Build a dyadic covariate matrix (X)

Description

Build a dyadic covariate matrix (X) from a given nodal covariate matrix.

Usage

BuildX(nodecov, unaryCol = NULL, unaryFunc = NULL, 
	binaryCol = NULL, binaryFunc = NULL, includeIntercept = TRUE) 

Arguments

Value

A dyadic covariate matrix with {N \choose 2} rows, columns 1 and 2 are node ids, column 3 is all ones (if requested) and then one column for each given element of unaryCol and binaryCol.

Assigns colnames depending on type of unaryFunc and binaryFunc and colnames of nodecov.

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

See Also

SimulateDyadicLinearERGM for simulating a contact network based on a dyadic covairate matrix, and epinet for performing inference on the network and epidemic model parameters.

Examples

# make some nodal covariates
set.seed(3)
mycov = data.frame(id = 1:5, xpos = rnorm(5), ypos = rnorm(5), 
	house = c(1, 1, 2, 2, 2), gender = c(0, 0, 0, 1, 1))
# make matrix 
dyadCov = BuildX(mycov, unaryCol = c(4, 5), unaryFunc = c("match", "match"), 
	binaryCol = list(c(2, 3)), binaryFunc = "euclidean")

Hagelloch measles data.

Description

Epidemic data derived from a measles outbreak in the town of Hagelloch, Germany in 1861. 188 individuals were infected over the course of the epidemic. (One individual was removed from this dataset.)

Consists of two files: HagellochTimes and HagellochDyadCov. These two files contain the data necessary to analyze the Hagelloch measles data.

HagellochTimes contains 187 rows (one for each individual included) and 5 columns: NodeID (a numerical index ranging from 1 to 187); Putative Parent (the ID of the individual considered most likely to have been responsible for infecting this person, as determined by Osterle); Exposure time, Infectious time, and Removal time (the time index in days at which the individual entered the Exposed, Infectious, and Removed states, respectively). Note that Exposure times are not known for this data set. See references below for details regarding the determination of Infectious and Removal times.

HagellochDyadCov is a matrix of dyadic covariates corresponding to the individuals in the Hagelloch data set. Contains one row for each dyad (pair of individuals) in the population. The first two columns are the Node IDs for the two individuals in the dyad. The third column is a column of all 1 values, used as a baseline or intercept term. Columns 4, 5, and 6 are indicator variables for whether the two individuals in the dyad are in the same household, are both in classroom 1, or both in classroom 2, respectively. Column 7 is the household distance between the two individuals in the dyad, measured in units of 2.5m, Columns 8 and 9 are indicator variables based on whether both individuals in the dyad are male or female, respectively. Column 10 is the age difference (in years) between the two individuals in the dyad.

Usage

data(Hagelloch)

Format

See above.

Source

Thanks to Peter Neal for providing this data set. This data was originally collected by Pfeilsticker:

Pfeilsticker, A. (1863). Beitrage zur Pathologie der Masern mit besonderer Berucksichtigung der statistischen Verhaltnisse, M.D. thesis, Eberhard-Karls Universitat, Tubingen.

and later modified by Osterle:

Oesterle, H. (1992). Statistiche Reanalyse einer Masernepidemie 1861 in Hagelloch, M.D. Thesis, Eberhard-Karls Universitat, Tubingen.

References

Neal, P. and Roberts, G. (2004). Statistical inference and model selection for the 1861 Hagelloch measles epidemic. Biostatistics 5 (2), 249.

Set control parameters for epinet MCMC algorithm

Description

Sets parameter values that control the MCMC algorithm used by epinet to produce posterior samples.

Usage

MCMCcontrol(nsamp, thinning, extrathinning = FALSE, burnin = 0, 
	seed = floor(runif(1, 0, 2^30)), etapropsd)

Arguments

Details

Auxiliary function that can be used to set parameter values that control the MCMC algorithm used by epinet to produce posterior samples. This function is only used in conjunction with the epinet function.

nsamp is the number of samples that will be produced for each of the model parameters.

thinning is the thinning interval, e.g., to return every 10^{th} sample, use thinning = 10.

