Abstract
Accurate estimates of subnational health and demographic indicators are critical for informing policy. Many countries collect relevant data using complex household surveys, but when data are limited, direct weighted estimates of small area proportions may be unreliable. Area level models treating these direct estimates as response data can improve precision but often require known sampling variances of the direct estimators for all areas. In practice, the sampling variances are estimated, so standard approaches do not account for a key source of uncertainty. To account for variability in the estimated sampling variances, we propose a hierarchical Bayesian spatial area level model for small area proportions that smooths both the estimated proportions and sampling variances to produce point and interval estimates of rates of interest. We demonstrate the performance of our approach via simulation and application to vaccination coverage and HIV prevalence data from the Demographic and Health Surveys.