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Min Zhang, PhD

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Min Zhang, PhD. Xiaohui Kong. Garrick L. Wallstrom, PhD. RODS Laboratory ... Hogan WR, Cooper GC, Wallstrom GL, Wagner MM, Depinay J-M. ... – PowerPoint PPT presentation

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Title: Min Zhang, PhD


1
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

2
Background
  • Evaluation of detection algorithms
  • Real data
  • Semi-synthetic
  • Outbreak simulation
  • Direct simulation of effects
  • Disease-specific models

3
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

4
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

5
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

6
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

7
Temporal template f
  • f is defined to be a probability density
    function that is zero outside of an outbreak
    interval 0,T)

8
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)

9
Example 1-parameter settings
  • Outbreak magnitude
  • C300 captured cases
  • Template function
  • a linear increasing function during 0,T) (T3
    days)
  • Generation algorithm
  • Each of the three algorithms

10
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)
11
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

12
Spatial-Temporal Template
  • f is defined to be a bounded function

13
Forms of Spatial-temporal simulation
  • General form
  • Independent form
  • Lagged form

14
Setting fs
  • fs(s) defines the probability that each captured
    case is assigned to tract s

vs - coverage ns - population rs - elevated
disease risk
Hs - captured historical non- outbreak
cases in tract s rs - elevated disease risk
15
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)

16
Example 2 parameter setting
  • Outbreak magnitude C4000 cases
  • Template function
  • rs a linear decreasing function of distance from
    the outbreak center S015213 in Pittsburgh area.
  • The lag function a function of the distance d
    (in km) from S0
  • fT(t) is a lognormal function
  • with the mean 5.6 days.
  • Poisson process generation

fT(t)
t
17
Example 2 Day 0
18
Example 2 Day 1
19
Example 2 Day 2
20
Example 2 Day 3
21
Example 2 Day 4
22
Example 2 Day 5
23
Example 2 Day 6
24
Example 2 Day 7
25
Example 2 Day 8
26
Example 2 Day 9
27
Example 2 Day 10
28
Example 2 Day 11
29
Example 2 Day 12
30
Example 2 Day 13
31
Example 2 Day 14
32
Example 2 Day 15
33
Example 2 Day 16
34
Example 2 Day 17
35
Example 2 Day 18
36
Example 2 Day 19
37
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

38
BARD (Bayesian Aerosol Release Detector)
Weather Data
Release Parameters
BARD Simulator
ED (Emergency Department) visit Data
  • BARD a disease-specific outbreak simulator

39
BARD Simulation
Affected zip codes in Pittsburgh area
40
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

41
Evaluation of the simulator using BARD data
  • The spatial-temporal template f is a bounded
    function of space s and time t
  • Estimate 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

42
Estimation of and
  • We assume that and are smooth
    functions of space
  • Maximum likelihood estimation for each block
    group
  • Computing a spatially-weighted average of the
    maximum likelihood estimates

43
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
    statistic using block groups and days for bins.
  • Use Monte Carlo simulation to compute p-values

44
Results
45
Discussion
0.1kg release
0.5kg release
P-value
P-value
Counts/block
Counts/block
46
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.

47
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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