A SPACE TIME PERMUTATION SCAN STATISTIC WITH IRREGULAR SHAPE FOR DISEASE OUTBREAK DETECTION

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A SPACE TIME PERMUTATION SCAN STATISTIC WITH
IRREGULAR SHAPE FOR DISEASE OUTBREAK DETECTION

• Marcelo A. Costa, Martin Kulldorff, Renato M.
  Assunção
• Harvard Pilgrim Health Care
• Harvard Medical School

Laboratório de Estatística Espacial
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Objective

• To develop a methodology for detecting irregular
  space-time cluster using the space time
  permutation scan statistic.
• The methodology includes sequential Monte Carlo
  simulation and distribution approximation to
  estimate the error type I.

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Irregular Shapes - Review

• Duczmal and Assunção. Simulated annealing
  strategy for the detection of arbitrary shaped
  spatial clusters (2004).
• Patil and Taillie. Upper level set scan statistic
  for detecting arbitrarily shaped hotspots (2004).
• Tango and Takahashi. A flexibly shaped spatial
  scan statistic for detecting clusters (2005).
• Assunção, Costa, Tavares and Ferreira. Fast
  detection of arbitrarily shaped disease clusters
  (2006).
• Kulldorff, Huang and Duczmal. An elliptical
  spatial scan statistic (2006).
• Wieland, Brownstein, Berger and Mandl. Accurate
  detection of arbitrarily shaped spatial disease
  clusters (2006) ISDS Conference.
• Lukasz P. Wawryniak, GraphScan Detection and
  Analysis of Free-Form Spatio-Temporal Patterns
  (2006) ISDS Conference.
• Assunção R, Costa M, Tavares A, Ferreira S, Fast
  Detection of Arbitrary Shaped Disease Clusters,
  Statistics in Medicine. 2006.
• Takahashi K, Kulldorff M, Tango T and Yie K, A
  Flexible Space-Time Scan Statistic for Disease
  Outbreak Detection and Monitoring, ISDN, 2006.
• Costa M, Assunção R, Kulldorff M, Constrained
  Spanning Tree Algorithms for Irregular Spatial
  Clustering. 2007. (submitted)

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Constrained Spanning Trees MLink (Maximum Link)
Growing Process
Adjacency Information
02860 02864 02906 02864 02860 02019 02093
02762 02895 02864 01504 02019 02864 02093
01504 02093 02864 02762 02056 02035 02762 02864
02093 02760 02864 02762 02703 02703 02860 02864
02760 02048 02739 02770
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Space Time Permutation (Cilinder)
M. Kulldorff, R. Heffernan, J. Hartman, R.
Assunção and F. Mostashari. A Space-Time
Permutation Scan Statistic for Disease Outbreak
Detection. PLoS Med 2(3), 2005.
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Space Time - Irregular in Space only
t
x
y
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Irregular in Space and Time
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Cluster Growing Process
time 2
time 1
time 0
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Sequential Monte Carlo Simulation (h)

• Generate simulated statistics under the null
  hypothesis until h values greater or equal the
  observed one are seen, or until the number of
  simulations reaches n -1.
• l is the number of simulations at the exact
  moment when h values are reached.
• g is the number of simulated statistics greater
  or equals the observed one (?), g lt h.

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Sequential Monte Carlo

• Advantage It decreases the number of Monte Carlo
  Simulation under the null hypothesis.
• Disadvantage The minimum p-value depends on the
  maximum number of simulation, n.

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Gumbel Distribution

• Abrams A, Kulldorff M, Kleinman K.
  Empirical/Asymptotic P-Values for Monte
  Carlo-based Hypothesis Testing an Application to
  Cluster Detection Using the Scan Statistic ISDS,
  2005
• Extreme Value Distribution
• The Method of Moments
• where ? is Eulers constant, S is the sample
  standard deviation and x is the sample mean
• Advantage It decreases the number of Monte Carlo
  simulations under the alternative hypothesis.

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HVMA Data

• Influenza Illness 13 and over (Emergency Room)
• Zip codes 206
• Historical Data 2004 - 2005
• Period of Surveillance January to December 2005
• Cases Episodes
• Max. temporal scanning window 7 days
• Sequential Monte Carlo h 50, n 1,000.

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ILI13 ZIP codes and Graph Structure
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Irregular in Space and Time versus SaTScan
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Detected Cluster in 09/03/2005SaTScan - Circular
1.Location IDs included. 02478, 02476, 02472
Coordinates / radius.. (42.397426 N, 71.177085
W) / 2.62 km Time frame............ 2005/8/28
- 2005/9/3 (7 days) Number of cases....... 3
Expected cases........ 0.21 Observed /
expected... 13.972 Test statistic........
5.140450 Monte Carlo rank...... 735/10000
P-value............... 0.0735 Recurrence
interval... 14 days
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Detected Cluster in 09/03/2005MLink - Irregular
1.Location IDs included. 02421, 02452, 02453,
02472, 02478 Time frame............ 2005/8/28
- 2005/9/3 (7 days) Number of cases....... 3
Expected cases........ 0.147408 Observed /
expected... 20.3516 Test statistic........
6.20219 P-value............... 0.00138053
Recurrence interval... 724 days
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Conclusions

• We succeeded in implementing a Space Time
  permutation methodology with irregular shape,
  optimized computational cost and higher p-value
  resolution
• Flexible method to detect disease outbreaks
• Sequential Monte Carlo and Gumbel distribution
  reduce the computational cost
• Future work simulation study