Adaptive Likelihood Ratio Scans for the Detection of Space-Time Clusters

Living reference work entry


This work presents a methodology to detect space-time clusters, based on adaptive likelihood ratios (ALRs), which preserves the martingale structure of the regular likelihood ratio. Monte Carlo simulations are not required to validate the procedure’s statistical significance, because the upper limit for the false alarm rate of the proposed method depends only on the quantity of evaluated cluster candidates, thus allowing the construction of a fast computational algorithm. The quantity of evaluated clusters is also significantly reduced, by using another adaptive scheme to prune many unpromising clusters, further increasing the computational speed. Performance is evaluated through simulations to measure the average detection delay and the probability of correct cluster detection. Applications for thyroid cancer in New Mexico and hanseniasis in children in the Brazilian Amazon are shown.


Spatial analysis Space-time clusters Sequential analysis Adaptive likelihood ratio Simulation 



The authors were funded with grants from the Brazilian agencies CAPES, UFAM, CNPq, and FAPEMIG.


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Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversidade Federal do AmazonasManausBrazil
  2. 2.Campus Pampulha, Department of StatisticsUniversidade Federal de Minas GeraisBelo HorizonteBrazil

Section editors and affiliations

  • Joseph Glaz
    • 1
  • Markos V. Koutras
    • 2
  1. 1.Department of StatisticsUniversity of ConnecticutStorrsUSA
  2. 2.Dept. of Statistics and Insurance Science, University of PiraeusPiraeusGreece

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