Novel Bayesian Methods for Biomedical Applications
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In this dissertation, we introduce three novel Bayesian methods, motivated by and applied to biomedical applications. We focus on inferring heterogeneity to obtain better understanding of symptoms, which acts as a key step towards the ultimate goal of precision medicine. Our projects fall within the realm of matrix deconvolution and clustering methods. While there are tons of literature on both matrix deconvolution and clustering, novel methods are always needed when a new clinical question arises or a dataset with different characteristics appears. This motivates us to develop state-of-the-art models to meet the up-to-date demands. For example, to infer tumor heterogeneity as a decomposition of gene expression data into a mixture of latent subclones, we develop BayRepulsive, a Bayesian repulsive deconvolution model, leveraging the determinantal point process as a repulsive prior to model latent tumor subclones for parsimonious and biologically interpretable results. To understand the heterogeneity in patients with diverse periodontal diseases (PD) patterns, we develop BAREB, a Bayesian repulsive biclustering method that can simultaneously cluster the PD patients and their tooth sites after taking the patient- and site-level covariates into consideration. In addition, since PD is the leading cause for tooth loss, the missing data mechanism is non-ignorable. Such nonrandom missingness is incorporated into BAREB. To investigate the impact of antiretroviral (ART) drugs on depression symptom among patients with human immunodeficiency virus (HIV), we develop BAGEL, a Bayesian graphical model that can study the personalized effect of ART drugs on depression and cluster patients into subgroups by taking into account the heterogeneous HIV population at same time. In the end, we offer three novel Bayesian tools for inferring heterogeneity. In what follows we present detailed descriptions and applications of these three methods. Simulation studies show that they are able to accurately estimate the clustering, and to compare favorably to alternatives. For real world application, we apply methods to datasets from clinical studies, and obtain desirable and interpretable results, which in turn offer meaningful biological interpretation and assists clinical prog- nosis and treatment. A major contribution of this paper is the Rcpp implementation of our methodologies, available in the R packages.