The application of statistical network models in disease research

Summary Host social structure is fundamental to how infections spread and persist, and so the statistical modelling of static and dynamic social networks provides an invaluable tool to parameterise realistic epidemiological models. We present a practical guide to the application of network modelling frameworks for hypothesis testing related to social interactions and epidemiology, illustrating some approaches with worked examples using data from a population of wild European badgers Meles meles naturally infected with bovine tuberculosis. Different empirical network datasets generate particular statistical issues related to non-independence and sampling constraints. We therefore discuss the strengths and weaknesses of modelling approaches for different types of network data and for answering different questions relating to disease transmission. We argue that statistical modelling frameworks designed specifically for network analysis offer great potential in directly relating network structure to infection. They have the potential to be powerful tools in analysing empirical contact data used in epidemiological studies, but remain untested for use in networks of spatio-temporal associations. As a result, we argue that developments in the statistical analysis of empirical contact data are critical given the ready availability of dynamic network data from bio-logging studies. Furthermore, we encourage improved integration of statistical network approaches into epidemiological research to facilitate the generation of novel modelling frameworks and help extend our understanding of disease transmission in natural populations.

[1]  Ellen Brooks-Pollock,et al.  Measured Dynamic Social Contact Patterns Explain the Spread of H1N1v Influenza , 2012, PLoS Comput. Biol..

[2]  Roger Th. A. J. Leenders,et al.  Modeling social influence through network autocorrelation: constructing the weight matrix , 2002, Soc. Networks.

[3]  Damien R. Farine,et al.  Estimating uncertainty and reliability of social network data using Bayesian inference , 2015, Royal Society Open Science.

[4]  W. Edmunds,et al.  Dynamic social networks and the implications for the spread of infectious disease , 2008, Journal of The Royal Society Interface.

[5]  Leah B. Shaw,et al.  Effects of community structure on epidemic spread in an adaptive network , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  M. Tranmer,et al.  Using the relational event model (REM) to investigate the temporal dynamics of animal social networks , 2015, Animal Behaviour.

[7]  Ruth M. Ripley,et al.  Manual for RSiena , 2011 .

[8]  U. Brandes,et al.  Modeling frequency and type of interaction in event networks , 2013, Corvinus Journal of Sociology and Social Policy.

[9]  Mark S. Mizruchi,et al.  Structure and bias in the network autocorrelation model , 2010, Soc. Networks.

[10]  P. E. Kopp,et al.  Superspreading and the effect of individual variation on disease emergence , 2005, Nature.

[11]  Meggan E Craft,et al.  Raccoon contact networks predict seasonal susceptibility to rabies outbreaks and limitations of vaccination. , 2015, The Journal of animal ecology.

[12]  Darren M. Scott,et al.  Weight matrices for social influence analysis: An investigation of measurement errors and their effect on model identification and estimation quality , 2008, Soc. Networks.

[13]  Sreeram V Ramagopalan,et al.  Risk of venous thromboembolism in people admitted to hospital with selected immune-mediated diseases: record-linkage study , 2011, BMC medicine.

[14]  Indar W. Ramnarine,et al.  Effect of gyrodactylid ectoparasites on host behaviour and social network structure in guppies Poecilia reticulata , 2011, Behavioral Ecology and Sociobiology.

[15]  Adrian E. Raftery,et al.  Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models , 2009, Soc. Networks.

[16]  A. King,et al.  Contact Network Structure Explains the Changing Epidemiology of Pertussis , 2010, Science.

[17]  Tom A. B. Snijders,et al.  Introduction to stochastic actor-based models for network dynamics , 2010, Soc. Networks.

[18]  Mark S. Mizruchi,et al.  The effect of density on the level of bias in the network autocorrelation model , 2008, Soc. Networks.

[19]  Luke Rendell,et al.  Network-Based Diffusion Analysis Reveals Cultural Transmission of Lobtail Feeding in Humpback Whales , 2013, Science.

