Application of Nonlinear Data Analysis Methods to Locating Disease Clusters

1
Application of Nonlinear Data Analysis Methods to
Locating Disease Clusters

• Linda Moniz and William Peter
• International Society for Disease Surveillance
• Track 1 Surveillance Innovations - Spatial
  Method Innovations
• Raleigh, NC
• December 4, 2008

2
The Problem

• Daily reports of syndrome counts by clinic or
  home zip code.
• In this study we focus on the respiratory
  syndrome.
• We need to detect any unusual clusters of
  disease, quickly
• These detections are for health departments and
  need to be done in real time, updated daily,
  automated.
• Whats unusual and whats a cluster?
• Can dynamical methods assist currently used
  operational algorithms?

3
Operational Algorithms

• Many operationally utilized clustering methods
  are based the Kulldorff Scan Statistic (1997).
• This algorithm is an individually most powerful
  test under ideal circumstances.
• This algorithm finds the most unlikely cluster in
  a space given the expected distribution. It
  calculates the significance using a Monte-Carlo
  process.
• The shapes of the clusters are generally
  pre-determined by the algorithm.
• Much current research into clustering revolves
  around improving the Scan Statistics speed
  and/or accuracy.
• Scan Statistics are prone to false alerts when
  the algorithm is tuned for sensitivity.
• Can we use dynamical methods to filter the
  false alerts?
• We use a recent C-implementation of the scan
  statistic a collaboration of APL/CDC/SAIC that
  works well and is fast (uses a Gumbel
  distribution).

4
Data - Particulars

• About 3 years of data from a network of
• Clinics in the S.W. USA, all with the same
• reporting and care protocol GOOD DATA

5
Re-examination of the Problem

• This is a dynamical problem as well as a
  statistical problem. A cluster is a set of
  locations with shared dynamics.
• We proposed de-coupling the detection of unusual
  behavior and the clustering of unusual behavior.
• First, see if there are detections.
• Secondly, see if the detections cluster in space.
  
• Lastly, see if the clustering is coincidental or
  if there is evidence of shared dynamics at the
  cluster locations.

• Detections in the same place
• Do they have evidence of shared dynamics?

6
Spatial Clustering Detection

• We use the ACE algorithm to see if detections
  cluster spatially.
• The ACE algorithm is a particle-mesh heuristic
  that can find any shaped cluster, based on
  adaptive criteria.
• The results we see here did not require spatial
  clustering we used clinic-level data at 16
  clinics throughout the U.S. Southwest.
• The method must be used for home zip-code level
  data, which counts disease cases for hundreds of
  zip codes.
• To VERIFY that the spatial clusters are related,
  we use Transfer Entropy (Schreiber, 2000) to test
  for information transfer between proposed
  locations in the cluster.

7
Detection

• Viboud et al. (2003) used Lorenzs Method of
  Analogues(1969) to retrospectively analyze and
  predict flu seasons across France over 10 years.
  Their results were much more accurate than
  currently used statistical methods.
• We will use the Method of Analogues prospectively
  and with an adaptation we use the data itself to
  determine a threshold level for unusual behavior.
  
• We use the data to determine the parameters for
  the method (the number of neighbors (7), and the
  number of days used in the forecast (1).
• These parameters gave optimal prediction in the
  testing period (60 days) for nearly all zip
  codes time series.

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Prediction The Method of Analogues
Weight these observations to produce a
prediction for the circled point
.9995
.9565
.9175
.98
Prediction .9995 (.3705) .9565(.2743 )
.9175(.3551 ) .9585
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Transfer Entropy

• Consider transition probabilities of a system at
  spatial site X
• p(xi1
  xi).
• What happens if we also consider the information
  at site Y?
• p(xi1 xi, yi).
• If Y gives no information about X, p(xi1 xi,
  yi ) p(xi1 xi).
• Otherwise, we can define the Transfer Entropy
  from Y to X

• Transfer Entropy from Y to X tells us how much we
  can learn
• about site Xs dynamics by monitoring Y.

10
Testing Method

• We compare our method with a fast, efficient
  method the APL/CDC/SAIC scan statistic.
• Problem We have 3 years worth of historical
  data. We do not know if there were any outbreaks
  of disease in the historical data.
• In order to test or compare any detection
  algorithm, we inject artificial disease clusters
  on top of the real data and see if they can be
  detected.
• We also see if other, spurious clusters are
  detected (false alerts?).
• We choose a geometry/location for which the
  APL/CDC/SAIC algorithm has poor sensitivity and
  is prone to false alarms.

