Weighted log-rank statistic to compare shared-path adaptive treatment strategies

Adaptive treatment strategies (ATSs) more 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 designs, are useful to assess ATSs where the interest is in comparing the entire sequence of treatments, including the patient's intermediate response. In this paper, we introduce the notion of shared-path and separate-path ATSs and propose a weighted log-rank statistic to compare overall survival distributions of multiple two-stage ATSs, some of which may be shared-path. Large sample properties of the statistic are derived and the type I error rate and power of the test are compared with the standard log-rank test through simulation.