If exposure and / or infective times are being inferred and we wish to return the inferred values of these times (along with the inferred transmission tree), set extrathinning equal to an integer specifying the extra thinning interval for these values. Because returning values for a large number of nodes can be very space-intensive, an extra thinning interval can be given as a multiple of the thinning interval for the other parameters. For example, using thinning = 10 and extrathinning = 20 will return the values of the inferred exposure and infective times and transmission tree every 200 iterations, and the values of the other parameters every 10 iterations. If these inferred values are not desired, set this variable to FALSE.

burnin controls the number of burn-in iterations to be run by the MCMC algorithm before samples begin to become recorded.

etapropsd is a vector of length k, where k is the number of eta (network) parameters in the model, including the intercept. These are tuning parameters for the MCMC algorithm.

Value

A list with arguments as components.

Author(s)

Chris Groendyke cgroendyke@gmail.com

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

epinet for generating posterior samples of the parameters, and priorcontrol for specifying prior distributions and their hyperparameters.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat=dcm, eta=-1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist="gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)

## Not run: 
# Note: This may take a few minutes to run.
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M = net, N = N, beta = 1, ki = 3, thetai = 7, ke = 3, latencydist = "gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)

## End(Not run)

Simulate an epidemic on a contact network

Description

Simulate the spread of an epidemic across an (undirected) contact network.

Usage

SEIR.simulator(M, N, beta, ki, thetai, ke = ki, thetae = thetai, 
    latencydist = "fixed", latencyperiod = 0) 

Arguments

Details

Takes as input an undirected network, given in edgelist matrix format, which is the same format returned by SimulateDyadicLinearERGM. Randomly chooses an initial infective individual. The infection spreads randomly across edges in the network according to exponential infective periods with mean \frac{1}{beta}. An infective individual remains in the exposed state for a either a fixed period of time given by latencyperiod or a time described by a gamma RV with parameters ke and thetae (mean = ke \cdot thetae, var = ke \cdot thetae^2). After this exposed period, an infected person moves to the Infected state, at which point they can infect susceptible individuals. The infective individuals are removed after an infective period whose length is governed by a gamma RV with parameters ki and thetai (mean = ki \cdot thetai, var = ki \cdot thetai^2). Once an individual is removed, they cannot be re-infected and cannot infect others.

Value

matrix consisting of one row for each individual in the population. Each row contains (in columns 1 - 5, respectively): the node infected, the infecting node, the time of infection, the time of transition from exposed to infective, and the time of removal. The times are shifted so that the first removal occurs at time 0. The rows corresponding to the susceptible members of the population (i.e., the individuals that were not infected during the course of the epidemic) are placed after those for the infected individuals.

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz,

See Also

SimulateDyadicLinearERGM for simulating an Erdos-Renyi contact network, epinet for performing inference on the network and epidemic model parameters, and plot.epidemic and epi2newick for plotting functions.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N,nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")

Simulates an ERGM network using given covariate values

Description

Simulates a random ERGM network using a given matrix of covariate values and a corresponding vector of parameter values.

Usage

SimulateDyadicLinearERGM(N, dyadiccovmat, eta)

Arguments

Details

dyadiccovmat is an {N \choose 2} by (k+2) matrix containing the dyadic covariates for the population, where N is the number of individuals in the population and k is the number of dyadic covariates used in the model. The matrix contains one row for each dyad (pair of nodes). Columns 1 and 2 give the ID of the two nodes comprising the dyad, and the remaining k columns give the covariate values; eta is the vector of parameters corresponding to the covariates.

For this class of dyadic independence network, the probability of an edge between individuals i and j is p_{\{i,j\} }, where

\log \left( \frac{p_{\{i,j\} }}{1-p_{\{i,j\} }} \right) = \sum_{k} \eta_k X_{\{i,j\},k}

More information about this type of model can be found in Groendyke et al. (2012).

Value

a network in edgelist matrix format

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Groendyke, C., Welch, D. and Hunter, D. 2012. A Network-based Analysis of the 1861 Hagelloch Measles Data, Biometrics, 68-3.

See Also

SEIR.simulator for simulating an SEIR epidemic over a network.

Examples

# Construct a network of 30 individuals
set.seed(3)
N <- 30
# Build dyadic covariate matrix
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)

# Another example
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)

Prints a transmission tree in Newick format.

Description

Prints a simulated or inferred transmission tree in Newick format.