11
Injected Data

• We inject both 50 cases and 100 cases on top of
  the real clinic data.
• These cases are distributed according to a
  lognormal epidemic curve, spatially over 3
  clinics.
• We choose 5 different times of the year (labeled
  A-E) to inject the data and consider detections
  for each one separately.
• Affected zip codes are CZ3, CZ5 (center of the
  epidemic), CZ10.

12
Detections - Analogue Method and Scan Statistics
There were also detections at other zip codes.
At the time of Inject E there were detections at
zips CZ7 and CZ9 for the Analogue method and
clusters detected at several zip codes for
the Scan Statistics
13
Detection of Shared Dynamics Via Transfer Entropy

• For each zip code with a detection for Inject E
  we looked at (normalized) Transfer Entropy before
  the injection period and after the injection
  period.
• This included TE between zip codes that did not
  include the injects.
• We compared this with the same (normalized)
  differences in Transfer Entropy without injects.
• Transfer Entropy increased between zip codes that
  had injects and stayed the same between zip codes
  that did not have injects.

14
Results

• Whether or not there was a detection at site CZ3,
  CZ10 or CZ5, the Transfer Entropy still showed an
  increase during the inject period.
• We computed TE for injections E and observed the
  same behavior in both inject periods.
• The detections together with the TE results
  showed that CZ3, CZ5 and CZ10 were in a cluster
  (definition shared dynamics plus a detection at
  one or more of the zips) during the inject
  period.
• The Scan Statistics missed the center of the
  inject cluster and in some cases, the cluster
  itself.
• Our method used a 60-day baseline for detection,
  the same as used for the Scan statistics, but
  used the entire time series up to injection D and
  E to calculate Transfer Entropy for those inject
  periods.

15
Conclusions/Further Work

• With minimal tuning, the detection capability of
  the Method of Analogues was as good or better in
  most of these cases than the Scan Statistics.
• Detection sensitivity could be increased with
  some more investigation into optimal parameters
  and weighting of observations.
• The Transfer Entropy results show there is
  potential for identifying clustering behavior
  rather than just spatial coincidence.
• This method has potential but there are
  adaptability questions. It is difficult to get a
  reliable density estimation for TE with sparse
  time series.
• This problem is not as serious as it seems
  clinics with low background case levels generally
  have few false alarms. False alarms for
  locations with high background case levels are
  the larger problem.
• We hope to use these results to encourage
  research in dynamical analysis of these data.
• Fundamental Question how does a outbreak or
  bioterrorism event differ dynamically from the
  normal background dynamics?

16
Acknowledgements

• Thanks to the organizers and sponsors!
• Thanks to the APL IRAD program for partially
  funding this research.
• The APL/CDC/SAIC scan statistic was developed
  under an RO1 grant from CDC.
• References
• Kuldorff , M. A spatial scan statistic.
  Communications in Statistics Theory and Methods
  26(6) (1997).
• Lorenz, EN. Atmospheric predictability as
  revealed by naturally occurring analogues. J.
  Atmosphere Sci 26 (1969).
• Schreiber, T. Measuring information transfer.
  PRL 85(2) (2000).
• Viboud et al. Prediction of the spread of
  influenza epidemics by the method of analogues.
  American Journal of Epidemiology 158 (10) (2003).

17
ACE Algorithm
Dx 2.2 Dy 2.2 Ng 100

• Create a simple, coarse grid over the data points

3. Now add agents with rules to move along
mesh to find points with high densities.
2. Weight each point to its nearest grid
point by interpolation GRID points get the
mass!
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ACE Algorithm
m(i,j1)
m 10.5
m(i1,j)
m(i-1,j)
m 10.8
m12.7
m(i,j-1)
m 2.6
m10.5
m 1.1
ACE finds all clusters, with relative weights.
Rule-based Agent searching through masses at grid
points.
m10.8
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Dynamics of a Process

• A statistical analysis of a time series treats
  each state of the system as a random process that
  is governed by a distribution of the states only.
  
• A dynamical analysis of a time series assumes
  that each state is determined by the immediately
  previous state.

• The expected value (mean) of both is the same
• The next state of the blue line is 11, the next
  state of the red line is 8.

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Differences in Transfer Entropy for Injects D.