A Bayesian analysis of a proportion under non-ignorable non-response.

Area of Science:

• * Public Health Statistics
• * Survey Methodology
• * Biostatistics

Background:

• * The National Health Interview Survey (NHIS) is a key source for U.S. population health status assessment.
• * Household doctor visits serve as a crucial health indicator, but survey non-response poses a significant challenge.
• * Non-respondents may differ from respondents, potentially biasing health estimates.

Purpose of the Study:

• * To estimate the proportion of U.S. households with at least one doctor visit.
• * To investigate and adjust for non-ignorable non-response mechanisms in health survey data.
• * To develop a statistical model accounting for state-level variations in non-response.

Main Methods:

• * Employed a hierarchical Bayesian selection model to address non-ignorable non-response.
• * Utilized a 'borrow strength' approach across states, similar to small area estimation, due to parameter identifiability issues.
• * Conducted simulation studies comparing ignorable and non-ignorable models.

Main Results:

• * Demonstrated that non-response mechanisms are non-ignorable in some U.S. states.
• * Found that 95% credible intervals for household doctor visit probabilities and response probabilities provide valuable insights.
• * Inference on doctor visit probabilities was generally consistent across different models.

Conclusions:

• * Non-ignorable non-response significantly impacts health indicator estimates from surveys like NHIS.
• * The proposed Bayesian model effectively adjusts for non-response, enhancing data reliability.
• * Findings highlight the importance of accounting for non-response mechanisms in public health surveillance.