| The aggregate data study design (Prentice and Sheppard, 1995) aims to estimate exposure effects by regressing population-based disease rates on covariate data from survey samples in each population group. The design is motivated by the need to accurately estimate individual-level associations between exposures with limited within-population variability, such as dietary fat intake, and the risk of chronic diseases. By incorporating individual-level exposure and confounder data, the aggregate data study design can overcome many of the sources of bias that are inherent to ecological studies. In this work, we further develop the aggregate data model in the context of Bayesian disease mapping in order to allow for spatial correlation among disease rates across populations. We show how we can integrate the aggregate and disease-mapping models in order to provide an intuitive and generalizable approach to the modeling of spatial effects while retaining the efficiency of the exposure effect estimation. The parameters of this hierarchical aggregate data model can be estimated using a modified Gibbs sampling procedure.;We demonstrate through simulation studies that the proposed model yields improvements in estimation, and is fairly robust to the additional parametric assumptions of the model. In particular, under independent disease rates, the exposure effect variance and the exchangeable random effects variance are more accurately estimated than under the original aggregate data model. Estimation of the exposure effect is shown to be insensitive to the specification of the prior variance of the exposure effect, and the prior distributions of the two random effects variance components. Under a variety of data scenarios, the hierarchical aggregate data model gives relatively unbiased estimates of the exposure effect using covariate data from a sample of 100 (of a total of 5000) individuals per group. However, smaller sample sizes resulted in attenuation of the exposure effect estimates, especially under a reduced ratio of between-group to total covariate variation. |
