SHORTAGE LEVEL OF MATCHING KIDNEY AND PANCREAS ORGANS FOR IMPLANT IS ESTIMATED

Organ transplants are increasingly done worldwide. The organ donors might be dead or alive. There are legal, ethical, medical and administrative issues to procure organs and to transplant them. However, the donor’s organs must fully match the recipient’s requirement before they are quickly transported as the time is the essence. The kidney or pancreas organs are more in demand. When a recipient needs two organs such as the kidney and pancreas, the requirements are made tighter and the process of finding both organs becomes tougher and longer. The patients register and wait with a hope to find both matching organs to be implanted. Because of their need for two matching organs, the patients ’ waiting time prolongs. In general, the number of waiting patients, y = 0,1,2,…., for r = 1,2,…., number of matching organs follows a negative binomial frequency pattern with (1-p)r denoting the chance of finding r matching organs by any one waiting patient and py denoting the collective chance for y patients not finding r organs. In reality, there is always a shortage of organs for waiting patients. When there is a shortage level, 0≤φ<1 of organs of the types from the living/dead donors increases, the chance for all the y waiting patients of not finding r organs should increase by a factor of 1-φ and the chance for any single patient to find r organs decreases accordingly. This idea triggers a need to tweak the negative binomial distribution and it is done in this article. The data for USA indicate that the kidne