Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used ICAR model, which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on a directed acyclic graph (DAG) representation of the spatial dependence. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated random effects, can also directly model the outcome from dependent data like images and networks. Theoretical results establish a link between the parameters in our model and the variance and covariances of the random effects. Substantive simulation studies demonstrate that the improved interpretability of our model reaps benefits in terms of accurately recovering the latent spatial random effects as well as for inference on the spatial covariance parameters. Under modest spatial correlation, our model far outperforms the CAR models, while the performances are similar when the spatial correlation is strong. We also assess sensitivity to the choice of the ordering in the DAG construction using theoretical and empirical results which testify to the robustness of our model. We also present a large-scale public health application demonstrating the competitive performance of the model.

BackgroundNeuroimaging studies have identified obesity-related differences in the brain's resting state activity. An imbalance between homeostatic and reward aspects of ingestive behaviour may contribute to obesity and food addiction. The interactions between early life adversity (ELA), the reward network and food addiction were investigated to identify obesity and sex-related differences, which may drive obesity and food addiction. MethodsFunctional resting state magnetic resonance imaging was acquired in 186 participants (high body mass index [BMI]: ≥25: 53 women and 54 men; normal BMI: 18.50-24.99: 49 women and 30 men). Participants completed questionnaires to assess ELA (Early Traumatic Inventory) and food addiction (Yale Food Addiction Scale). A tripartite network analysis based on graph theory was used to investigate the interaction between ELA, brain connectivity and food addiction. Interactions were determined by computing Spearman rank correlations, thresholded at q < 0.05 corrected for multiple comparisons. ResultsParticipants with high BMI demonstrate an association between ELA and food addiction, with reward regions playing a role in this interaction. Among women with high BMI, increased ELA was associated with increased centrality of reward and emotion regulation regions. Men with high BMI showed associations between ELA and food addiction with somatosensory regions playing a role in this interaction. ConclusionsThe findings suggest that ELA may alter brain networks, leading to increased vulnerability for food addiction and obesity later in life. These alterations are sex specific and involve brain regions influenced by dopaminergic or serotonergic signalling.

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