Usage

epi2newick(epi)

epi2newickmcmc(mcmcoutput, index = dim(mcmcoutput$transtree)[2])

Arguments

Details

Converts the epinet epidemic format into a transmssion tree represented as a Newick string which is the standard tree format used in phylogenetics. There are many packages available to analyse Newick format trees such as the ape package, IcyTree and FigTree.

Value

A character string representing the epidemic transmission tree in Newick format. Note that this string contains control characters that can be removed by using cat

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Rambaut A. 2014. FigTree v1.4. http://tree.bio.ed.ac.uk/software/figtree/. Vaughan T. 2015. IcyTree https://icytree.org.

See Also

epinet for generating posterior samples of the parameters, print.epinet and summary.epinet for printing basic summary information about an epinet object, write.epinet for writing parameter and transmission tree posterior samples to file, and plot.epinet for plotting the posterior samples of the transmission tree.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist="gamma")
cat(epi2newick(exampleepidemic))

## Not run: 
# Build covariates
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov,binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0, -7)
net <- SimulateDyadicLinearERGM(N = N,dyadiccovmat = dyadCov,eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M=net,N=N,beta=1,ki=3,thetai=7,ke=3,latencydist="gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)
cat(epi2newickmcmc(out))
## End(Not run)

Uses epidemic data to perform Bayesian inference on a contact network

Description

Performs Bayesian inference on parameters for an SEIR epidemic model and a random graph model, given recovery (and perhaps also exposure/infective) times for each individual infected during the course of an epidemic.

Usage

epinet(formula, epidata, dyadiccovmat, mcmcinput = MCMCcontrol(), 
	priors = priorcontrol(), verbose = TRUE)

Arguments

Details

Uses exposed, infective, and removal times from the infected nodes of an epidemic in order to perform inference on the parameters of the network and epidemic models.

The formula will consist of variables (column names) found in the dyadiccovmat parameter. By default, the model will include an intercept term.

epidata is an N row by 5 column array giving the identity, likely parent, and exposed, infective, and removal times for each of the N individuals in the population, as well as the values of any nodal covariates. Column 1 gives the ID (an integer) of the node, and column 2 gives the identity of the probable parent of the node (if known). Columns 3, 4, and 5 give the exposed, infective, and removal times. Individuals who were not infected during the course of the epidemic should have NA coded in columns 3, 4, and 5; the records for these individuals should appear AFTER those corresponding to the individuals that were infected during the epidemic. Note that if the times are not internally consistent, an error message will be generated and no inference will be performed. It is necessary to include data for exposure and infective times, even if these values are not known (in this case, set the respective entries to NA).

Any data rows corresponding to individuals not infected during the course of the epidemic, if present, must occur at the end of the array, after all rows for infected individuals. These rows must have removal times of NA.

dyadiccovmat is an {N \choose 2} row by (k+2) column matrix containing the dyadic covariates for the population, where N is the number of individuals in the population and k is the number of dyadic covariates used in the model. The matrix contains one row for each dyad (pair of nodes). Columns 1 and 2 give the ID of the two nodes comprising the dyad, and the remaining k columns give the covariate values.

Uses an algorithm similar to that described in Groendyke and Welch (2018), Groendyke et al. (2010), and Britton and O'Neill (2002).

Value

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

Groendyke, C., Welch, D. and Hunter, D. 2012. A Network-based Analysis of the 1861 Hagelloch Measles Data, Biometrics, 68-3.

Groendyke, C., Welch, D. and Hunter, D. 2010. Bayesian inference for contact networks given epidemic data, Scandinavian Journal of Statistics, 38-3.

Britton, T. and O'Neill, P.D. 2002. Bayesian inference for stochastic epidemics in populations with random social structure, Scandinavian Journal of Statistics, 29-3.

See Also

BuildX for building a dyadic covariate matrix, MCMCcontrol for specifying control parameters for the MCMC algorithm, priorcontrol for specifying prior distributions and their hyperparameters, epi2newick and write.epinet for writing the output of the algorithm to file, and plot.epinet for plotting the posterior samples of the transmission tree.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N,nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat=dcm, eta=-1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist="gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)

## Not run: 
# Note: This may take a few minutes to run.
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M = net, N = N, beta = 1, ki = 3, thetai = 7, ke = 3, latencydist = "gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)

## End(Not run)

Internal epinet Objects

Description

Internal epinet functions.

