Surveillance for Count Time Series Using the Classic Farrington Method

Implements the procedure of Farrington et al. (1996). At each time point of the specified range, a GLM is fitted to predict the counts. This is then compared to the observed counts. If the observation is above a specific quantile of the prediction interval, then an alarm is raised.

Usage

# original interface for a single "disProg" time series
algo.farrington(disProgObj, control=list(
    range=NULL, b=5, w=3, reweight=TRUE, verbose=FALSE, plot=FALSE,
    alpha=0.05, trend=TRUE, limit54=c(5,4), powertrans="2/3",
    fitFun="algo.farrington.fitGLM.fast"))

# wrapper for "sts" data, possibly multivariate
farrington(sts, control=list(
    range=NULL, b=5, w=3, reweight=TRUE, verbose=FALSE,
    alpha=0.05), ...)

Arguments

disProgObj

an object of class "disProg" (a list including observed and state time series).

control

list of control parameters

range: Specifies the index of all timepoints which should be tested. If range is NULL the maximum number of possible weeks is used (i.e. as many weeks as possible while still having enough reference values).
b: how many years back in time to include when forming the base counts.
w: windows size, i.e. number of weeks to include before and after the current week
reweight: Boolean specifying whether to perform reweight step
trend: If TRUE a trend is included and kept in case the conditions documented in Farrington et al. (1996) are met (see the results). If FALSE then NO trend is fit.
verbose: Boolean indicating whether to show extra debugging information.
plot: Boolean specifying whether to show the final GLM model fit graphically (use History|Recording to see all pictures).
powertrans: Power transformation to apply to the data. Use either "2/3" for skewness correction (Default), "1/2" for variance stabilizing transformation or "none" for no transformation.
alpha: An approximate (two-sided) $(1-\alpha)$ prediction interval is calculated.
limit54: To avoid alarms in cases where the time series only has about 0-2 cases the algorithm uses the following heuristic criterion (see Section 3.8 of the Farrington paper) to protect against low counts: no alarm is sounded if fewer than $cases=5$ reports were received in the past $period=4$ weeks. limit54=c(cases,period) is a vector allowing the user to change these numbers. Note: As of version 0.9-7 the term "last" period of weeks includes the current week - otherwise no alarm is sounded for horrible large numbers if the four weeks before that are too low.
fitFun: String containing the name of the fit function to be used for fitting the GLM. The options are algo.farrington.fitGLM.fast (default) and algo.farrington.fitGLM or algo.farrington.fitGLM.populationOffset. See details of algo.farrington.fitGLM for more information.

sts

an object of class "sts".

...

arguments for wrap.algo, e.g., verbose=FALSE.

Details

The following steps are performed according to the Farrington et al. (1996) paper.

fit of the initial model and initial estimation of mean and overdispersion.
calculation of the weights omega (correction for past outbreaks)
refitting of the model
revised estimation of overdispersion
rescaled model
omission of the trend, if it is not significant
repetition of the whole procedure
calculation of the threshold value
computation of exceedance score

Value

For algo.farrington, a list object of class "survRes"

with elements alarm, upperbound, trend, disProgObj, and control.

For farrington, the input "sts" object with updated alarm, upperbound and control slots, and subsetted to control$range.

Author

M. Höhle

References

A statistical algorithm for the early detection of outbreaks of infectious disease, Farrington, C.P., Andrews, N.J, Beale A.D. and Catchpole, M.A. (1996), J. R. Statist. Soc. A, 159, 547-563.

Examples

#load "disProg" data
data("salmonella.agona")

#Do surveillance for the last 42 weeks
n <- length(salmonella.agona$observed)
control <- list(b=4,w=3,range=(n-42):n,reweight=TRUE, verbose=FALSE,alpha=0.01)
res <- algo.farrington(salmonella.agona,control=control)
plot(res)

#Generate Poisson counts and create an "sts" object
set.seed(123)
x <- rpois(520,lambda=1)
stsObj <- sts(observed=x, frequency=52)

if (surveillance.options("allExamples")) {
#Compare timing of the two possible fitters for algo.farrington
range <- 312:520
system.time( sts1 <- farrington(stsObj, control=list(range=range,
                       fitFun="algo.farrington.fitGLM.fast"), verbose=FALSE))
system.time( sts2 <- farrington(stsObj, control=list(range=range,
                       fitFun="algo.farrington.fitGLM"), verbose=FALSE))
#Check if results are the same
stopifnot(upperbound(sts1) == upperbound(sts2))
}