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Process Driven Template

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									Estimation and Validation of an
     Outbreak Simulator
               Min Zhang, PhD
                Xiaohui Kong
          Garrick L. Wallstrom, PhD
               RODS Laboratory
    Department of Biomedical Informatics
    University of Pittsburgh, Pittsburgh, PA
                  Background
• Evaluation of detection algorithms
  – Real data
  – Semi-synthetic
• Outbreak simulation
  – Direct simulation of effects
  – Disease-specific models
                        Outline
• Template-Driven Spatial-Temporal Outbreak
  Simulator
  Zhang M, Wallstrom GL, Template-Driven spatial-temporal
  outbreak simulation for outbreak detection evaluation, AMIA
  2008 annual symposium, Washington D.C., Nov. 2008.
• BARD (Bayesian Aerosol Release Detector)
  Hogan WR, Cooper GC, Wallstrom GL, Wagner MM, Depinay J-
  M. The Bayesian aerosol release detector. Stat Med 2007.
  26(29): 5225-52.
• Evaluation of the simulator using BARD data
                       Outline
• Template-Driven Spatial-Temporal Outbreak
  Simulator
 Zhang M, Wallstrom GL, Template-Driven spatial-temporal
  outbreak simulation for outbreak detection evaluation, AMIA
  2008 annual symposium, Washington D.C., Nov. 2008.
• BARD (Bayesian Aerosol Release Detector)
  Hogan WR, Cooper GC, Wallstrom GL, Wagner MM, Depinay J-
  M. The Bayesian aerosol release detector. Stat Med 2007.
  26(29): 5225-52.
• Evaluation of the simulator using BARD data
   Template-Driven Spatial-Temporal
         Outbreak Simulator
The template-driven spatial-temporal simulator:
• Is a flexible non-disease-specific simulator
• Uses simple simulation methods and minimal
  parameters
• Simulates either temporal or spatial-temporal
  event time data
   Temporal outbreak simulation
Three components for temporal simulation:
  – Outbreak magnitude: C
    the number of expected number of the captured outbreak
    cases during the outbreak
  – Temporal template: 
    a function that describes how the rate of new cases
    change over time
  – Generation algorithm
    three approaches to generate event times according to the
    user-defined template function
        Temporal template f
f is defined to be a probability density
function that is zero outside of an outbreak
interval [0,T):
         Generation algorithms
• Deterministic generation
  – Create C event times in a regular non-random
    pattern
• Independent generation
  – Draw C random samples according to function 
• Poisson process generation
  – Generate event times according to the
    heterogeneous rate function:
                      (t)=C*(t)
   Example 1-parameter settings
• Outbreak magnitude:
  C=300 captured cases
• Template function:
  – a linear increasing function
    during [0,T) (T=3 days)



• Generation algorithm:
  – Each of the three algorithms
Example 1-simulation
Figure 1. Simulated visit times using a
linear template function. Hourly-
aggregated visit times are created using
deterministic (a), independent (b), and
Poisson process (c) generation.            (a)




                                           (b)




                              Figure 1.

                                           (c)
     Spatial-Temporal Simulation
Three components for spatial-temporal simulation:
  – Outbreak magnitude: C
    the number of expected number of the captured outbreak
    cases during the outbreak
  – Spatial temporal template: 
    a function that describes how the rate of new cases change
    over space and time
  – Generation algorithm
    three approaches to generate event times according to the
    user-defined spatial-temporal template function
     Spatial-Temporal Template
f is defined to be a bounded function :
 Forms of Spatial-temporal simulation


General form

  – Independent form

  – Lagged form
                           Setting fs

• fs(s) defines the probability that each captured
  case is assigned to tract s




     vs - coverage                Hs - captured historical non-
     ns - population                    outbreak cases in tract s
     rs - elevated disease risk   rs - elevated disease risk
             Generation Algorithms
• Deterministic generation
  – Distribute C event times in a regular spatial-temporal pattern
• Independent generation
  – Determine the number of cases in each tract by simulating one
    draw from a multinomial distribution:


    where,
• Poisson process generation
  – Generate event times to each tract independently according to
    a Poisson process with rate function:
                            (t)=C*(s,t)
   Example 2 – parameter setting
• Outbreak magnitude: C=4000 cases
• Template function:
  – rs: a linear decreasing function of
    distance from the outbreak center
    S0=15213 in Pittsburgh area.
  – The lag function: a function of the
    distance d (in km) from S0
                                    f (t)
  – fT(t) is a lognormal function
                                    T




   with the mean 5.6 days.
                                                  QuickTime™ and a
                                                    decompressor
                                            are neede d to see this picture.




