Learning genetic and environmental graphical models from family data.

Many challenging problems in biomedical research rely on understanding how variables are associated with each other and influenced by genetic and environmental factors. Probabilistic graphical models (PGMs) are widely acknowledged as a very natural and formal language to describe relationships among variables and have been extensively used for studying complex diseases and traits. In this work, we propose methods that leverage observational Gaussian family data for learning a decomposition of undirected and directed acyclic PGMs according to the influence of genetic and environmental factors. Many structure learning algorithms are strongly based on a conditional independence test. For independent measurements of normally distributed variables, conditional independence can be tested through standard tests for zero partial correlation. In family data, the assumption of independent measurements does not hold since related individuals are correlated due to mainly genetic factors. Based on univariate polygenic linear mixed models, we propose tests that account for the familial dependence structure and allow us to assess the significance of the partial correlation due to genetic (between-family) factors and due to other factors, denoted here as environmental (within-family) factors, separately. Then, we extend standard structure learning algorithms, including the IC/PC and the really fast causal inference (RFCI) algorithms, to Gaussian family data. The algorithms learn the most likely PGM and its decomposition into two components, one explained by genetic factors and the other by environmental factors. The proposed methods are evaluated by simulation studies and applied to the Genetic Analysis Workshop 13 simulated dataset, which captures significant features of the Framingham Heart Study.