# Surveillance for Count Time Series Using the Classic Farrington Method

`algo.farrington.Rd`

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`

.

## See also

`algo.farrington.fitGLM`

,
`algo.farrington.threshold`

An improved Farrington algorithm is available as function
`farringtonFlexible`

.

## 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))
}
```