Covariate-dependent bayesian models for heterogeneous populations

In this thesis, we propose two novel Bayesian models for the analysis of health and genomic data, for which traditional methods are often found to be inefficient or unsuitable. Our approaches are motivated by the emerging field of precision medicine, whose ultimate goal is to select the optimal treatment accounting for patient and disease’s variability. The main distinctive mark of statistical methodology in the precision medicine paradigm is to leverage patients’ heterogeneity to obtain subject-specific inference. First, motivated by a microbiota study on patients affected by colorectal cancer, we propose a model designed to analyze data that exhibit a hierarchical structure induced by measurements from multiple tissues of the same patient. Our goal is to capture patients’ heterogeneity and similarities in terms of effects altering microbiota composition. Building upon the Dirichlet-multinomial model, we propose a flexible regression model, where coefficients are allowed to be smooth functions of the covariates. This results in a subject-specific model where varying coefficients include two-way linear and non-linear interactions as special cases. This allows us to recover associations and interactions patterns that may be specific for each individual rather than estimated at population level. In the second contribution, we develop a predictive model for the selection of the personalized optimal treatment in oncology, when a predictive signature and a set of prognostic biomarkers are available. Predictive covariates are used to drive a clustering process that results in homogeneous groups of patients. This step is integrated into a prognostic model to predict response to competing treatments for new untreated patients. Finally, a utility-based approach allows us to select the treatment that ensures the larger predicted utility for new patients, based on their genetic profiles. We employed a Bayesian nonparametric model for random partition to build our integrative approach. In particular, we explored the use of the Normalized Generalized Gamma process as cohesion function in a product partition model with covariates. In contrast with existing methods, we jointly estimate model-based clustering and treatment assignment from the data, and hence treatment selection fully accounts for patients’ variability.