epimcmc {EpiILM}

Monte Carlo Simulation

Description

Runs an MCMC algorithm for the estimation of specified model parameters

Usage

epimcmc (object, tmin = NULL, tmax,

         niter, sus.par.ini, trans.par.ini = NULL, beta.ini = NULL, spark.ini = NULL,

         Sformula = NULL, Tformula = NULL,

         pro.sus.var, pro.trans.var = NULL, pro.beta.var = NULL, pro.spark.var = NULL,

         prior.sus.dist, prior.trans.dist = NULL, prior.beta.dist = NULL,

         prior.spark.dist = NULL, prior.sus.par, prior.trans.par, prior.beta.par = NULL,

         prior.spark.par = NULL, adapt = FALSE, acc.rate = NULL)

Arguments

object

An object of class epidata that can be the output of epidata or as.epidata.

tmin

The first time point at which the infection occurs, default value is one.

tmax

The last time point at which data is observed.

niter

Number of MCMC iterations.

sus.par.ini

Initial value(s) of the susceptibility parameter(s) (>0).

trans.par.ini

Initial value(s) of the transmissibility parameter(s) (>0).

beta.ini

Initial value(s) of the spatial parameter(s) (>0) or the network parameter(s) (>0) if contact network is used.

spark.ini

Initial value of the spark parameter (>=0).

Sformula

An object of class formula. See formula

Individual-level covariate information associated with susceptibility can be passed through this argument. An expression of the form ~ model is interpreted as a specification that the susceptibility function, \Omega_S(i) is modelled by a linear predictor specified symbolically by the model term. Such a model consists of a series of terms separated by + and - operators. If there is no susceptibility covariate information, Sformula is null.

Tformula

An object of class formula. See formula

Individual-level covariate information associated with transmissibility can be passed through this argument. An expression of the form ~ -1+model is interpreted as a specification that the transmissibility function, \Omega_T(j) is modelled by a linear predictor specified symbolically by the model terms without the incorporation of the intercept term. Such a model consists of a series of terms separated by + and - operators. If there is no transmissibility covariate information, Tformula is null.

pro.sus.var

Proposal density variance(s) for susceptibility parameter(s). If a zero value is assigned to the proposal variance of any parameter, the parameter is considered fixed to its sus.par.ini value.

pro.trans.var

Proposal density variance(s) for transmissibility parameter(s). If a zero value is assigned to the proposal variance of any parameter, the parameter is considered fixed to its sus.par.ini value.

pro.beta.var

Proposal density variance(s) for beta parameter(s). If a zero value is assigned to the proposal variance of any parameter, the parameter is considered fixed to its sus.par.ini value.

pro.spark.var

Proposal density variance for the spark parameter.

prior.sus.dist

Select the prior distribution(s) for the susceptibility parameter(s) with the choice of "halfnormal" for positive half normal distribution, "gamma" for gamma distribution and "uniform" for uniform distribution

prior.trans.dist

Select the prior distribution(s) for the transmissibility parameter(s) with the choice of "halfnormal" for positive half normal distribution, "gamma" for gamma distribution and "uniform" for uniform distribution

prior.beta.dist

Select the prior distribution(s) for the beta parameter(s) with the choice of "halfnormal" for half normal distribution, "gamma" for gamma distribution and "uniform" for uniform distribution

prior.spark.dist

Select the prior distribution for the spark parameter with the choice of "halfnormal" for half normal distribution, "gamma" for gamma distribution and "uniform" for uniform distribution

prior.sus.par

A vector (matrix) of the prior distribution parameters for updating the susceptibility parameter(s).

prior.trans.par

A vector (matrix) of the prior distribution parameters for updating the transmissibility parameter(s).

prior.beta.par

A vector (matrix) of the prior distribution parameters for updating the kernel parameter(s).

prior.spark.par

A vector of the prior distribution parameters for updating the spark parameter.

adapt

To enable the adaptive MCMC method in the MCMC function, default is FALSE.

acc.rate

To set an acceptance rate. This option will be ignored if adapt = FALSE. See MCMC for more details.

Details

Independent Gaussian random walks are used as the Metropolis-Hastings MCMC proposal for all parameters. The epimcmc function depends on the MCMC function from the adaptMCMC package.

Value

Returns an object of class epimcmc that contains:

type:

the compartmental framework model used in the analysis.

kernel.type:

the used kernel.type in the function (distance-based or network-based).

Estimates:

the MCMC output of the updated model parameters.

Loglikelihood:

the loglikelihood of the updated model parameters.

Fullsamples:

the MCMC output of all the model parameters (including fixed parameters).

n.sus.par:

the number of parameters in the susceptibility function.

n.trans.par:

the number of parameters in the transmissibility function.

n.ker.par:

the number of parameters in the kernel function.

References

Rob Deardon, Xuan Fang, and Grace P. S. Kwong (2015). Statistical modelling of spatio-temporal infectious disease tranmission in Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases, (Ed: D. Chen, B. Moulin, J. Wu), John Wiley & Sons.. Chapter 11.

See Also

summary.epimcmc, plot.epimcmc, epidata, epilike, pred.epi.

Examples

## Example 1:  spatial SI model
# generate 100 individuals

x <- runif(100, 0, 10)

y <- runif(100, 0, 10)

covariate <- runif(100, 0, 2)

out1 <- epidata(type = "SI", n = 100, Sformula = ~covariate, tmax = 15,
               sus.par = c(0.1, 0.3), beta = 5.0, x = x, y = y)

alphapar1 <- matrix(c(1, 1, 1, 1), ncol = 2, nrow = 2)

betapar1 <- c(10, 2)

epi <- epimcmc(object = out1, tmin = 1, tmax = 15,
               niter = 1000, sus.par.ini = c(1, 1), beta.ini = 1,
               Sformula = ~covariate, pro.sus.var = c(0.5, 0.3), pro.beta.var = 0.1,
               prior.sus.dist = c("gamma", "gamma"), prior.beta.dist = "gamma",
               prior.sus.par = alphapar1, prior.beta.par = betapar1,
               adapt = TRUE, acc.rate = 0.5)
epi

## Example 2:  spatial SIR model

lambda <- rep(3, 100)

out2 <- epidata(type = "SIR", n = 100, tmax = 15, sus.par = 0.3, beta = 5.0, infperiod = lambda,
        x = x, y = y)

alphapar2 <- c(1, 1)
betapar2 <- c(1, 1)

epi2 <- epimcmc(object = out2, tmin = 1, tmax = 15,
               niter = 1000, sus.par.ini = 1, beta.ini = 1,
               Sformula = NULL, pro.sus.var = 0.3, pro.beta.var = 0.1,
               prior.sus.dist = "gamma", prior.beta.dist = "gamma",
               prior.sus.par = alphapar2, prior.beta.par = betapar2,
               adapt = FALSE, acc.rate = NULL)
epi2