Function for simulating a time series and creating an sts object. As the counts are generated using a negative binomial distribution one also gets the (1-alpha) quantile for each timepoint (can be interpreted as an in-control upperbound for in-control values). The baseline and outbreaks are created as in Noufaily et al. (2012).

sts_creation(theta, beta, gamma1, gamma2, m, overdispersion, dates,
  sizesOutbreak, datesOutbreak, delayMax, alpha, densityDelay)

Arguments

theta

baseline frequency of reports

beta

time trend

gamma1

seasonality

gamma2

seasonality

m

seasonality

overdispersion

size parameter of rnbinom for the parameterization with mean and dispersion

dates

dates of the time series

sizesOutbreak

sizes of all the outbreaks (vector)

datesOutbreak

dates of all the outbreaks (vector)

delayMax

maximal delay in time units

alpha

alpha for getting the (1-alpha) quantile of the negative binomial distribution at each timepoint

densityDelay

density distribution for the delay

References

Noufaily, A., Enki, D.G., Farrington, C.P., Garthwaite, P., Andrews, N.J., Charlett, A. (2012): An improved algorithm for outbreak detection in multiple surveillance systems. Statistics in Medicine, 32 (7), 1206-1222.

Examples

set.seed(12345)
# Time series parameters
scenario4 <- c(1.6,0,0.4,0.5,2)
theta <- 1.6
beta <- 0
gamma1 <-0.4
gamma2 <- 0.5
overdispersion <- 1
m <- 1
# Dates
firstDate <- "2006-01-01"
lengthT=350
dates <- as.Date(firstDate) + 7 * 0:(lengthT - 1)
# Maximal delay in weeks
D=10
# Dates and sizes of the outbreaks
datesOutbreak <- as.Date(c("2008-03-30","2011-09-25"))
sizesOutbreak <- c(2,5)
# Delay distribution
data("salmAllOnset")
in2011 <- which(isoWeekYear(epoch(salmAllOnset))$ISOYear == 2011)
rT2011 <- salmAllOnset@control$reportingTriangle$n[in2011,]
densityDelay <- apply(rT2011,2,sum, na.rm=TRUE)/sum(rT2011, na.rm=TRUE)
# alpha for the upperbound
alpha <- 0.05
# Create the sts with the full time series
stsSim <- sts_creation(theta=theta,beta=beta,gamma1=gamma1,gamma2=gamma2,m=m,
                       overdispersion=overdispersion,
                       dates=dates,
                       sizesOutbreak=sizesOutbreak,datesOutbreak=datesOutbreak,
                       delayMax=D,densityDelay=densityDelay,
                       alpha=alpha)
plot(stsSim)