Details

These are not intended to be called by the user and are only used by other functions.

Calculate the Effective Sample Size

Description

Calculate the Effective Sample Size for a marginal posterior sample obtained via MCMC

Usage

ess(x, ignoreBurnin = FALSE, burninProportion = 0.1)

Arguments

Details

Calculates the effective sample size of x based on an estimate of the lag autocorrelation function. Details of the method are in Section 11.5 of Bayesian Data Analysis, Third Edition, 2013, Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin.

Value

Returns the estimated effective sample size for the last (1-burninProportion) samples in x.

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B., 2013 Bayesian Data Analysis, Third Edition, (Section 11.5), Boca Raton, Florida: CRC Press.

Examples

	set.seed(8)
	x <- runif(1000)
	# expect ESS of close to 900 as samples are iid
	ess(x, ignoreBurnin = TRUE)
	# no burnin to ignore so ess is actually close to 1000
	ess(x, ignoreBurnin = FALSE)
	
	# ESS is a rough measure at best
	ess(1:1000,ignoreBurnin = FALSE)	

Plot the spread of an epidemic

Description

Plot the spread of an epidemic over a contact network.

Usage

## S3 method for class 'epidemic'
plot(x, lwd = 1, leaf.labs = TRUE, leaf.cex = 0.75,
    zero.at.start = FALSE, main = "Transmission Tree", xlab = "Time", 
    ylab= "", e.col = "black", i.col = "red", lty.transmission = 3, 
    marktransitions = TRUE, label.trans = "|", cex.trans = 0.5, ...)

Arguments

Details

Plots a simulated epidemic, or indicating the path that the infection took during the epidemic (the transmission tree) and the times that each node entered the Exposed, Infective, and Removed states. The default plotting parameter values work well for epidemics up to about 50 - 60 infecteds and the function requires at least 2 infecteds. For a larger number of infecteds, it is recommended to use pdf and adjust plotting dimensions.

Only works for full data, i.e., the transmission tree must be fully specified and all times for infected individuals must be known.

Value

returns no value. Strictly invoked for the plotting side effect.

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

SEIR.simulator for producing simulated epidemics. plot.epinet produces similar plots for transmission trees inferred as part of the epinet inference routine.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")

# Plot the simulated epidemic
plot(exampleepidemic)

Plot the spread of an epidemic

Description

Plot the spread of an epidemic over a contact network.

Usage

## S3 method for class 'epinet'
plot(x, index = dim(x$transtree)[2],
    lwd = 1, leaf.labs = TRUE, leaf.cex = 0.75, zero.at.start = FALSE, 
    main = "Transmission Tree", xlab = "Time", ylab= "", 
    e.col = "black", i.col = "red", lty.transmission = 3,
    marktransitions = TRUE, label.trans = "|", cex.trans = 0.5, ...)

Arguments

Details

Plots the output from the link{epinet} function indicating the path that the infection took during the epidemic (the transmission tree) and the times that each node entered the Exposed, Infective, and Removed states. The default plotting parameter values work well for epidemics up to about 50 - 60 infecteds. For a larger number of infecteds, it is recommended to use pdf and adjust plotting dimensions.

Value

returns no value. Strictly invoked for the plotting side effect.

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

epinet for performing inference on the network and epidemic model parameters. The functions epi2newick and write.epinet offer other options for outputting inferred parameter samples and transmission trees.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")

# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, extrathinning = 10, 
    etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Delete Exposure and Infection times; will infer these in the MCMC algorithm
exampleepidemic[, 3:4] <- NA
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol,
     verbose = FALSE)

# Plot starting state of epidemic from chain 
plot(examplemcmc, index = 1)

# Plot final state of epidemic from chain 
plot(examplemcmc)

Prints an epidemict object

Description

Prints an object created by the SEIR.simulator simulation routine.

Usage

	## S3 method for class 'epidemic'
print(x, ...)
	

Arguments

Details

Prints the epidemic inference object, including the exposure, infectious, and recovery times of each node in the epidemic.

Value

Strictly invoked for side effect.

