University of Minnesota Ph.D. dissertation. July 2017. Major: Biostatistics. Advisors: Dipankar Bandyopadhyay, Lynn Eberly. 1 computer file (PDF); x, 129 pages.Analysis of asymmetric data poses several unique challenges. In this thesis, we propose a series of parametric models under the Bayesian hierarchical framework to account for asymmetry (arising from non-Gaussianity, tail behavior, etc) in both continuous and discrete response data. First, we model continuous asymmetric responses assuming normal random errors by using a dynamic linear model discretized from a differential equation which absorbs the asymmetry from the data generation mechanism. We then extend the skew-normal/independent parametric family to accommodate spatial clustering and non-random missingness observed in asymmetric continuous responses, and demonstrate its utility in obtaining precise parameter estimates and prediction in presence of skewness and thick-tails. Finally, under a latent variable formulation, we use a generalized extreme value (GEV) link to model multivariate asymmetric spatially-correlated binary responses that also exhibit non-random missingness, and show how this proposal improves inference over other popular alternative link functions in terms of bias and prediction. We assess our proposed method via simulation studies and two real data analyses on public health. Using simulated data, we investigate the performance of the proposed method to accurately accommodate asymmetry along with other data features such as spatial dependency and non-random missingness simultaneously, leading to precise posterior parameter estimates. Regarding data illustrations, we first validate the efficiency in using differential equations to handle skewed exposure assessment responses derived from an occupational hygiene study. Furthermore, we also conduct efficient risk evaluation of various covariates on periodontal disease responses from a dataset on oral epidemiology. The results from our investigation re-establishes the significance of moving away from the normality assumption and instead consider pragmatic distributional assumptions on the random model terms for efficient Bayesian parameter estimation under a unified framework with a variety of data complexities not earlier considered in the two aforementioned areas of public health research
