Title: Bayesian Modeling for Mental Health Surveys
Description: Sample surveys are often used to collect data for obtaining estimates of finite population quantities, such as disease prevalence. However, non-response and sampling frame under-coverage can cause the survey sample to differ from the target population in important ways. To reduce bias in the survey estimates that can arise from these differences, auxiliary information about the target population from sources including administrative files or census data can be used. Survey weighting is one approach commonly used to reduce bias. Although weighted estimates are relatively easy to obtain, they can be inefficient in the presence of highly dispersed weights. Model-based estimation in survey research offers advantages of improved efficiency in the presence of sparse data and highly variable weights. However, these models can be subject to model misspecification. In this dissertation, we propose Bayesian penalized spline regression models for survey inference about proportions in the entire population as well as in sub-populations.

The proposed methods incorporate survey weights as covariates using a penalized spline to protect against model misspecification. We show by simulations that the proposed methods perform well, yielding efficient estimates of population proportion for binary survey data in the presence of highly dispersed weights and robust to model misspecification for survey outcomes. We illustrate the use of the proposed methods to estimate the prevalence of lifetime temper dysregulation disorder among National Guard service members overall and in sub-populations defined by gender and race using the Ohio Army National Guard Mental Health Initiative 2008-2009 survey data. We further extend the proposed framework to the setting where individual auxiliary data for the population are not available and utilize a Bayesian bootstrap approach to complete model-based estimation of current and undiagnosed depression in Hispanics/Latinos of different national backgrounds from the 2015 Washington Heights Community Survey.