Estimating Clusters from Multivariate Binary Data via Hierarchical Bayesian Boolean Matrix Factorization

• Activity Number: 625 - Personalized/Precision Medicine II
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Zhenke Wu* and Livia Casciola-Rosen and Antony Rosen and Scott Zeger
• Companies: University of Michigan and Johns Hopkins University School of Medicine and Johns Hopkins University School of Medicine and Johns Hopkins Biostatistics
• Keywords: Binary matrix factorization; restricted latent class models; Markov chain Monte Carlo; Clustering; Measurement Error; Autoimmune Diseases

Abstract

An ongoing challenge in subsetting autoimmune disease patients is to define autoantibody signatures produced against a library of elemental molecular machines each comprised of multiple component autoantigens. It is of significant value to quantify both components of the machines and the striking variations in their frequencies among individuals. Based on multivariate binary responses that represent subject­level presence or absence of proteins over a grid of molecular weights, we develop a Bayesian hierarchical model that represents observations as aggregation of a few unobserved machines where the aggregation varies by subjects. Our approach is to specify the model likelihood via factorization into two latent binary matrices: machine profiles and individual factors. Given latent factorization, we account for inherent uncertainties in immunoprecipitation, errors in measurement or both using sensitivities and specificities of protein detection. The posterior distribution for the numbers of patient clusters and machines are estimated from data. We demonstrate the proposed method by analyzing patients gel electrophoresis autoradiography (GEA) data for patient subsetting.