Non-parametric estimation of survival probabilities with a time-dependent exposure switch: Application to (simulated) heart transplant data

Background: To summarize the survival experience of patients waiting for heart transplant and to compare it with the post-transplant survival it is not possible to use the Kaplan-Meier estimator considering the intervention status as fixed in time because of the well known “immortal time bias” issue. Methods: We reviewed and applied to a simulated dataset the available methods to perform a non-parametric analysis accounting for the time-varying nature of the transplant status. Specifically we considered the Simon-Makuch estimator and the recently proposed “clock-back” estimator. Results: We showed that the Simon-Makuch estimator for the survival of patients on list is unbiased but the corresponding estimator of the post-transplant survival is not reliable for non-markov contexts like the one considered. Instead, if the semi-Markov assumption could be postulated (the post-transplant mortality depends mainly on the time since transplant and not on the waiting time to the intervention), the "clock-back" estimator produces valid results. Conclusion: We enlightened the importance of testing the process memory assumptions (e.g. Markov properties) in order to choose the approach more reliable. Moreover, we recommend the use of the Simon-Makuch method to study the survival of patients before the intervention and the use of the "clock back" estimator for the post-intervention survival in semi-markovian contexts.