Lung transplantation is a specialized procedure used to treat chronic end-stage respiratory diseases. Due to the scarcity of lung donors, constructing fair and equitable lung transplant allocation methods is an issue that has been addressed with different strategies worldwide. This work aims to describe how Italy's "national protocol for the management of surplus organs in all transplant programs" functions through an online app to allocate lung transplants. We have developed two probability models to describe the allocation process among the various transplant centers. An online app was then created. The first model considers conditional probabilities based on a protocol flowchart to compute the probability for each area and transplant center to receive each n-th organ in the period considered. The second probability model is based on the generalization of the binomial distribution to correlated binary variables, which is based on Bahadur's representation, to compute the cumulative probability for each transplant center to receive at least nth organs. Our results show that the impact of the allocation of a surplus organ depends mostly on the region where the organ was donated. The discrepancies shown by our model may be explained by a discrepancy between the northern and southern regions in relation to the number of organs donated.
Keywords: excess organs; probability model; protocol; shiny app; surplus lungs.