  Prostate cancer patients who undergo prostatectomy are closely monitored for recurrence and metastasis using routine prostate-specific antigen (PSA) measurements. When PSA levels rise, salvage therapies are recommended to decrease the risk of metastasis. However, due to the side effects of these therapies and to avoid over-treatment, it is important to understand which patients and when to initiate these salvage therapies. In this work, we use the University of Michigan Prostatectomy registry Data to tackle this question. Due to the observational nature of this data, we face the challenge that PSA is simultaneously a time-varying confounder and an intermediate variable for salvage therapy. We define different causal salvage therapy effects defined conditionally on different specifications of the longitudinal PSA history. We then illustrate how these effects can be estimated using the framework of joint models for longitudinal and time-to-event data. All proposed methodology is implemented in the freely-available R package JMbayes2. 
Using Joint Models for Longitudinal and Time-to-Event Data to   Investigate the Causal Effect of Salvage Therapy after Prostatectomy