Time‐to‐Event Modeling of Competing Risks With Intervening States in Transplantation

The criteria for the selection of who among the persons on the waiting is to receive an organ that has become available and who is to be placed on the list to begin with are the most contentious issues in organ transplantation. The decisions of whom to list and whom to transplant should take into account the net benefit to the individual patient and to the affected group as a whole. We present a method to compute the survival benefit by means of fully parametric modeling of the competing events (transplantation, death while awaiting the transplant, removal for other reasons), taking into account the transplant as an intervening state on the path to death post-transplant, and apply it to decisions whether to list or not list and whether to transplant or to leave on the waiting list or to remove from the list. The data were obtained from the Organ Procurement and Transplantation Network. They describe the outcomes of listings in January, 1996 through June, 1999, with a follow up of at least 1 year possible for all cases. The models produce estimates of event probabilities that accord well with the observed probabilities and predictions of the survival benefit due to transplantation that range from small negative values to increases in survival probability of 20–40% points in liver and heart transplantation, with the larger benefits generally seen in the more severely ill transplant candidates. These estimates are stable under variations of case mix, as ascertained by bootstrap analysis. The survival benefit of alternative actions can be calculated for the complex circumstances encountered clinically – competing sequential events whose probability evolves over time. The range and stability of the estimates are sufficient to permit the use of this measure to rank candidates for listing and for transplantation.