A Bayesian Framework for Combining Probability and Non-Probability Samples in Small Area Estimation

Music City Center 

The integration of probability (PS) and non-probability (NPS) samples offers a promising avenue for robust small area estimation, addressing challenges such as sample representation, measurement error, and sample size limitations. We propose a Bayesian hierarchical framework that leverages the complementary strengths of PS and NPS. We consider the scenario when the binary outcome measure of interest is measured in both studies but subject to measurement error. We introduce latent variables for binary outcomes and link them via a shared dependency structure. This approach provides a principled mechanism to utilize the representativeness of PS and the scale of NPS in estimating small-area means. Our methodology is demonstrated through applications to data from the Health and Retirement Study (HRS) and Electronic Health Records (EHR), offering insights into practical implications and utility in real-world settings. Preliminary simulation studies validate the efficacy and robustness of the proposed framework, highlighting its potential for broader application. This work contributes to the development of advanced statistical methods for combining disparate data sources and enhancing the precision and reliability of small area estimates.

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