Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We solve this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges are valued, thus greatly expanding the scope of networks applied researchers can subject to statistical analysis

Can Geographical Factors Determine the Choices of Farmers in the Ethiopian Highlands to Trade in Livestock Markets?

Proximity and affiliation to the local market appear to be two of the most relevant factors to explain farmer's choices to select a particular trading point. Physical barriers may limit the options , especially in developing countries. A network of villages linked by traders/farmer-traders sharing livestock markets was built with field data collected in 75 villages from 8 kebelles in the Wassona Werna wereda of the Ethiopian Highlands. Two exponential random graph models were fitted with various geographical and demographic attributes of the nodes (dyadic independent model) and three internal network structures (dyadic dependent model). Several diagnostic methods were applied to assess the goodness of fit of the models. The odds of an edge where the distance to the main market Debre Behran and the difference in altitude between two connected villages are both large increases significantly so that villages far away from the main market and at different altitude are more likely to be linked in the network than randomly. The odds of forming an edge between two villages in Abamote or Gudoberet kebelles are approximately 75% lower than an edge between villages in any other kebelles (p<0.05). The conditional log-odds of two villages forming a tie that is not included in a triangle, a 2-star or a 3-star is extremely low, increasing the odds significantly (p<0.05) each time a node is in a 2-star structure and decreasing it when a node is in a 3-star (p<0.05) or in a triangle formation (p<0.05)), conditional on the rest of the network. Two major constraining factors, namely distance and altitude, are not deterrent for the potential contact of susceptible small ruminant populations in the Highlands of Ethiopia

The interplay of microscopic and mesoscopic structure in complex networks

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks

Incorporating Model Uncertainty into Spatial Predictions

We consider a modeling approach for spatially distributed data. We are concerned with aspects of statistical inference for Gaussian random fields when the ultimate objective is to predict the value of the random field at unobserved locations. However the exact statistical model is seldom known before hand and is usually estimated from the very same data relative to which the predictions are made. Our objective is to assess the effect of the fact that the model is estimated, rather than known, on the prediction and the associated prediction uncertainty. We describe a method for achieving this objective. We, in essence, consider the best linear unbiased prediction procedure based on the model within a Bayesian framework. These ideas are implemented for the spring temperature over the region in the north- ern United States based on the stations in the United States historical climatological network reported in Karl, Williams, Quinlan &amp; Boden (1990)

Modelling the public health impact of male circumcision for HIV prevention in high prevalence areas in Africa

Background: Recent clinical trials in Africa, in combination with several observational epidemiological studies, have provided evidence that male circumcision can reduce HIV female-to-male transmission risk by 60% or more. However, the public health impact of large-scale male circumcision programs for HIV prevention is unclear. Methods: Two mathematical models were examined to explore this issue: a random mixing model and a compartmental model that distinguishes risk groups associated with sex work. In the compartmental model, two scenarios were developed, one calculating HIV transmission and prevalence in a context similar to the country of Botswana, and one similar to Nyanza Province, in western Kenya. Results: In both models, male circumcision programs resulted in large and sustained declines in HIV prevalence over time among both men and women. Men benefited somewhat more than women, but prevalence among women was also reduced substantially. With 80% male circumcision uptake, the reductions in prevalence ranged from 45% to 67% in the two "countries", and with 50% uptake, from 25% to 41%. It would take over a decade for the intervention to reach its full effect. Conclusion: Large-scale uptake of male circumcision services in African countries with high HIV prevalence, and where male circumcision is not now routinely practised, could lead to substantial reductions in HIV transmission and prevalence over time among both men and women

Bayesian statistical modelling of human protein interaction network incorporating protein disorder information

<p>Abstract</p> <p>Background</p> <p>We present a statistical method of analysis of biological networks based on the exponential random graph model, namely p2-model, as opposed to previous descriptive approaches. The model is capable to capture generic and structural properties of a network as emergent from local interdependencies and uses a limited number of parameters. Here, we consider one global parameter capturing the density of edges in the network, and local parameters representing each node's contribution to the formation of edges in the network. The modelling suggests a novel definition of important nodes in the network, namely <it>social</it>, as revealed based on the local <it>sociality </it>parameters of the model. Moreover, the sociality parameters help to reveal organizational principles of the network. An inherent advantage of our approach is the possibility of hypotheses testing: <it>a priori </it>knowledge about biological properties of the nodes can be incorporated into the statistical model to investigate its influence on the structure of the network.</p> <p>Results</p> <p>We applied the statistical modelling to the human protein interaction network obtained with Y2H experiments. Bayesian approach for the estimation of the parameters was employed. We deduced <it>social </it>proteins, essential for the formation of the network, while incorporating into the model information on protein disorder. <it>Intrinsically disordered </it>are proteins which lack a well-defined three-dimensional structure under physiological conditions. We predicted the fold group (ordered or disordered) of proteins in the network from their primary sequences. The network analysis indicated that protein disorder has a positive effect on the connectivity of proteins in the network, but do not fully explains the interactivity.</p> <p>Conclusions</p> <p>The approach opens a perspective to study effects of biological properties of individual entities on the structure of biological networks.</p