Advancements in Bayesian Methods for Personalized Medicine

Personalized medicine is a rapidly evolving and transformative approach in healthcare. As the complexity and volume of data continue to grow, more advanced methodologies are needed to effectively implement personalized strategies. In this manuscript, we develop novel Bayesian methodologies specifically designed to handle high-dimensional data and identify complex patterns more accurately. The thesis consists of three main contributions. Firstly, we propose a Bayesian model for optimizing dynamic treatment regimes, a practical framework within personalized medicine, to address the uncertainty in identifying optimal decision sequences and incorporate dimensionality reduction to manage high-dimensional individual covariates. To achieve this, the model is augmented to accommodate counterfactual variables. Additionally, we introduce a novel class of spike-and-slab priors for the multi-stage selection of significant factors, to favor the sharing of information across stages. The second primary contribution of this manuscript is an extension of the Bayesian model with spike-and-slab priors to accommodate frameworks with more than two stages. We use this model specification to identify significant molecular biomarkers and clinical parameters influencing drug effects on estimated Glomerular Filtration Rate (eGFR) using a type II diabetes dataset. Specifically, the dataset we analyze is derived from the PROVALID study, a prospective observational study encompassing a diverse range of chronic kidney disease stages. Lastly, we introduce mixed Bayesian networks to tackle causal structure learning across diverse data types, facilitating a more accurate representation of causal dependencies by a directed acyclic graph. We present that under this model, the causal structure between mixed functional data can be uniquely identifiable under certain mild conditions. Furthermore, we develop a Bayesian framework to infer the adjacency matrix of the directed acyclic graph with inherent uncertainty quantification.