Research Article Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach Tayeb Mohammadi, 1 Soleiman Kheiri, 2 and Morteza Sedehi 3 1 Student’s Research Committee, Shahrekord University of Medical Sciences, Shahrekord, Iran 2 Social Health Determinants Research Center, Shahrekord University of Medical Sciences, Shahrekord, Iran 3 Epidemiology and Biostatistics Department, Shahrekord University of Medical Sciences, Shahrekord, Iran Correspondence should be addressed to Soleiman Kheiri; kheiri@skums.ac.ir Received 14 April 2016; Accepted 16 August 2016 Academic Editor: Dong Song Copyright © 2016 Tayeb Mohammadi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recognizing the factors afecting the number of blood donation and blood deferral has a major impact on blood transfusion. Tere is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-infated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. Te data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero- infation parameter, and regression coefcients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-infated Poisson model were ftted on the data and were compared using the deviance information criteria (DIC). Te results showed that the bivariate zero-infated Poisson regression model ftted the data better than the other models. 1. Introduction Blood transfusion is so important in health system that it plays a big part in saving many people’s lives in normal and emergency situations. Furthermore, it has a noticeable impact on improving the quality of life and consequently the life expectancy of chronic patients. Nevertheless, many patients either die due to lack of access to safe blood transfusion or at least sufer from it. According to the World Health Organization report, about one percent of the population of every country is in need of blood donation [1]. Today, the need for blood and its products is increasing day by day [2]. Since some diseases may be caused by blood transfusion, screening the donors and detecting potential healthy donors are of great importance [3]. For that matter, lack of healthy donors has always been a serious problem for blood banks to supply sufcient and healthful blood [4, 5]. Terefore, one of the main goals of blood transfusion centers is detecting and preserving healthy donors and preventing unhealthful blood donation which may cause many diseases to be created or aggravated [2]. Nonetheless, even from among those who are eligible to donate blood only a small portion really become blood donors [6]. Inasmuch as the screening test is done at each donation to separate healthful from unhealthful blood, the more the blood donation is, the higher the chances of getting healthful blood will be. Tat is why recognizing the factors which infuence blood donation is of great importance in attracting potential donors and turning them into regular donors [3]. From among all the laboratory screening methods to prevent the transference of infection through blood, the only truly efective method is to select healthy donors and not allow ineligible donors to donate blood [7]. People who are not eligible to donate blood are called “deferred donors” [8]. Most deferrals are “temporary” and exist due to taking certain medications before donation, high or low blood pressure, anemia, high-risk behavior, and so forth. Tese deferrals Hindawi Publishing Corporation Computational and Mathematical Methods in Medicine Volume 2016, Article ID 7878325, 7 pages http://dx.doi.org/10.1155/2016/7878325