An Estimation Framework for Combining Probability and Non-probability Samples

Survey researchers are increasingly adopting hybrid sampling designs to address the limitations of traditional probability sampling, especially when studying rare or hard-to-reach populations. Challenges such as high screening costs, low statistical efficiency, and operational constraints make purely probability-based approaches impractical in many contexts. This article uses public data from the National Health and Nutrition Examination Survey to demonstrate how one can make population estimates from a hybrid sampling strategy that combines data from a stratified, multistage probability sample with data from a non-probability sample within the same primary sampling units as the probability sample. We outline a framework and discuss methods for analyzing data from a hybrid sample such as this, where covariates and survey outcomes are observed in both the probability and non-probability samples. We present a case study to illustrate the framework. We provide the case study R code in the supplementary material.