortality rate can peak early and then decline. Dose-ranging Phase II clinical trials are essential for developing new therapies for EMDs. However, most dose-finding trials do not analyze mortality as a time-to-event endpoint. We propose three Bayesian dose-response time-to-event models for a secondary mortality analysis of a clinical trial: a two-group (active treatment vs control) model, a three-parameter sigmoid EMAX model, and a hierarchical EMAX model. The study also incorporates one specific active treatment as an active comparator in constructing three new models. We evaluated the performance of these six models and a very popular independent model using simulated data motivated by a randomized Phase II clinical trial focused on identifying the most effective hyperbaric oxygen dose to achieve favorable functional outcomes in patients with severe traumatic brain injury. The results show that the three-group, EMAX, and EMAX model with an active comparator produce the smallest averaged mean squared errors and smallest mean absolute biases. We provide a new approach for time-to-event analysis in early-phase dose-ranging clinical trials for EMDs. The EMAX model with an active comparator can provide valuable insights into the mortality analysis of new EMDs or other conditions that have changing risks over time. The restricted mean survival time, a function of the model's hazards, is recommended for displaying treatment effects for EMD research.