[20]  Matt J Keeling,et al.  Host-parasite interactions between the local and the mean-field: how and when does spatial population structure matter? , 2007, Journal of theoretical biology.

[21]  Damien R. Farine,et al.  Animal social network inference and permutations for ecologists in R using asnipe , 2013 .

[22]  M. Craft.  Infectious disease transmission and contact networks in wildlife and livestock , 2015, Philosophical Transactions of the Royal Society B: Biological Sciences.

[23]  James Moody,et al.  Structural effects of network sampling coverage I: Nodes missing at random , 2013, Soc. Networks.

[24]  Ira B Schwartz,et al.  Fluctuating epidemics on adaptive networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  M. Keeling,et al.  Spatially extended host-parasite interactions: the role of recovery and immunity. , 2007, Theoretical population biology.

[26]  Pavel N Krivitsky,et al.  Exponential-family random graph models for valued networks. , 2011, Electronic journal of statistics.

[27]  Pavel N Krivitsky,et al.  Fitting Position Latent Cluster Models for Social Networks with latentnet. , 2008, Journal of statistical software.

[28]  Michael Schaub,et al.  Bayesian Population Analysis using WinBUGS: A Hierarchical Perspective , 2011 .

[29]  Brenda McCowan,et al.  Linking social and pathogen transmission networks using microbial genetics in giraffe (Giraffa camelopardalis). , 2014, The Journal of animal ecology.

[30]  Garry Robins,et al.  An introduction to exponential random graph (p*) models for social networks , 2007, Soc. Networks.

[31]  Stuart Bearhop,et al.  Performance of Proximity Loggers in Recording Intra- and Inter-Species Interactions: A Laboratory and Field-Based Validation Study , 2012, PloS one.

[32]  Glenna F. Nightingale,et al.  Quantifying diffusion in social networks: a Bayesian approach , 2014 .

[33]  E. Xing,et al.  Discrete Temporal Models of Social Networks , 2006, SNA@ICML.

[34]  V. Jansen,et al.  Modelling the influence of human behaviour on the spread of infectious diseases: a review , 2010, Journal of The Royal Society Interface.

[35]  Carter T. Butts,et al.  4. A Relational Event Framework for Social Action , 2008 .

[36]  Bruce A. Desmarais,et al.  Stochastic weighted graphs: Flexible model specification and simulation , 2015, Soc. Networks.

[37]  Matt J. Keeling,et al.  Networks and the Epidemiology of Infectious Disease , 2010, Interdisciplinary perspectives on infectious diseases.

[38]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.

[39]  Paul C. Cross,et al.  Wildlife contact analysis: emerging methods, questions, and challenges , 2012, Behavioral Ecology and Sociobiology.

[40]  Kevin N Laland,et al.  The effect of task structure on diffusion dynamics: Implications for diffusion curve and network-based analyses , 2010, Learning & behavior.

[41]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[42]  Charles L Nunn,et al.  Network-based diffusion analysis: a new method for detecting social learning , 2009, Proceedings of the Royal Society B: Biological Sciences.

[43]  D. Croft,et al.  Using Social Network Measures in Wildlife Disease Ecology, Epidemiology, and Management , 2017, Bioscience.

[44]  Garry Robins,et al.  Bayesian analysis for partially observed network data, missing ties, attributes and actors , 2013, Soc. Networks.

[45]  Bruce A. Desmarais,et al.  Statistical Inference for Valued-Edge Networks: The Generalized Exponential Random Graph Model , 2011, PloS one.

[46]  K. Holekamp,et al.  Topological effects of network structure on long-term social network dynamics in a wild mammal. , 2015, Ecology letters.

[47]  A. Thornton,et al.  Experimentally induced innovations lead to persistent culture via conformity in wild birds , 2014, Nature.

[48]  T. Tregenza,et al.  Analysing animal social network dynamics: the potential of stochastic actor‐oriented models , 2017, The Journal of animal ecology.

