Knee replacement is the most commonly used surgical treatment for knee
arthritis. It has been reported that knee replacement rates vary acro
ss both regions and counties. This paper used data from Medicare patie
nts to develop explanations for the variation. One problem with our da
ta is that we do not have patient level information for Medicare patie
nts who did not have a knee replacement during the study period. There
fore, even though our data have a natural hierarchical structure (regi
on, county, patient), we cannot use a typical hierarchical model for t
he analysis due to missing patient level information. In this paper, w
e used a two-stage approach to analyse our data. In the first stage, w
e used an extra Poisson regression to model within-region variation of
knee replacement rates while adjusting for the type of patient demogr
aphic information we had, and in the second stage, we used an empirica
l Bayes method to model between-region variation of knee replacement r
ates.