Combining small-area smoking prevalence estimates from multiple surveys

Combining information from multiple surveys can improve the quality of small-area estimates. Customary approaches include the multiple-frame method and the statistical matching method. However, these techniques require individual data, whereas in practice often only aggregate estimates are available. Commercial surveys usually produce aggregate estimates without clear description of the methodology used. In this context bias modelling is crucial, for which we propose a series of Bayesian hierarchical models. These allow for additive biases, which are exchangeable between small-areas within surveys, and include the possibility of estimating correlations between data sources and trends over time. Our objective is to obtain combined estimates of smoking prevalence in each of the 48 local authorities across the East of England from seven data sources, which provide smoking prevalence estimates at the local authority level, but vary by time, sample size and methodology. The estimates adjust for the biases in commercial surveys but incorporate useful information from all the sources to provide more accurate and precise estimates. Our approach is more general than other methods and uses prevalence rates rather than individual data. It provides estimates of smoking prevalence in each area, based essentially on meta-analysis of synthetic estimates, and tools to evaluate the amount of bias in each data source.