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Constrained spanning tree algorithms for irregularly-shaped spatial clustering

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  • Costa, Marcelo Azevedo
  • Assunção, Renato Martins
  • Kulldorff, Martin

Abstract

Spatial clustering methodologies that are capable of detecting and delineating irregular clusters can provide information about the geographical spread of various diseases under surveillance. This paper proposes and compares three spatial scan statistics designed to detect clusters with irregular shapes. The proposed methods use geographical boundary information to construct a graph in which a cluster growing process is performed based on likelihood function maximization. Constraints on cluster shape are imposed through early stopping, a double connection requirement and a maximum linkage criteria. The methods are evaluated using simulated data sets with either circular or irregular clusters, and compared to the circular and elliptic scan statistics. Results show that for circular clusters, the standard circular scan statistic is optimal, as expected. The double connection, elliptic maximum linkage scan statistics also achieve good results. For irregularly-shaped clusters, the elliptic, maximum linkage and double connected scan statistics are optimal for different cluster models and by different evaluation criteria, but the circular scan statistic also performs well. If the emphasis is on statistical power for cluster detection, the simple circular scan statistic is attractive across the board choice. If the emphasis is on the accurate determination of cluster size, shape and boundaries, the double connected, maximum linkage and elliptical scan statistics are often more suitable choices. All methods perform well though, with the exception of the unrestricted dynamic minimum spanning tree scan statistic and the early stopping scan statistic, which we do not recommend.

Suggested Citation

  • Costa, Marcelo Azevedo & Assunção, Renato Martins & Kulldorff, Martin, 2012. "Constrained spanning tree algorithms for irregularly-shaped spatial clustering," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1771-1783.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1771-1783
    DOI: 10.1016/j.csda.2011.11.001
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    References listed on IDEAS

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    1. Duczmal, Luiz & Assuncao, Renato, 2004. "A simulated annealing strategy for the detection of arbitrarily shaped spatial clusters," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 269-286, March.
    2. Kulldorff, Martin & Tango, Toshiro & Park, Peter J., 2003. "Power comparisons for disease clustering tests," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 665-684, April.
    3. Julian Besag & James Newell, 1991. "The Detection of Clusters in Rare Diseases," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 154(1), pages 143-155, January.
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    2. Ali Abolhassani & Marcos O. Prates & Safieh Mahmoodi, 2023. "Irregular Shaped Small Nodule Detection Using a Robust Scan Statistic," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 141-162, April.
    3. Self, Stella & Nolan, Melissa, 2024. "A Bayesian spatial scan statistic for multinomial data," Statistics & Probability Letters, Elsevier, vol. 206(C).

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