Causal inference in meta-analyses with Dirichlet process mixture models and Bayesian networks

Music City Center 

We propose a flexible framework for conducting meta-analyses from published papers. The method approximates the joint probability density function for similar variables in each constituent paper with a hierarchical Dirichlet process Gaussian mixture model. Hyperparameters for the mixture component parameters and the mixing proportions are allowed to correlate among subsets of papers with similar properties. With this posterior for the density function, we generate new and complete data observations for use in causal inference with structure learning on Bayesian networks. This framework incorporates whole datasets in the meta-analysis, provides a flexible means to handle heterogeneity in study design with correlated hyperparameters, and mitigates issues with causal sufficiency endemic to causal inference with Bayesian networks by combining latent and observed variables across studies. We apply this technique to studies of the gut microbiome, show that its predictions are viable, and demonstrate the key insights it offers. While open data access continues to proliferate, we proffer a novel means of data reuse.

meta-analysis

causal inference

Dirichlet process mixture model

Bayesian hierarchical modeling

Bayesian network

data reuse 

Section on Bayesian Statistical Science