Frequentist and Bayesian Modeling in the Presence of Unmeasured Confounding

Biostatistical studies of medical data are extremely important in distinguishing relationships between drugs or treatments and the patient's medical response. These studies generally use data from large health care databases, which provide immense amounts of information while allowing the researcher to analyze long-term effects that may not be shown in a typical randomized controlled trial. However, when using large databases, one must be particularly aware of the effect of unmeasured confounding on statistical models. Confounding arises when factors unrelated to the particular study have a hidden effect on observed health outcomes. Bayesian statistics provides a mechanism for model fitting which synthesizes the data with prior information about bias, allowing the researcher to control confounding through the inclusion of additional variables from independent datasets. In this thesis I will provide a background of the proposed method as well its application to two independent analyses: predictors of low birth weight babies and predictors of parental separation anxiety.