surveillance (version 1.12.1)

algo.rogerson: Modified CUSUM method as proposed by Rogerson and Yamada (2004)

Description

Modified Poisson CUSUM method that allows for a time-varying in-control parameter $\theta_{0,t}$ as proposed by Rogerson and Yamada (2004). The same approach can be applied to binomial data if distribution="binomial" is specified.

Usage

algo.rogerson(disProgObj, control = list(range = range,
   theta0t = NULL, ARL0 = NULL, s = NULL, hValues = NULL,
   distribution = c("poisson","binomial"), nt = NULL, FIR=FALSE, 
   limit = NULL, digits = 1))

Arguments

disProgObj

object of class disProg that includes a matrix with the observed number of counts

control

list with elements [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Value

• Returns an object of class survRes with elements
• alarm
  indicates whether the CUSUM signaled at time $t$ or not (1 = alarm, 0 = no alarm)
• upperbound
  CUSUM values $S_{t}$
• disProgObj
  disProg object
• control
  list with the alarm threshold $h$ and the specified control object

Details

The CUSUM for a sequence of Poisson or binomial variates $x_t$ is computed as $$S_t = \max {0, S_{t-1} + c_t (x_t- k_t)} , \, t=1,2,\ldots ,$$ where $S_0=0$ and $c_t=\frac{h}{h_t}$; $k_t$ and $h_t$ are time-varying reference values and decision intervals. An alarm is given at time $t$ if $S_t \geq h$.

If FIR=TRUE, the CUSUM starts with a head start value $S_0=\frac{\code{h}}{2}$ at time $t=0$. After an alarm is given, the FIR CUSUM starts again at this head start value. The procedure after the CUSUM gives an alarm can be determined by limit. Suppose that the CUSUM signals at time $t$, i.e. $S_t \geq h$.For numeric values of limit, the CUSUM is bounded above after an alarm is given,i.e. $S_{t}$ is set to $\min{\code{limit} \cdot h,S_{t}}$.Using limit=0 corresponds to resetting $S_t$ to zero after an alarm as proposed in the original formulation of the CUSUM. If FIR=TRUE, $S_{t}$ is reset to $\frac{\code{h}}{2}$ (i.e. limit=$\frac{\code{h}}{2}$ ). If limit=NULL, no resetting occurs after an alarm is given.

References

Rogerson, P. A. and Yamada, I. Approaches to Syndromic Surveillance When Data Consist of Small Regional Counts. Morbidity and Mortality Weekly Report, 2004, 53/Supplement, 79-85

See Also

hValues

Examples

# simulate data
set.seed(123)
data <- simHHH(control = list(coefs = list(alpha =-0.5, gamma = 0.4,
               delta = 0.6)),length=300)

# extract mean used to generate the data
lambda <- data$endemic

# determine a matrix with h values
hVals <- hValues(theta0 = 10:150/100, ARL0=500, s = 1, distr = "poisson")

# apply modified Poisson CUSUM
res <- algo.rogerson(data$data,
            control=c(hVals, list(theta0t=lambda,range=1:300)))
plot(res)