A Network‐based Analysis of the 1861 Hagelloch Measles Data
Identifieur interne : 001F44 ( Main/Exploration ); précédent : 001F43; suivant : 001F45A Network‐based Analysis of the 1861 Hagelloch Measles Data
Auteurs : Chris Groendyke [États-Unis] ; David Welch [États-Unis, Nouvelle-Zélande] ; David R. Hunter [États-Unis]Source :
- Biometrics [ 0006-341X ] ; 2012-09.
English descriptors
- Teeft :
- Actual outbreak, Actual outbreak pattern, Algorithm, Bayesian, Bayesian inference, Biometrics, Britton, Candidate models, Contact network, Contact networks, Contact structure, Containment, Containment strategy, Covariates, Current address, Data sets, Degree distribution, Development core team, Disease data, Dyad, Dyadic, Dyadic covariates, Dyadic dependence model, Edge formation, Electronic version, Epidemic, Epidemic curves, Epidemic data, Epidemic model, Epidemic models, Epidemic parameters, Epidemiology, Ergm, Ergm network structure, Extra parameters, Further discussion, Gender homophily, Graph model, Groendyke, Hagelloch, Hagelloch data, Hagelloch measles data, Hagelloch measles epidemic, House distance, House distance parameter, Independence model, Infectious class, Infectious contact, Infectious contacts, Infectious group, Infectious individuals, Infectious period, Infectious periods, Infectious state, Keeling, Many cases, Mcmc, Mcmc algorithm, Meaningful statements, Measles, Measles data, Measles outbreak, Model selection, Network analysis, Network model, Network model parameters, Network models, Network parameters, Network structure, Node, Outbreak, Parameter, Parameter estimates, Parameter values, Pennsylvania state university, Population interactions, Posterior, Posterior density, Posterior distribution, Posterior distributions, Present analysis, Previous analyses, Previous works, Random graph model, Random graph models, Random graphs, Reproduction number, Reversible jump markov chain monte carlo, Right panel, Rjmcmc algorithm, Same household, Scandinavian journal, School class, Secondary infections, Seir, Seir epidemic model, Social network analysis, Social networks, Software, Software package, Spatial distance, Standard deviations, Statistical inference, Stochastic, Stochastic epidemics, Stochastic seir epidemic model, Susceptible individuals, Total time, Transmission process, Transmission rate, Transmission rates, Transmission tree, Ultimate size, University park, Unknown number.
Abstract
Summary In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential‐family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible‐exposed‐infectious‐removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma‐distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population—separate from the transmission process—as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model—the network, transmission tree, network parameters, and SEIR parameters—and perform Bayesian model selection to find the best‐fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.
Url:
DOI: 10.1111/j.1541-0420.2012.01748.x
Affiliations:
- Nouvelle-Zélande, États-Unis
- Pennsylvanie
- University Park (Pennsylvanie)
- Université d'État de Pennsylvanie
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<term>Actual outbreak pattern</term>
<term>Algorithm</term>
<term>Bayesian</term>
<term>Bayesian inference</term>
<term>Biometrics</term>
<term>Britton</term>
<term>Candidate models</term>
<term>Contact network</term>
<term>Contact networks</term>
<term>Contact structure</term>
<term>Containment</term>
<term>Containment strategy</term>
<term>Covariates</term>
<term>Current address</term>
<term>Data sets</term>
<term>Degree distribution</term>
<term>Development core team</term>
<term>Disease data</term>
<term>Dyad</term>
<term>Dyadic</term>
<term>Dyadic covariates</term>
<term>Dyadic dependence model</term>
<term>Edge formation</term>
<term>Electronic version</term>
<term>Epidemic</term>
<term>Epidemic curves</term>
<term>Epidemic data</term>
<term>Epidemic model</term>
<term>Epidemic models</term>
<term>Epidemic parameters</term>
<term>Epidemiology</term>
<term>Ergm</term>
<term>Ergm network structure</term>
<term>Extra parameters</term>
<term>Further discussion</term>
<term>Gender homophily</term>
<term>Graph model</term>
<term>Groendyke</term>
<term>Hagelloch</term>
<term>Hagelloch data</term>
<term>Hagelloch measles data</term>
<term>Hagelloch measles epidemic</term>
<term>House distance</term>
<term>House distance parameter</term>
<term>Independence model</term>
<term>Infectious class</term>
<term>Infectious contact</term>
<term>Infectious contacts</term>
<term>Infectious group</term>
<term>Infectious individuals</term>
<term>Infectious period</term>
<term>Infectious periods</term>
<term>Infectious state</term>
<term>Keeling</term>
<term>Many cases</term>
<term>Mcmc</term>
<term>Mcmc algorithm</term>
<term>Meaningful statements</term>
<term>Measles</term>
<term>Measles data</term>
<term>Measles outbreak</term>
<term>Model selection</term>
<term>Network analysis</term>
<term>Network model</term>
<term>Network model parameters</term>
<term>Network models</term>
<term>Network parameters</term>
<term>Network structure</term>
<term>Node</term>
<term>Outbreak</term>
<term>Parameter</term>
<term>Parameter estimates</term>
<term>Parameter values</term>
<term>Pennsylvania state university</term>
<term>Population interactions</term>
<term>Posterior</term>
<term>Posterior density</term>
<term>Posterior distribution</term>
<term>Posterior distributions</term>
<term>Present analysis</term>
<term>Previous analyses</term>
<term>Previous works</term>
<term>Random graph model</term>
<term>Random graph models</term>
<term>Random graphs</term>
<term>Reproduction number</term>
<term>Reversible jump markov chain monte carlo</term>
<term>Right panel</term>
<term>Rjmcmc algorithm</term>
<term>Same household</term>
<term>Scandinavian journal</term>
<term>School class</term>
<term>Secondary infections</term>
<term>Seir</term>
<term>Seir epidemic model</term>
<term>Social network analysis</term>
<term>Social networks</term>
<term>Software</term>
<term>Software package</term>
<term>Spatial distance</term>
<term>Standard deviations</term>
<term>Statistical inference</term>
<term>Stochastic</term>
<term>Stochastic epidemics</term>
<term>Stochastic seir epidemic model</term>
<term>Susceptible individuals</term>
<term>Total time</term>
<term>Transmission process</term>
<term>Transmission rate</term>
<term>Transmission rates</term>
<term>Transmission tree</term>
<term>Ultimate size</term>
<term>University park</term>
<term>Unknown number</term>
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<front><div type="abstract" xml:lang="en">Summary In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential‐family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible‐exposed‐infectious‐removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma‐distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population—separate from the transmission process—as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model—the network, transmission tree, network parameters, and SEIR parameters—and perform Bayesian model selection to find the best‐fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.</div>
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