Statistical approaches for drug effectiveness studies after liver transplant have used a survival model with changes in treatment as a time-dependent covariate. However, the approach requires that changes in the time-dependent covariate be unrelated to survival outcome. Usually this is not the case, as one drug may be discontinued and an alternative chosen due to the declining health status of the patient. Other approaches examine only subjects who remain on the same drug over a time window, which discards valuable data and may lead to biased effects since this excludes data related to early deaths and to individuals who perform poorly on the drug and had to switch treatments. Because of these issues there are conflicting results seen in the evaluation of immunosuppressive drug effectiveness after liver transplant. We propose a joint survival outcome model with a time-to-drug-change event and a terminal event in graft failure that is useful in drug effectiveness studies where subjects are discontinued from an immunosuppressant (in favour of alternative treatment) due to health reasons. We also include a longitudinal biomarker component. The model takes account of the dependencies across out- comes through shared random effects. Using a Markov chain Monte Carlo approach, we fit the joint model to data from liver transplant recipients from the Scientific Registry for Transplant Recipients.