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

SEIR.simulator for simulating an epidemic, summary.epidemic for the summary method of an epidemic object, and plot.epidemic for plotting a visual display of the epidemic.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
print(exampleepidemic)

Print basic information about an epinet object

Description

Prints some general information about an object created by the epinet inference routine.

Usage

	## S3 method for class 'epinet'
print(x, ...)
	

Arguments

Details

Prints some basic information about an epinet inference object, including the call, network parameters in the model, and number of iterations of the MCMC algorithm.

Value

Strictly invoked for side effect.

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

epinet for generating posterior samples of the parameters, and plot.epinet for plotting the posterior samples of the transmission tree.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)
print(examplemcmc)

## Not run: 
# Note: This may take a few minutes to run.
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M = net, N = N, beta = 1, ki = 3, thetai = 7, ke = 3, latencydist = "gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)
print(out)

## End(Not run)

Set prior distributions and hyperparameters for epinet MCMC algorithm

Description

Sets the prior distributions and corresponding hyperparameters to be used in the epinet MCMC algorithm.

Usage

priorcontrol(bprior, tiprior, teprior, etaprior, kiprior, keprior, 
	priordists = "gamma", betapriordist = priordists, thetaipriordist = priordists, 
	thetaepriordist = priordists, etapriordist = "normal", kipriordist = priordists, 
	kepriordist = priordists, parentprobmult = 1)

Arguments

Details

Auxiliary function that can be used to set prior distributions and parameter values that control the MCMC algorithm used by epinet to produce posterior samples. This function is only used in conjunction with the epinet function.

The type of prior distribution (default is gamma / inverse gamma) can be specified for all epidemic parameters (i.e., all parameters except the eta network parameters) using priordists or for each parameter individually. Either uniform or gamma / inverse gamma priors can be chosen. (The two theta parameters use inverse gamma prior distributions, while the other epidemic parameters use gamma priors.)

The parameters of the epidemic parameter prior distributions are given as vectors of (two) hyper-parameters. If the uniform prior is being used for a parameter, then the hyper-parameters are the lower and upper limits of the distribution. If the gamma distribution is being used with parameters c and d, then the prior mean is c \cdot d and the prior variance is c \cdot d^2. If the inverse gamma distribution is being used with parameters c and d, then the prior mean is \frac{d}{c-1} and the prior variance is \frac{d^2}{(c-1)^2 \cdot (c-2)}.

For the network parameters (the eta parameters), the only prior assumption currently implemented is a set of independent normal distributions.

etaprior contains the hyper-parameters for the prior distributions of the eta parameters. This is a vector of 2k values, giving the mean and standard deviation of each distribution (i.e., the first two entries are the mean and standard deviation of the prior distribution for the first eta parameter, the next two entries are the mean and standard deviation of the prior distribution for the second eta parameter, etc.)

The default prior distribution for the parent of each node is uniform on all of the other nodes. To specify a non-uniform distribution, use column 2 of epidata and set parentpriormult to an integer multiplier greater than 1.

Value

A list with arguments as components.

Author(s)

Chris Groendyke cgroendyke@gmail.com

References

Groendyke, C. and Welch, D. 2018. epinet: An R Package to Analyze Epidemics Spread across Contact Networks, Journal of Statistical Software, 83-11.

See Also

epinet for generating posterior samples of the parameters and MCMCcontrol for specifying control parameters for the MCMC algorithm.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)

Summarize simulated epidemic

Description

Prints a summary of an epidemic simulated by the SEIR.simulator simulation routine.

Usage

	## S3 method for class 'epidemic'
summary(object, ...)
	

Arguments

Details

Prints a summary of the simulated epidemic, including the number of individuals infected over the course of the epidemic, the number remaining susceptible throughout the epidemic, the total size of the population, and length of the epidemic.

Value

Strictly invoked for side effect.

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz

See Also

SEIR.simulator for simulating an epidemic, and plot.epidemic for plotting the simulated epidemic.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
summary(exampleepidemic)

Summarize posterior samples from epinet object

Description

Prints summaries of posterior samples generated by the epinet inference routine.

Usage

	## S3 method for class 'epinet'
summary(object, ...)
	

Arguments

Details

Prints summaries of the epidemic and network parameters of an epinet inference object. Epidemic parameters are beta, thetae, ke, thetai, and ki. Network parameters are specified in the model formula, and may include an intercept term.

