Learning Gaussian Graphical Models from Correlated Data

Zeyuan Song^1,2*Sophia Gunn³Stefano Monti⁴Gina Peloso⁵Ching-Ti Liu⁵Kathryn Lunetta⁵Paola Sebastiani^1,2,6

• ¹School of Medicine, Tufts University, Boston, Massachusetts, United States
• ²Institute for Clinical Research and Health Policy Studies, Tufts Medical Center, Boston, United States
• ³New York Genome Center, New York, New York, United States
• ⁴Section of Computational Biomedicine, School of Medicine, Boston University, Boston, Massachusetts, United States
• ⁵Department of Biostatistics, School of Public Health, Boston University, Boston, Massachusetts, United States
• ⁶Data Intensive Study Center, Tufts University, Medford, Massachusetts, United States

Gaussian Graphical Models (GGMs) are a type of network modeling that uses partial correlation rather than correlation for representing complex relationships among multiple variables. The advantage of using partial correlation is to show the relation between two variables after “adjusting” for the effects of other variables and leads to more parsimonious and interpretable models. There are well established procedures to build GGMs from a sample of independent and identical distributed observations. However, many studies include clustered and longitudinal data that result in correlated observations and ignoring this correlation among observations can lead to inflated Type I error. In this paper, we propose a cluster-based bootstrap algorithm to infer GGMs from correlated data. We use extensive simulations of correlated data from family-based studies to show that the proposed bootstrap method does not inflate the Type I error while retaining statistical power compared to alternative solutions when there are sufficient number of clusters. We apply our method to learn the GGM that represents complex relations between 47 Polygenic Risk Scores generated using genome-wide genotype data from the Long Life Family Study. By comparing it to the conventional methods that ignore within-cluster correlation, we show that our method controls the Type I error well without power loss.