Multiple random change points in survival analysis with applications to clinical trials

There is often a presence of random change points (RCPs) with varying timing of hazard rate change among patients in survival analysis within oncology trials. This is in contrast to fixed change points in piecewise constant hazard models, where the timing of hazard rate change remains the same for all subjects. However, currently there is a lack of appropriate statistical methods to effectively tackle this particular issue. This article presents novel statistical methods that aim to characterize these complex survival models. These methods allow for the estimation of important features such as the probability of an event occurring and being censored, and the expected number of events within the clinical trial, prior to any specific time, and within specific time intervals. They also derive expected survival time and parametric expected survival and hazard functions for subjects with any finite number of RCPs. Simulation studies validate these methods and demonstrate their reliability and effectiveness. Real clinical data from an oncology trial is also used to apply these methods. The applications of these methods in oncology trials are extensive, including estimating hazard rates and rate parameters of RCPs, assessing treatment switching, delayed onset of immunotherapy, and subsequent anticancer therapies. They also have value in clinical trial planning, monitoring, and sample size adjustment. The expected parametric survival and hazard functions provide a thorough understanding of the behaviors and effects of RCPs in complex survival models.