It is a well known fact that race and ethnicity specificc variations exist in the treatment and survival of cancer patients. Studies based on breast cancer patients admitted to community hospitals in U.S depicted that there is significant difference in patterns of care between black and white breast cancer patients with blacks receiving lower quality and quantity of care. In this study, we look at this problem from a different perspective, treating the hospitals as small areas, and employing Bayesian techniques for parameter estimation. Two separate models are constructed to estimate the odds ratio of receiving liver scan (a pattern of care) for blacks and whites. The first model uses hospital-specific information while the second one uses pooled hospital data by borrowing strength from neighbouring hospitals. We have used the non-central hyper-geometric distribution as the basis for constructing the likelihood while estimation has been carried out using the griddy Metropolis-Hastings sampler. We apply our methodology on a National Cancer Institute (NCI) database. Although our results corroborate some of the observations from previous studies, it proposes a computationally attractive alternative to the established procedures in formulating and analyzing this problem.