# Spatio-temporal cluster detection

`stcd.Rd`

Shiryaev-Roberts based prospective spatio-temporal cluster detection as in Assuncao & Correa (2009).

## Arguments

- x
Vector containing spatial x coordinate of the events.

- y
Vector containing spatial y coordinate of the events.

- t
Vector containing the time points of the events. It is assumed that the vector is sorted (early->last).

- radius
Radius of the cluster to detect.

- epsilon
Relative change of event-intensity within the cluster to detect. See reference paper for an explicit definition.

- areaA
Area of the observation region A (single number) -- This argument is currently ignored!

- areaAcapBk
Area of A \ B(s_k,rho) for all k=1,...,n (vector). This argument is currently ignored!

- threshold
Threshold limit for the alarm and should be equal to the desired Average-Run-Length (ARL) of the detector.

- cusum
(logical) If

`FALSE`

(default) then the Shiryaev-Roberts detector is used as in the original article by Assuncao & Correa (2009), i.e. \(R_n = \sum_{k=1}^n \Lambda_{k,n}\), where \(\Lambda_{k,n}\) denotes the likelihood ratio between the in-control and out-of control model. If`TRUE`

, CUSUM test statistic is used instead. Here, $$R_n = \max_{1\leq k \leq n} \Lambda_{k,n}$$. Note that this has implications on what threshold will sound the alarm (CUSUM threshold needs to be smaller).

## Details

Shiryaev-Roberts based spatio-temporal cluster detection based on the work in Assuncao and Correa (2009). The implementation is based on C++ code originally written by Marcos Oliveira Prates, UFMG, Brazil and provided by Thais Correa, UFMG, Brazil during her research stay in Munich. This stay was financially supported by the Munich Center of Health Sciences.

Note that the vectors `x`

, `y`

and `t`

need to be of the
same length. Furthermore, the vector `t`

needs to be sorted (to
improve speed, the latter is not verified within the function).

The current implementation uses a call to a C++ function to perform the actual computations of the test statistic. The function is currently experimental -- data type and results may be subject to changes.

## Value

A list with three components

- R
A vector of the same length as the input containing the value of the test statistic for each observation.

- idxFA
Index in the x,y,t vector causing a possible alarm. If no cluster was detected, then a value of

`-1`

is returned here.- idxCC
index in the x,y,t vector of the event containing the cluster. If no cluster was detected, then a value of

`-1`

is returned here.

## References

Assuncao, R. and Correa, T. (2009), Surveillance to detect emerging space-time clusters, Computational Statistics & Data Analysis, 53(8):2817-2830.

## Examples

```
if (require("splancs")) {
# load the data from package "splancs"
data(burkitt, package="splancs")
# order the times
burkitt <- burkitt[order(burkitt$t), ]
#Parameters for the SR detection
epsilon <- 0.5 # relative change within the cluster
radius <- 20 # radius
threshold <- 161 # threshold limit
res <- stcd(x=burkitt$x,
y=burkitt$y,
t=burkitt$t,
radius=radius,
epsilon=epsilon,
areaA=1,
areaAcapBk=1,
threshold=threshold)
#Index of the event
which.max(res$R >= threshold)
}
```