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ISDS 2012 Conference Abstracts

Multiple Source Spatial Cluster Detection Through Multi-
criteria Analysis
Luiz H. Duczmal*1, Alexandre C. L. Almeida2, Fabio R. da Silva1 and Martin Kulldorff3

1Universidade Federal de Minas Gerais, Belo Horizonte, Brazil; 2Universidade Federal de São João del-Rei, Ouro Branco, Brazil;
3Harvard Medical School, Boston, MA, USA

Objective
To incorporate information from multiple data streams of disease

surveillance to achieve more coherent spatial cluster detection using
statistical tools from multi-criteria analysis.

Introduction
Multiple data sources are essential to provide reliable information

regarding the emergence of potential health threats, compared to sin-
gle source methods [1,2]. Spatial Scan Statistics have been adapted
to analyze multivariate data sources [1]. In this context, only ad hoc
procedures have been devised to address the problem of selecting the
most likely cluster and computing its significance. A multi-objective
scan was proposed to detect clusters for a single data source [3].

Methods
For simplicity, consider only two data streams. The j-th objective

function evaluates the strength of candidate clusters using only in-
formation from the j-th data stream. The best cluster solutions are
found by maximizing two objective functions simultaneously, based
on the concept of dominance: a point is called dominated if it is worse
than another point in at least one objective, while not being better
than that point in any other objective [4]. The nondominated set con-
sists of all solutions which are not dominated by any other solution.
To evaluate the statistical significance of solutions, a statistical ap-
proach based on the concept of attainment function is used [4].

Results
The two datasets are standardized brain cancer mortality rates for

male and female adults for each of the 3111 counties in the 48 con-
tiguous states of the US, from 1986 to 1995 [5].

We run the circular scan and plot the (m(Zi),w(Zi)) points in the
Cartesian plane, where m(Zi) and w(Zi) are the LLR for the zone Zi
in the men’s and women’s brain cancer map, respectively, and i,
i=1,...,N(r) is the set of all circular zones up to a radius r>0. The non-
dominated set is inspected to observe possible correlations between
the two maps regarding brain cancer clustering (Figure 1); e.g., the
upper inset map has high LLR value on women’s map, but not on
men’s; the inverse happens to the lower inset map. Other nondomi-
nated clusters in the middle have lower LLR values on both datasets.
The first two examples have comparatively lower p-value (they be-
long to the two “knees” in the nondominated set), as computed using
the attainment surfaces (not shown in the figure).

Conclusions
The multi-criteria multivariate approach has several advantages:

(i) the representation of the evaluation function for each datastream
is very clear, and does not suffer from an artificial, and possibly con-
fusing mixture with the other datastream evaluations; (jj) it is possi-
ble to attribute, in a rigorous way, the statistical significance of each
candidate cluster; (iii) it is possible to analyze and pick-up the best
cluster solutions, as given naturally by the non-dominated set.

Part of the solution set in the LLR(male) X LLR(female) space of the
male/female brain cancer datasets for the US counties map. Clusters are in-
dicated by blue points, with the non-dominated solutions represented by
small red circles. The inset maps depict the geographic location of the clus-
ters found in the US counties map (yellow circles) for two sample non-dom-
inated solutions.

Keywords
spatial scan statistic; Multi-criteria; attainment surface; Multiple data
stream

Acknowledgments

The authors acknowledge the grants from CNPq and Capes.

References

[1] Kulldorff M, Mostashari F, Duczmal L, Yih K, Kleinman K, Platt
R.(2007) Multivariate Scan Statistics for Disease Surveillance. Stat
Med,26,1824-1833.

[2] Jonsson et al. Analysis of simultaneous space-time clusters of Campy-
lobacter spp. in humans and in broiler flocks using a multiple dataset
approach (2010). IJ Health Geogr,9:48

[3] Duczmal L, Cançado ALF, Takahashi RHC (2008) Geographic De-
lineation of Disease Clusters through multi-objective Optimization. J
Comp Graph Stat,17:243-262.

[4] Cançado ALF, Duarte AR, Duczmal L, Ferreira SJ, Fonseca CM, Gon-
tijo ECDM (2010). Penalized likelihood and multiobjective spatial
scans for the detection and inference of irregular clusters. IJ Health
Geogr,9:55.

[5] Fang Z, Kulldorff M, Gregorio DI (2004). Brain cancer mortality in
the United States, 1986 to 1995: A geographic analysis. Neuro-On-
cology 03-045, May 6.

*Luiz H. Duczmal
E-mail: duczmal@ufmg.br

Online Journal of Public Health Informatics * ISSN 1947-2579 * http://ojphi.org * 5(1):e11, 2013