Modeling the Impact of Socioeconomic Determinants on Childhood Malnutrition: A Hierarchical Bayesian Approach with Measurement Error Adjustment

Problem considered: Reliable estimation of childhood malnutrition remains a major public health challenge in low-and middle-income countries, where large-scale surveys such as the Demographic and Health Surveys (DHS) often suffer from measurement error and data heterogeneity. Ignoring these issues can bias prevalence estimates and distort the identification of socioeconomic determinants. Methods: This study develops a hierarchical Bayesian logistic regression model that accounts for both measurement error and clustering effects by region and survey year. The model incorporates known sensitivity and specificity to adjust for outcome misclassification and includes random effects to capture between-region and temporal variability. Using simulated DHS-like data, the corrected model was compared to an uncorrected counterpart in terms of key performance metrics-prevalence, area under the Receiver Operating Characteristic(ROC) curve (AUC), and accuracy-across survey years (2004, 2011, 2018, and 2022). Results: The Bayesian correction improved predictive accuracy and reduced bias in prevalence estimates. The corrected model achieved consistently higher AUC values (0.882-0.930) compared to the uncorrected model (0.878-0.928), and exhibited lower mean squared error (0.121 vs. 0.137). The inclusion of regional and temporal random effects effectively captured unobserved heterogeneity. Posterior parameter estimates revealed several significant socioeconomic predictors influencing child malnutrition. Conclusion: The proposed Bayesian hierarchical framework demonstrates improved accuracy and robustness in estimating malnutrition prevalence when accounting for measurement error. These findings highlight the importance of error correction and multilevel modeling for more reliable health policy decision-making based on survey data.