Fit a Two-Component Epidemic Model using MCMC — algo.twins • surveillance

Fits a negative binomial model as described in Held et al. (2006) to an univariate time series of counts.

This is an experimental implementation that may be removed in future versions of the package.

Usage

algo.twins(disProgObj, control=list(burnin=1000, filter=10,
   sampleSize=2500, noOfHarmonics=1, alpha_xi=10, beta_xi=10,
   psiRWSigma=0.25,alpha_psi=1, beta_psi=0.1, nu_trend=FALSE,
   logFile="twins.log"))

Arguments

disProgObj

object of class disProg

control

control object:

burnin: Number of burn in samples.
filter: Thinning parameter. If filter = 10 every 10th sample is after the burn in is returned.
sampleSize: Number of returned samples. Total number of samples = burnin+filter*sampleSize
noOfHarmonics: Number of harmonics to use in the modelling, i.e. \(L\) in (2.2) of Held et al (2006).
alpha_xi: Parameter \(\alpha_{\xi}\) of the hyperprior of the epidemic parameter \(\lambda\)
beta_xi: Parameter \(\beta_{\xi}\) of the hyperprior of the epidemic parameter \(\lambda\)
psiRWSigma: Starting value for the tuning of the variance of the random walk proposal for the overdispersion parameter \(\psi\).
alpha_psi: Parameter \(\alpha_{\psi}\) of the prior of the overdispersion parameter \(\psi\)
beta_psi: Parameter \(\beta_{\psi}\) of the prior of the overdispersion parameter \(\psi\)
nu_trend: Adjust for a linear trend in the endemic part? (default: FALSE)
logFile: Base file name for the output files. The function writes three output files in the current working directory getwd(). If logfile = "twins.log" the results are stored in the three files twins.log, twins.log2 and twins.log.acc.
twins.log contains the returned samples of the parameters \(\psi\), \(\gamma_{0}\), \(\gamma_{1}\), \(\gamma_{2}\), K, \(\xi_{\lambda}\) \(\lambda_{1},...,\lambda{n}\), the predictive distribution of the number of cases at time \(n+1\) and the deviance.
twins.log2 contains the sample means of the variables \(X_{t}, Y_{t}, \omega_{t}\) and the relative frequency of a changepoint at time t for t=1,...,n and the relative frequency of a predicted changepoint at time n+1.
twins.log.acc contains the acceptance rates of \(\psi\), the changepoints and the endemic parameters \(\gamma_{0}\), \(\gamma_{1}\), \(\gamma_{2}\) in the third column and the variance of the random walk proposal for the update of the parameter \(\psi\) in the second column.

Note

This function is not a surveillance algorithm, but only a modelling approach as described in the Held et. al (2006) paper.

Note also that the function writes three logfiles in the current working directory getwd(): twins.log, twins.log.acc and twins.log2. Thus you need to have write permissions in the current working directory.

Value

Returns an object of class atwins with elements

control: specified control object
disProgObj: specified disProg-object
logFile: contains the returned samples of the parameters \(\psi\), \(\gamma_{0}\), \(\gamma_{1}\), \(\gamma_{2}\), K, \(\xi_{\lambda}\) \(\lambda_{1},...,\lambda{n}\), the predictive distribution and the deviance.
logFile2: contains the sample means of the variables \(X_{t}, Y_{t}, \omega_{t}\) and the relative frequency of a changepoint at time t for t=1,...,n and the relative frequency of a predicted changepoint at time n+1.

References

Held, L., Hofmann, M., Höhle, M. and Schmid V. (2006): A two-component model for counts of infectious diseases. Biostatistics, 7, pp. 422--437.

Author

M. Hofmann and M. Höhle and D. Sabanés Bové

Examples

# Load the data used in the Held et al. (2006) paper
data("hepatitisA")

# Fix seed - this is used for the MCMC samplers in twins
set.seed(123)

# Call algorithm and save result (use short chain without filtering for speed)
oldwd <- setwd(tempdir())  # where logfiles will be written
otwins <- algo.twins(hepatitisA,
                     control=list(burnin=500, filter=1, sampleSize=1000))
setwd(oldwd)

# This shows the entire output (use ask=TRUE for pause between plots)
plot(otwins, ask=FALSE)

# Direct access to MCMC output
hist(otwins$logFile$psi,xlab=expression(psi),main="")
if (require("coda")) {
    print(summary(mcmc(otwins$logFile[,c("psi","xipsi","K")])))
}