Value

Strictly invoked for side effect.

Author(s)

Chris Groendyke cgroendyke@gmail.com, David Welch david.welch@auckland.ac.nz

See Also

epinet for generating posterior samples of the parameters, and plot.epinet for plotting the posterior samples of the transmission tree.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)
summary(examplemcmc)

## Not run: 
# Note: This may take a few minutes to run.
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M = net, N = N, beta = 1, ki = 3, thetai = 7, ke = 3, latencydist = "gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)
summary(out)

## End(Not run)

Writes posterior samples from an epinet object to an output file

Description

Outputs posterior samples of an object created by the epinet inference routine; creates two output files.

Usage

write.epinet(out, filename)

Arguments

Details

Writes two output files corresponding to the output produced from the epinet inference function. The first is a .log file, containing the posterior samples from the epidemic parameters in tab delimited form. [This .log file can be read by Tracer, which calculates summary statististics and diagnostics, and displays trace plots, histograms, etc.] The second file (which is only written if the transmission trees are returned from the inference routine), is a .trees file, containing the inferred transmission trees, output in Newick format.

Value

Strictly invoked for side effect.

Author(s)

David Welch david.welch@auckland.ac.nz, Chris Groendyke cgroendyke@gmail.com

References

Rambaut A., Suchard M., Xie D., Drummond A.J. 2014. Tracer v1.6. http://beast.community/tracer.html.

See Also

epinet for generating posterior samples of the parameters, print.epinet and summary.epinet for printing basic summary information about an epinet object, epi2newickmcmc for printing an inferred transmission tree to the screen in Newick format, and plot.epinet for plotting the posterior samples of the transmission tree.

Examples

# Simulate an epidemic through a network of 30
set.seed(3)
N <- 30
# Build dyadic covariate matrix (X)
# Have a single covariate for overall edge density; this is the Erdos-Renyi model
nodecov <- matrix(1:N, nrow = N)
dcm <- BuildX(nodecov)
# Simulate network and then simulate epidemic over network
examplenet <- SimulateDyadicLinearERGM(N, dyadiccovmat = dcm, eta = -1.8)
exampleepidemic <- SEIR.simulator(examplenet, N = 30, 
    beta = 0.3, ki = 2, thetai = 5, latencydist = "gamma")
# Set inputs for MCMC algorithm
mcmcinput <- MCMCcontrol(nsamp = 5000, thinning = 10, etapropsd = 0.2) 
priorcontrol <- priorcontrol(bprior = c(0, 1), tiprior = c(1, 3), teprior = c(1, 3), 
    etaprior = c(0, 10), kiprior = c(2, 8), keprior = c(2, 8), priordists = "uniform")
# Run MCMC algorithm on this epidemic
# Note: Not enough data or iterations for any real inference
examplemcmc <- epinet( ~ 1, exampleepidemic, dcm, mcmcinput, priorcontrol)
## Not run: write.epinet(examplemcmc, "examplemcmc")

## Not run: 
# Note: This may take a few minutes to run.
set.seed(1)
N <- 50
mycov <- data.frame(id = 1:N, xpos = runif(N), ypos = runif(N))
dyadCov <- BuildX(mycov, binaryCol = list(c(2, 3)),binaryFunc = c("euclidean"))
# Build network
eta <- c(0,-7)
net <- SimulateDyadicLinearERGM(N = N, dyadiccovmat = dyadCov, eta = eta)
# Simulate epidemic
epi <- SEIR.simulator(M = net, N = N, beta = 1, ki = 3, thetai = 7, ke = 3, latencydist = "gamma")
# Run MCMC routine on simulated epidemic
mcmcinput <- MCMCcontrol(nsamp = 1000000, thinning = 100, etapropsd = c(1, 1))
priors <- priorcontrol(bprior = c(0, 4), tiprior = c(1, 15), teprior = c(1, 15), 
	etaprior = c(0, 10, 0, 10), kiprior = c(1, 7), keprior = c(1, 7), priordists = "uniform")
out <- epinet(~ xpos.ypos.L2Dist, epidata = epi, dyadiccovmat = dyadCov,
	mcmcinput = mcmcinput, priors = priors)
write.epinet(out, "SampleInferenceOutput")

## End(Not run)