Knee replacement is the most commonly used surgical treatment for knee arthritis. It has been reported that knee replacement rates vary across both regions and counties. This paper used data from Medicare patients to develop explanations for the variation. One problem with our data is that we do not have patient level information for Medicare patients who did not have a knee replacement during the study period. Therefore, even though our data have a natural hierarchical structure (region, county, patient), we cannot use a typical hierarchical model for the analysis due to missing patient level information. In this paper, we used a two-stage approach to analyse our data. In the first stage, we used an extra Poisson regression to model within-region variation of knee replacement rates while adjusting for the type of patient demographic information we had, and in the second stage, we used an empirical Bayes method to model between-region variation of knee replacement rates.