Composite estimation of drug prevalences for sub-state areas - ARCHIVED

The Gallup Organization has been conducting household surveys to study state-wide prevalences of alcohol and drug (e.g., cocaine, marijuana, etc.) use. Traditional design-based survey estimates of use and dependence for counties and select demographic groups have unacceptably large standard errors because sample sizes in sub-state groups are two small. Synthetic estimation incorporates demographic information and social indicators in estimates of prevalence through an implicit regression model. Synthetic estimates tend to have smaller variances than design-based estimates, but can be very homogeneous across counties when auxiliary variables are homogeneous. Composite estimates for small areas are weighted averages of design-based survey estimates and synthetic estimates. A second problem generally not encountered at the state level but present for sub-state areas and groups concerns estimating standard errors of estimated prevalences that are close to zero. This difficulty affects not only telephone household survey estimates, but also composite estimates. A hierarchical model is proposed to address this problem. Empirical Bayes composite estimators, which incorporate survey weights, of prevalences and jackknife estimators of their mean squared errors are presented and illustrated.