  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.
