Survival Analysis of Shared-Path Adaptive Treatment Strategies

Adaptive treatment strategies closely mimic the reality of a physician's prescription process where the physician prescribes a medication to his/her patient and based on that patient's response to the medication, modifies the treatment. Two-stage randomization designs, more generally, sequential multiple assignment randomization trial (SMART) designs, are useful to assess adaptive treatment strategies where the interest is in comparing the entire sequence of treatments, including the patient's intermediate response. In this dissertation, we introduce the notion of shared-path and separate-path adaptive treatment strategies and propose weighted log-rank statistics to compare overall survival distributions of two shared-path or multiple two-stage adaptive treatment strategies. Large sample properties of the statistics are derived and the type I error rate and power of the tests are compared to standard statistics through simulation. We also propose a sample size equation to power a two-stage SMART comparing the overall survival of multiple adaptive treatment strategies.\ud \ud Public health significance: The treatment of many diseases and illnesses, especially those which are chronic (cancer, AIDS, depression, substance abuse, ADHD), includes sequences of treatments based on the individual's characteristics, behaviors, and responses. Treatment is inherently dynamic, but often, clinical trials are not designed or analyzed to take this dynamic feature into account. We present methods to adequately power and analyze clinical trials with time-to-event data which aim to compare these individualized sequences of treatments or adaptive treatment strategies. Through these methods and by comparing adaptive treatment strategies, patient outcomes can be operationalized and improved over time.\u