Incorporating small-area estimation into mediation analyses with areal datasets

Various methods have been employed in the medical literature to conduct mediation analyses with areal datasets. These analyses are typically performed to understand why age-adjusted incidence or mortality rates vary by county or ZIP code-level characteristics. Two primary approaches are commonly used: the "Calculation before mediation" (C-BM) approach, where age-adjusted rates are calculated from the raw data for each areal unit and used as the outcome in the mediation analysis, and the "Small-area estimation before mediation" (SAE-BM) approach, which uses pre-existing small-area estimates as the outcome in the mediation analysis. However, these approaches have significant limitations that can impact the inferences around mediation effects and the overall conclusions of a mediation analysis. In this paper, we propose a new method, the "Small-area estimation within mediation" (SAE-WM) approach, for conducting mediation analyses with areal datasets. This method integrates Bayesian small-area estimation techniques into the mediation analysis outcome model, allowing for precise estimation of mediation effects with areal datasets. We conduct a simulation study to demonstrate the advantages of the SAE-WM method for estimating mediation effects with areal datasets, while highlighting the pitfalls and potential problems with the C-BM and SAE-BM methods. We also illustrate an application of the SAE-WM method to assess whether healthcare access mediates the relationship between ZIP code-level socioeconomic environment and age-adjusted colorectal cancer incidence rates in Iowa.