Estimating the Prevalence of Depression by Area Using a Bayesian Pooled Model with Covariate Correction

In spite of nationwide large-scale surveys, sample size issues may arise when estimating for small areas such as towns. In these cases, hierarchical Bayesian pooling models can enhance the reliability of estimates by borrowing information from similar surrounding areas. Hierarchical Bayesian pooling models can share information between areas either directly or indirectly through hyperparameters defined in the prior distribution, thereby reinforcing limited sample information. However, an over-shrinkage problem can arise during the information-sharing process. This study aims to establish a structural model incorporating a generalized linear regression model with regional characteristic covariates for the hyperparameters responsible for sharing information between areas. This approach accounts for variations according to regional characteristic covariates while facilitating the sharing of regional information through intercept terms, thereby producing reliable small area estimates. Meanwhile, using the established hierarchical Bayesian regression model, we estimated the prevalence of depression in small areas, and identified and examined the covariates responsible for regional variations.