Analysis of multi-stage treatments for recurrent diseases.

Patients with a non-curable disease such as many types of cancer usually go through the process of initial treatment, a various number of disease recurrences and salvage treatments, and eventually death. The analysis of the effects of initial and salvage treatments on overall survival is not trivial. One may try to use disease recurrences and salvage treatments as time-dependent covariates in a Cox proportional hazards model. However, because disease recurrence is an intermediate outcome between initial treatment and final survival, the interpretation of such an estimation result is awkward. It does not estimate the causal effects of treatments on overall survival. Nevertheless, such causal effect estimates are critical for treatment decision making. Our approach to address this issue is that, at any treatment stage, for each patient, we compute a potential survival time if he or she would receive the optimal subsequent treatments, and use this potential survival time to do comparison between current-stage treatment groups. This potential survival time is assumed to follow an accelerated failure time model at each treatment stage and calculated by backward induction, starting from the last stage of treatment. By doing that, the effects on survival of different treatments at each stage can be consistently estimated and fairly compared. Under suitable conditions, these estimated effects have a causal interpretation. We evaluated the proposed model and estimation method by simulation studies and illustrated using the motivating, real data set that describes initial and salvage treatments for patients with soft tissue sarcoma.