[49]  A. Rinaldo,et al.  CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS. , 2011, Annals of statistics.

[50]  Carter T Butts,et al.  Constructing and Modifying Sequence Statistics for relevent Using informR in 𝖱. , 2015, Journal of statistical software.

[51]  R. Mcdonald,et al.  Multi-state modelling reveals sex-dependent transmission, progression and severity of tuberculosis in wild badgers , 2013, Epidemiology and Infection.

[52]  B. König,et al.  Infection-induced behavioural changes reduce connectivity and the potential for disease spread in wild mice contact networks , 2016, Scientific Reports.

[53]  Pavel N Krivitsky,et al.  Computational Statistical Methods for Social Network Models , 2012, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[54]  John Levi Martin,et al.  A General Permutation-Based QAP Analysis Approach for Dyadic Data from Multiple , 1999 .

[55]  Hawoong Jeong,et al.  Statistical properties of sampled networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  Richard James,et al.  Hypothesis testing in animal social networks. , 2011, Trends in ecology & evolution.

[57]  Kazuyuki Aihara,et al.  Epidemic spread in adaptive networks with multitype agents , 2011 .

[58]  Stuart Bearhop,et al.  Badger social networks correlate with tuberculosis infection , 2013, Current Biology.

[59]  Scott D. McClurg,et al.  Navigating the Range of Statistical Tools for Inferential Network Analysis , 2017 .

[60]  Charlotte C. Greenan,et al.  Diffusion of innovations in dynamic networks , 2015 .

[61]  Lynn B. Martin,et al.  Host behaviour–parasite feedback: an essential link between animal behaviour and disease ecology , 2016, Proceedings of the Royal Society B: Biological Sciences.

[62]  Tom A. B. Snijders,et al.  Exponential Random Graph Models for Social Networks , 2013 .

[63]  Bruce A. Desmarais,et al.  Extensions of Exponential Random Graph Models , 2015 .

[64]  A. Barrat,et al.  Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees , 2011, BMC medicine.

[65]  Shweta Bansal,et al.  Statistical inference to advance network models in epidemiology. , 2011, Epidemics.

[66]  David Krackhardt,et al.  Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions , 2007, Psychometrika.

[67]  Damien R. Farine,et al.  Constructing, conducting and interpreting animal social network analysis , 2015, The Journal of animal ecology.

[68]  J. Drewe,et al.  Who infects whom? Social networks and tuberculosis transmission in wild meerkats , 2010, Proceedings of the Royal Society B: Biological Sciences.

[69]  Bruce A. Desmarais,et al.  Temporal Exponential Random Graph Models with btergm: Estimation and Bootstrap Confidence Intervals , 2018 .

[70]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[71]  Shweta Bansal,et al.  The dynamic nature of contact networks in infectious disease epidemiology , 2010, Journal of biological dynamics.

[72]  Menna E. Jones,et al.  Simulating devil facial tumour disease outbreaks across empirically derived contact networks , 2012 .

[73]  Aya Kachi,et al.  A spatial model incorporating dynamic, endogenous network interdependence: A political science application , 2010 .

[74]  Menna E. Jones,et al.  Contact networks in a wild Tasmanian devil (Sarcophilus harrisii) population: using social network analysis to reveal seasonal variability in social behaviour and its implications for transmission of devil facial tumour disease. , 2009, Ecology letters.

[75]  James Moody,et al.  Network sampling coverage II: The effect of non-random missing data on network measurement , 2017, Soc. Networks.

[76]  Stuart Bearhop,et al.  The consequences of unidentifiable individuals for the analysis of an animal social network , 2015, Animal Behaviour.

[77]  Philip Leifeld,et al.  A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model , 2015, Network Science.

[78]  Meggan E Craft,et al.  Using contact networks to explore mechanisms of parasite transmission in wildlife , 2017, Biological reviews of the Cambridge Philosophical Society.