Estimation of the causal effects on survival of two-stage nonrandomized treatment sequences for recurrent diseases

In the treatment of cancer, patients commonly receive a variety of sequential treatments. The initial treatments administered following diagnosis can vary, as well as subsequent salvage regimens given after disease recurrence. This article considers the situation where neither initial treatments nor salvage treatments are randomized. Assuming there are no unmeasured confounders, we estimate the joint causal effects on survival of initial and salvage treatments, that is, the effects of two-stage treatment sequences. For each individual treatment sequence, we estimate the survival distribution function and the mean restricted survival time. Different treatment sequences are then compared using these estimates and their corresponding covariances. Simulation studies were conducted to evaluate the performance of the methods, including their sensitivity to the violation of the assumption of no unmeasured confounders. The methods are illustrated by a retrospective study of patients with soft tissue sarcoma, which motivated this research.