BAYESIAN METHODS FOR CORRELATED PREDICTORS AND CONFOUNDING VARIABLES IN EPIDEMIOLOGY

In epidemiology, it is common to have a set of outcomes, exposures, and confounding variables on different scales (i.e. continuous, count, categorical: nominal/ordinal). Confounding variables are expect to be correlated with exposures and at times exposures may be highly correlated among themselves which present model estimation complications. This is especially prevalent in environmental epidemiology, where studying the joint or simultaneous effect of chemical mixture or air pollution exposures on health for example is of interest. Dimension reduction techniques and shrinkage effect estimation are important tools to overcome these difficulties. Studying the multivariate dependence among mixed scale variables can aid investigators in developing analysis plans but mixed-scale distribution modeling is not a simple task. Specifically, it may be of interest to assess and quantify the degree of correlation among variables and or characterize different exposure-confounding variable profiles. Certain dimension reduction methods, such as, mixture models can do both, as well as, jointly model variables of mixed-scales. Shrinkage methods, on the other hand, do not transform a set of correlated variables but implement a bias-variance trade-off to address effect estimation. The overall goal of this research is to develop a suite of Bayesian methods for clustering via mixed-scale distributional modeling and variable selection. First, motivated by sophisticated Bayesian mixed-scale distribution modeling, we develop a joint model using modularized tensor factorization (MOTEF) as a simplification for ease of implementation and computation. The performance of MOTEF is assessed via a simulation study and applied to data from the National Birth Defects and Prevention Study (NBDPS) for mixed-scale multivariate profiling. Second, we develop a Bayesian semi-parametric model with variable selection for hierarchical interactions (BHIS). Its performance is assessed via simulation studies and applied to the Mount Sinai Children's Environmental Health Study. Lastly, building on Bayesian mixed-scale distribution modeling, we develop a joint mixture model for compositional data with essential zeros. The model is applied to accelerometry-assessed sedentary behavior and physical activity data from the Hispanic Community Health Study / Study of Latinos for describing activity profiles and health risk.Doctor of Philosoph