Small area estimation for health surveys

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their