Open Journal of Safety Science and Technology, 2012, 2, 98-107
http://dx.doi.org/10.4236/ojsst.2012.23013 Published Online September 2012 (http://www.SciRP.org/journal/ojsst)
Outbreak Detection of Spatio-Temporally
Smoothed Crashes
Ross Sparks, Chris Okugami, Sarah Bolt
CSIRO Mathematics, Informatics and Statistics, Sydney, Australia
Email: Ross.Sparks@csiro.au
Received May 1, 2012; revised June 10, 2012; accepted June 24, 2012
ABSTRACT
Spatio-temporal surveillance methods for detecting outbreaks are common with the SCAN statistic setting the bench-
mark. If the shape and size of the outbreaks are known, then the SCAN statistic can be trained to efficiently detect these,
however this is seldom the case. Therefore devising a plan that is efficient at detecting a range of outbreaks that vary in
size and shape is important in practical applications. So this paper introduces a method called EWMA Surveillance
Trees that uses a binary recursive partitioning approach to locate and detect outbreaks. This approach is explained and
then its performance is compared to that of the SCAN statistic in a series of simulation studies. While the SCAN statis-
tic is shown to remain the most effective at detecting outbreaks of a known shape and size, the EWMA Surveillance
Trees are shown to be more robust. The method is also applied to an example of actual data from motor vehicle crashes
in an area of Sydney Australia from 2000 to 2004 in order to detect dates and geographic regions with outbreaks of
crashes above the expected.
Keywords: Average Run Length; Exponential Weighted Moving Averages; Monitoring; Spatial Outbreaks;
Spatio-Temporal Smoothing; Crash Outbreaks
1. Introduction
The SCAN statistic [1] has been successful at prospec-
tively detecting space-time clusters. Kulldorff [2-4] has
developed SCAN plans and implemented them in the
SATSCAN software package for a variety of problems
including Bernoulli data, Poisson counts and a space-
time permutation model using only case data, amongst
others. However there are some important limitations to
this approach which will be addressed in this paper.
Firstly, the space-time permutation model compares in-
cidences to what is expected under the assumption that
all cases were independent of each other. That is, the
expected values are determined under the assumption
that there is no space-time interaction. Secondly, the spa-
tio-temporal SCAN statistic has been criticised by Woo-
dall et al. [5] and Han et al. [6] for not being as efficient
as the CUSUM [7,8] for outbreak detection. Lastly, the
ability to detect outbreaks most effectively is dependent
on the choice of shape and size of the scanning window.
However, the attractiveness of the SCAN technology
is that it is easy to understand, and therefore people use it.
For this reason, the SCAN statistic is implemented in this
paper as a benchmark for comparison. In our implemen-
tation, we considered the two dimensional scan statistic
used for detecting spatial clusters as discussed in detail in
the book by Glaz et al. [9]. To extend the method to the
detection of three-dimensional spatio-temporal clusters,
we use the lattice structure as outlined in Glaz et al. [9]
and then search over this structure for groups of rectan-
gular blocks of space and time in order to alarm for un-
usually high counts. The counts within the rectangular
blocks of space-time are compared to their respective
expected counts to measure their unusualness. Bounda-
ries of all significant geographical regions are outlined
on a map to indicate the geography of the outbreak.
The EWMA Surveillance Tree plan that is proposed in
this paper addresses all of the concerns raised above.
This plan also makes use of the fixed lattice structure
since this structure is well suited to the application of
Exponentially Weighted Moving Average (EWMA) tem-
poral smoothing of the counts. This smoothing improves
early detection over the moving average approach sug-
gested by Kulldorff and others. Therefore this EWMA
smoothing avoids the criticisms by Woodall et al. (2008)
and Han et al. (2008). Also, in this paper, we compare
incidences to historical expected values where the ex-
pected values can be space-time dependent. Therefore
clustered outbreaks are signaled in this paper when the
counts are higher than expected in a random local region.
Lastly, by doing away with the scanning window all to-
gether we have removed the need for this parameterisa-
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