• Poisson process generation
                                                                               t
Example 2 – Day 0
Example 2 – Day 1
Example 2 – Day 2
Example 2 – Day 3
Example 2 – Day 4
Example 2 – Day 5
Example 2 – Day 6
Example 2 – Day 7
Example 2 – Day 8
Example 2 – Day 9
Example 2 – Day 10
Example 2 – Day 11
Example 2 – Day 12
Example 2 – Day 13
Example 2 – Day 14
Example 2 – Day 15
Example 2 – Day 16
Example 2 – Day 17
Example 2 – Day 18
Example 2 – Day 19
                        Outline
• Template-Driven Spatial-Temporal Outbreak
  Simulator
  Zhang M, Wallstrom GL, Template-Driven spatial-temporal
  outbreak simulation for outbreak detection evaluation, AMIA
  2008 annual symposium, Washington D.C., Nov. 2008.
• BARD (Bayesian Aerosol Release Detector)
  Hogan WR, Cooper GC, Wallstrom GL, Wagner MM, Depinay J-
  M. The Bayesian aerosol release detector. Stat Med 2007.
  26(29): 5225-52.
• Evaluation of the simulator using BARD data
BARD (Bayesian Aerosol Release Detector)

       Release
                                Weather Data
     Parameters



                BARD Simulator



      ED (Emergency Department) visit
                    Data

       BARD: a disease-specific outbreak simulator
BARD Simulation




Affected zip codes in Pittsburgh area
                        Outline
• Template-Driven Spatial-Temporal Outbreak
  Simulator
  Zhang M, Wallstrom GL, Template-Driven spatial-temporal
  outbreak simulation for outbreak detection evaluation, AMIA
  2008 annual symposium, Washington D.C., Nov. 2008.
• BARD (Bayesian Aerosol Release Detector)
  Hogan WR, Cooper GC, Wallstrom GL, Wagner MM, Depinay J-
  M. The Bayesian aerosol release detector. Stat Med 2007.
  26(29): 5225-52.
• Evaluation of the simulator using BARD data
  Evaluation of the simulator using BARD data

 The spatial-temporal template f is a bounded
 function of space s and time t:

• Estimate f S: by the proportion of all cases that reside
  in block group s.
• We model the visit times in each block group by a
  single lognormal distribution with location-
  dependent parameters:
             T | S  s ~ lognormal( (s),  (s))
        Estimation of         ( s)and  (s)

We assume that  (and
                    s)        are smooth
                               ( s)
functions of space:
– Maximum likelihood estimation for each block
  group



– Computing a spatially-weighted average of the
  maximum likelihood estimates
             Compute P-Values
• Data from 100 BARD simulations in Pittsburgh
  region:
  – Group 1: 0.1kg release (50 data sets)
  – Group 2: 0.5kg release (50 data sets)
• Compute a Pearson goodness-of-fit test
                           2



  statistic using block groups and days for bins.
• Use Monte Carlo simulation to compute p-values
                  Results

                  P-value   P-value   Total
                  <0.05     >=0.05    dataset
    Group 1          21        29        50
(0.1kg release)
    Group 2          14        36        50
(0.5kg release)
                      Discussion

          0.1kg release                   0.5kg release




                                P-value
P-value




                 Counts/block                      Counts/block
                        Summary
• We previously introduced a non-disease specific simulator for
  creating outbreak data.
• We conducted a limited validation experiment using
  simulated releases from BARD.
• The validation experiment yielded mixed results. The
  simulator is sufficiently flexible to describe some (but not all)
  simulated releases from BARD.
• Further model validation should include estimation from real
  outbreak data.
• Despite these results, the simulator is a useful tool for semi-
  synthetic evaluation of detection algorithms.
            Acknowledgments
• This research was supported by a grant from
  the Centers for Disease Control and
  Prevention (R01PH000025). This work is
  solely the responsibility of its authors and do
  not necessarily represent the views of the
  CDC.
• We thank Dr. William Hogan for providing the
  BARD data, and Dr. Aurel Cami for technical
  assistance.

								
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