BAYESIAN ESTIMATION UNDER INFORMATIVE SAMPLING: INVESTIGATING THE ASSOCIATION BETWEEN DEPRESSION AND INFLAMMATION
Survey data is often collected using complex sampling designs so that the probability of being included in the study is related to the outcome of interest (i.e. informative sample). Recently, a novel fully-Bayesian method has been developed for modeling data under informative sampling. Initial results indicate that this novel construction reduces bias in variance estimates compared to other pseudo-Bayesian techniques. The performance of this method has yet to be compared to traditional Frequentist approaches, which typically rely on Taylor series linearization (TSL) or resampling techniques for standard error (SE) estimation. Here, we modeled the relationship between depression and inflammation using data from the National Health and Nutrition Examination Survey using both a the fully-Bayesian method and a Frequentist method, specifically weighted least squares regression with TSL variance estimation. Although fully-Bayesian and the standard Frequentist approach generated similar parameter estimates, the fully-Bayesian model tended to produce smaller SEs than the Frequentist method. These findings suggest that the fully-Bayesian method performs equivalently to traditional Frequentist methods and may even provide better variance estimates than those computed by TSL. The current findings also replicate previous findings that the relationship between inflammation and depression is likely influenced by alcohol use, smoking, and Body Mass Index (BMI), but must be interpreted cautiously due to the high level of missing data.