Bayesian Covariate-Dependent Quantile Directed Acyclic Graphical Models for Individualized Inference

TL;DR

The paper introduces qDAGx, a Bayesian method for individualized, covariate-dependent quantile DAGs that identify unique network structures at different quantiles using observational data, with applications in precision medicine.

Contribution

It develops a novel Bayesian approach for covariate-dependent quantile DAGs that can be individualized and identified without strong assumptions, scalable to large datasets.

Findings

Effective in inferring patient-specific protein interaction networks

Outperforms traditional mean regression methods in simulations

Demonstrates utility in lung cancer precision medicine

Abstract

We propose an approach termed ``qDAGx'' for Bayesian covariate-dependent quantile directed acyclic graphs (DAGs) where these DAGs are individualized, in the sense that they depend on individual-specific covariates. The individualized DAG structure of the proposed approach can be uniquely identified at any given quantile, based on purely observational data without strong assumptions such as a known topological ordering. To scale the proposed method to a large number of variables and covariates, we propose for the model parameters a novel parameter expanded horseshoe prior that affords a number of attractive theoretical and computational benefits to our approach. By modeling the conditional quantiles, qDAGx overcomes the common limitations of mean regression for DAGs, which can be sensitive to the choice of likelihood, e.g., an assumption of multivariate normality, as well as to the choice of priors. We demonstrate the performance of qDAGx through extensive numerical simulations and via an application in precision medicine, which infers patient-specific protein--protein interaction networks in lung cancer.