On Detecting Disease Outbreaks: Univariate and Multivariate Monitoring

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On Detecting Disease OutbreaksUnivariate and
Multivariate Monitoring

• Inbal Yahav
• With Galit Shmueli and Thomas Lotze
• The work was partially supported by NIH grant
  RFA-PH-05-126.

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Introduction to Biosurveillance
0

• Natural and Bioterrorist-related disease
  outbreaks can harm a large population at a fast
  rate.
• Early awareness and quick treatment can make the
  difference!
• We want to detect an outbreak as early as
  possible
• We focus on daily aggregates of pre-diagnostic
  data that form time series
• Multiple series within a single source or across
  multiple sources

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Desired Preliminaries
Publicly available
Data
Labeled
Where?
Signature
iid...
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Existing Preliminaries

• Insufficient, unlabeled data
• Multiple sources

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Projects

• Project Mimic (http//www.projectmimic.com/)

Lead Thomas Lotze
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Projects

• Algorithm Combination for Improved Performance in
  BioSurveillance Systems

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Projects

• Directionally-Sensitive Multivariate Control
  Charts

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Detecting Outbreaks

• Explainable Patterns
• Seasonality
• Holidays
• Day of Week

Output residuals (assumed to be Normal)
DOW

• Common methods
• Linear Regression (mostly used)
• 7-Day Differencing
• Moving Average
• Holt Winters (exponential smoothing)

Output binary (outbreak/ no outbreak)

• Common methods
• Shewhart
• CuSum
• EWMA

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Algorithm Combination for ImprovedPerformance in
BioSurveillance Systems
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Method Combination

• Idea linear combinations of methods
• The objective is defined as the following cost
  function

Residuals

• Residuals combination Vs. control charts
  combination

Control Chart
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Combining Monitoring Charts
Combine outputs
Residuals
Control Charts
Shewhart
?a1
010100011100000001000
?ai 1
CUSUM
?a2
0, 0.5, 0.8, 0, 0, 0, 0, 0.2, .
010110000000000001000
EWMA
?a3
000001010101010001000
Alert if output gt threshold
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Residuals Combination
Raw data
Residuals
Monitor
Combined Residuals
?a1
R1
?aiRi
? a2
R2
? a3
R3
?ai 1
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Benefits of Algorithm Combination

• Current methods capture different types of
  outbreak, but outbreak signature is unknown
• Multiple testing as a solution ? increases FA
  rate exponentially

? Combine Methods

• Alert threshold depends on data characteristics
  (mean, variance), but those may change over time

? Combine Dynamically
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Illustration
Inject 20 step outbreaks
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Illustration cont
Cost for different thresholds
CUSUM
EWMA
Shewhart
Shewhart ?(Shewhart) 1/2 ?(CUSUM) 1/4
?(EWMA) 1/4
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Illustration cont

• Different threshold
• Different combination rule
• (?i1/3)

Infinite possibilities to combine ? MIP
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Formulate as MIP
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Multivariate Analysis Directionally-Sensitive
Multivariate Control Charts with an Application
to BioSurveillance
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Introduction

• Multiple series
• Different diseases
• Multiple symptoms
• Multiple locations
• Multiple data sources
• Additional info as OTC
• Multiple univariate testing as a solution
• FA increases exponentially
• Miss weak multivariate outbreak signatures

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Introduction

• Improve detection using correlation between
  multiple series
• Main challenge directional sensitivity
  (increase in at least one of the means)

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Existing methods Non-Directional

• Multivariate Shewhart Hotelling
• Alert if
• Multivariate EWMA (Lowry et al 1992)

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Existing methods Directional Sensitive

• Hotelling (implementable)
• Follmann (1996) Correction to bi-directional
  Hotelling
• Testik and Runger (TR, 2006) Quadratic
  programming
• Both assume iid normal, known covariance matrix
• We generalize to Multivariate EWMA (with/ without
  restart)
• Which one performs better in practice??

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Evaluating Performance

• False alert rate
• Impact of cross correlation (magnitude)
• Number of series
• Robustness to assumptions
• Length of training data (unknown covariance
  matrix)
• Autocorrelation
• Multivariate Poisson Distribution
• True alert rate

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Flavor of Results FA
Higher variance
Higher bias
Distribution of FA as a function of training data
length
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Flavor of Results TA

• We inject outbreaks of size o
• to a subset s
• of the p series
• How does the true alert rate changes?

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Flavor of Results TA
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Flavor of Results Authentic Data
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Summary of Results

• All four methods require at least one year of
  data (!!) to estimate covariance matrix (when
  there are more than 5 series)
• TRs method performs slightly better for normally
  distributed data
• Follmanns is more robust to normality assumption
  (autocorrelation, Poisson data)

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Summary and Conclusion Remarks

• Two projects were presented with the goal of
  improving performance in BioSurveillance Systems
• Methods combination to preprocess and detect
  outbreak in univariate data
• Directionally-Sensitive Multivariate Control
  Charts extensive performance analysis
• We aim at defining monitoring guidelines to
  assist CDC and other biosurveillance systems
• When and how to monitor multivariate vs.
  univariate
• When and how to combine monitoring algorithms
• What performance can be expected in different
  cases

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For Aadditional Information

• Inbal Yahav
• iyahav_at_rhsmith.umd.edu
• http//www.rhsmith.umd.edu/faculty/phd/inbal/