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Combination antiretroviral therapy (ART) with at least three different drugs has become the standard of care for people with HIV (PWH) due to its exceptional effectiveness in viral suppression. However, many ART drugs have been reported to associate with neuropsychiatric adverse effects including depression, especially when certain genetic polymorphisms exist. Pharmacogenetics is an important consideration for administering combination ART as it may influence drug efficacy and increase risk for neuropsychiatric conditions. Large-scale longitudinal HIV databases provide researchers opportunities to investigate the pharmacogenetics of combination ART in a data-driven manner. However, with more than 30 FDA-approved ART drugs, the interplay between the large number of possible ART drug combinations and genetic polymorphisms imposes statistical modeling challenges. We develop a Bayesian approach to examine the longitudinal effects of combination ART and their interactions with genetic polymorphisms on depressive symptoms in PWH. The proposed method utilizes a Gaussian process with a composite kernel function to capture the longitudinal combination ART effects by directly incorporating individuals’ treatment histories, and a Bayesian classification and regression tree to account for individual heterogeneity. Through both simulation studies and an application to a dataset from the Women’s Interagency HIV Study, we demonstrate the clinical utility of the proposed approach in investigating the pharmacogenetics of combination ART and assisting physicians to make effective individualized treatment decisions that can improve health outcomes for PWH.

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model.

Bayesian networks have been widely used to generate causal hypotheses from multivariate data. Despite their popularity, the vast majority of existing causal discovery approaches make the strong assumption of a (partially) homogeneous sampling scheme. However, such assumption can be seriously violated, causing significant biases when the underlying population is inherently heterogeneous. To this end, we propose a novel causal Bayesian network model, termed BN-LTE, that embeds heterogeneous samples onto a low-dimensional manifold and builds Bayesian networks conditional on the embedding. This new framework allows for more precise network inference by improving the estimation resolution from the population level to the observation level. Moreover, while causal Bayesian networks are in general not identifiable with purely observational, cross-sectional data due to Markov equivalence, with the blessing of causal effect heterogeneity, we prove that the proposed BN-LTE is uniquely identifiable under relatively mild assumptions. Through extensive experiments, we demonstrate the superior performance of BN-LTE in causal structure learning as well as inferring observation-specific gene regulatory networks from observational data.