Level of Non-Matching Primary Transplant Cases According to Repeat Transplants Cases and a New Bivariate Poisson Distribution

In their practice, healthcare administrators and professionals often wonder about the non-matching level organs in transplants for the sake of future forecasting. Currently, there is no appropriate methodology to analyze the pertinent transplant data and describe the patterns. The lack of a suitable methodology in the literature originates from an incorrect impression that the primary transplant cases and the repeat transplant cases are two separate and independent Poisson probability processes. In fact, the actual data on the primary and repeat transplant cases in USA during the year 2014 indicate otherwise with a high degree of correlation between them. One wonders about the missing link and it hides in their model as this article articulates. The aims of this article are set to find an appropriate underlying model for the data and then construct an analytic methodology. In this research process, a novel and useful bivariate probability distribution is discovered and it is named here "seemingly independent bivariate Poisson distribution" for a lack of better title. Its statistical properties are derived, explained and illustrated. This new bivariate distribution helps not only to estimate the non-matching level of organs in the transplant cases but also to project the number of repeat transplant cases based on knowing the number of primary transplant cases and vice versa.