Bayesian Multi-study Factor Analysis for High-throughput Biological Data

TL;DR

This paper introduces a Bayesian multi-study factor analysis method that identifies shared and study-specific factors in high-throughput biological data, demonstrating superior performance and revealing meaningful gene patterns in breast cancer studies.

Contribution

It extends Multi-study Factor Analysis with a Bayesian sparse approach and develops novel identification and computational techniques for high-dimensional biological data.

Findings

Outperforms standard factor analysis in simulations

Identifies replicable gene patterns in breast cancer data

Provides an efficient Gibbs sampling algorithm

Abstract

This paper presents a new modeling strategy for joint unsupervised analysis of multiple high-throughput biological studies. As in Multi-study Factor Analysis, our goals are to identify both common factors shared across studies and study-specific factors. Our approach is motivated by the growing body of high-throughput studies in biomedical research, as exemplified by the comprehensive set of expression data on breast tumors considered in our case study. To handle high-dimensional studies, we extend Multi-study Factor Analysis using a Bayesian approach that imposes sparsity. Specifically, we generalize the sparse Bayesian infinite factor model to multiple studies. We also devise novel solutions for the identification of the loading matrices: we recover the loading matrices of interest ex-post, by adapting the orthogonal Procrustes approach. Computationally, we propose an efficient and fast Gibbs sampling approach. Through an extensive simulation analysis, we show that the proposed approach performs very well in a range of different scenarios, and outperforms standard Factor analysis in all the scenarios identifying replicable signal in unsupervised genomic applications. The results of our analysis of breast cancer gene expression across seven studies identified replicable gene patterns, clearly related to well-known breast cancer pathways. An R package is implemented and available on GitHub.