Methods and results for small area estimation using smoking data from the 2008 National Health Interview Survey

The National Health Interview Survey, conducted by the National Center for Health Statistics, is designed to provide reliable design-based estimates for a wide range of health-related variables for national and four major geographical regions of the USA. However, state-level or substate-level estimates are likely to be unreliable because they are based on small sample sizes. In this paper, we compare the efficiency of different area-level models in estimating smoking prevalence for the 50 US states and the District of Columbia. Our study is based on survey data from the 2008 National Health Interview Survey in conjunction with a number of potentially related auxiliary variables obtained from the American Community Survey, an ongoing large complex survey conducted by the US Census. A major portion of this study is devoted to the investigation of several methods for estimating survey sampling variances needed to implement an area-level hierarchical model. Based on our findings, a hierarchical Bayesian method that uses a survey-adjusted random sampling variance model to capture the complex survey sampling variability appears to be somewhat superior to the other considered area-level models in accounting for small sample behavior of estimated survey sampling variances. Several diagnostic procedures are presented to compare the proposed methods.