Empirical Bayes estimation of the prevalence of uninsured individuals by county in the state of Tennessee and analyses of predictive factors By Hoi K. Suen, Ed. D., Puiwa Lei, Ph.D., & Nicholas D. Warcholack, M.S. Systemics, Inc., State College, PA For The PROBE Laboratory Health Science Center University of Tennessee at Memphis 9/30/05 1. Introduction The objective of this project was to obtain the most stable estimate of the prevalence of individuals without health insurance, by county, throughout the state of Tennessee; such that the final estimates would have the least amount of random sampling error possible in spite of the inherent constraints of small samples. The effects of other factors on these rates were also examined. 2. Rationale There are 95 counties in Tennessee. In June 2005, the PROBE Laboratory of the University of Tennessee Health Science Center in Memphis was able to survey less than 5,000 individuals throughout the state, or an average of about 50 respondents per county. Such small samples rendered the initial county-level estimates of the proportion of uninsured residents inherently unstable with a large margin of error. In an effort to obtain stable proportion estimates with the least amount of estimation error, we used the Empirical Bayes (EB) estimation technique with the original survey data. Specifically, EB estimation was used in a “Known Variance” application of Hierarchical Linear Modeling (HLM). This model assumes that we have a moderately large sample (around 30 or more cases) and that the sampling distribution of the statistics is approximately normal with a sampling variance that is known. With 95 counties, we had a sample size of 95, exceeding the minimum assumption of 30. Additionally, we were able to use a natural log-odds function on the observed uninsured proportions for the counties from the survey. Thus, we were able to satisfy the assumptions of the statistical model reasonably well. EB estimate of prevalence of uninsured in Tennessee Page 1 of 20