Model

N : The total number of patients in an anthrax outbreak who are seen by clinicians.

DT : The time to detect the anthrax outbreak

Detection : The detection of the anthrax outbreak due to a patient being diagnosed with anthrax.

ti: The time when the ith case with anthrax is seen by a clinician.

wi: The probability that anthrax is diagnosed 4 hours after the

ith anthrax patient is seen by a clinician.

xi: The probability that anthrax is diagnosed 48 hours after the

ith anthrax patient is seen by a clinician.

vj: The probability that the jth patient with anthrax is not

diagnosed as having anthrax.

Si : The cases admitted in the interval (ti, ti + 44].

Modeling Clinician Detection Time of a Disease Outbreak Due to Inhalation AnthraxChristina Adamou, Gregory F. Cooper, Weng-Keen Wong (Oregon State University), John N. Dowling, William R. Hogan

RODS Laboratory, Center of Biomedical InformaticsUniversity of Pittsburgh, Pittsburgh, Pennsylvania

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Introduction

Goal: Develop a probabilistic model of the time for clinicians to detect a disease outbreak due to an outdoor release of anthrax spores in an assumed geographical region.

• Assume that clinicians have access only to traditional clinical information.

• Use the model to estimate an upper bound on the mean detection time of an anthrax outbreak by clinicians.

• How might this be useful?• Planning for anthrax outbreaks• Assessing the usefulness of computer-based outbreak detection algorithms

Main Assumptions:• A patient is only seen by a health care provider (clinician)

once (i.e., no return visits).

• Each clinician diagnoses a given case of inhalational anthrax (IA) independent of his or her prior cases and independent of the activities of other clinicians.

Key Parameters Used in Modeling Clinician Detection Time:Assume that each of the following probabilities is conditioned on a patient having IA.

1. P(IAseverity | Time)

2. P( XrayDone | IAseverity)

3. P( XRayResult| XRayDone, Time, IAseverity)

4. P(CultureDone | XRayResult, IAseverity)

5. P(CultureDone | MW, XRayResult, Time)

6. P(CulturePositive | CultureDone)

7. P(MW | XRayResult, Time)

MW: Widened mediastinum

References1. Meselson M, Guillemin J, Hugh-Jones M, Langmuir A,

Papova I, Shelokov A, Yampolskaya O. The Sverdlovsk anthrax outbreak of 1979. Science 1994;266:1202-1207.

2. Inglesby TV, O’Toole T, Henderson DA, Bartlett JG, Ascher MS, Eitzen E, et al. Anthrax as a biological weapon, 2002: Updated recommendations for management. JAMA 2002;287:2236-2252.

3. Brachman PS. Inhalation anthrax. Ann NY Acad Sci. 1980;353:83-93.

4. Penn CC, Klotz SA. Anthrax pneumonia Sem Resp Med 1997;12:28-30.

5. Jernigan JA, Stephens DS, Ashford DA, Omenaca C, Topiel MS, Galbraith M, et al. Bioterrorism-related inhalation anthrax: The first 10 cases reported in the United States. Emerg Infect Dis. 2001;7:933-944.

6. Hogan WR, Cooper GF, Wallstrom, GL., Wagner MM. The Bayesian aerosol release detector. In Proceedings of the National Syndromic Surveillance Conference [CD-ROM]. Boston, MA: Fleetwood Multimedia, Inc.; 2004.

Acknowledgments:This research was supported by grants from the National Science Foundation (IIS-0325581), the Department of Homeland Security (F30602-01-2-0550), and the Pennsylvania Department of Health (ME-01-737).

Results

The following table shows the results. The derived upper bound on clinician detection time varied from about 9 days for the smallest amount of assumed release to about 3 days for the largest amount.

Sensitivity Analysis:

• We used expert judgment to define confidence intervals for 11 of the key probabilities used in the model.

• We explored the values of those 11 parameters that maximize the average expected time of detection of anthrax by clinicians.

Results:

Conclusions

The model yielded an expected detection time of an outbreak of anthrax due to an airborne release of anthrax spores as being 3 to 9 days, depending on the assumed release amount. A sensitivity analysis resulted in an upper bound on the expected detection time of about 5 to 11 days, again depending on the assumed release amount.

MethodsThe Anthrax Outbreak Simulator [6]

• The simulator assumes the population distribution of Allegheny County, Pennsylvania.

• The incubation period is modeled with lognormal distributions, and varies based on the amount of spores inhaled. Greater airborne concentrations of anthrax lead to a shorter incubation periods

• We used the simulator to generate data sets corresponding to simulated releases of anthrax of the following amounts:

•1.0, 0.5, 0.25, 0.13 and 0.02.

• We created 100 data sets for each simulated release amount. Each data set has a unique release location.

Spatial distribution of anthrax cases over zip code centroids in varying

concentrations

List of anthrax cases(date, time, zip code)

Gaussian plume model of atmospheric dispersion and a model of inhalation

anthrax.

HeightQuantity of sporesLocation Wind

Figure 1: The possible ways that were modeled for a clinician to diagnose inhalational anthrax in a patient.

Admission of patient to the ED (time from infection is t)

Ex. t=3

X-ray performedEx. 0.0122

Other Xray abnormal

Ex. 0.0027Blood culturedEx. 0.10 if xray

normal0.00243 if xray

abnormal

X-ray normalEx. 0.99

X-ray not performedEx. 0.9878

X-ray abnormalEx. 0.01

Widened mediastinumEx. 0.0073

Patient is diagnosed with inhalational anthrax 24-48

hours after admission to the hospital

Ex. 0.0116

Patient is diagnosed with inhalational anthrax 0-4

hours after admission to the hospital

Ex. 8.9E-05

Blood cultured0.010475

1

1

1

1

( 4) ( 48)(1 ) (1 )

E[ | ]1

i

i

i i i i i k jNk S j

Ni

jj

t w t w x w v

DT Detectionv

Assumed amount of anthrax released

0.02 0.13 0.25 0.50 1.0

Estimated upper

bound on the expected detection time in days

9.30 4.09 3.25 3.08 3.05

Assumed amount of anthrax released

0.02 0.13 0.25 0.50 1.0

Estimated upper bound of the expecteddetection time in days

11.08 6.11 5.50 5.26 5.14