Modeling Clinician Detection Time of a Disease Outbreak Due to Inhalation Anthrax

1
Modeling Clinician Detection Time of a Disease
Outbreak Due to Inhalation Anthrax

• Christina Adamou, Gregory F. Cooper, Weng-Keen
  Wong (Oregon State University), John N. Dowling,
  William R. Hogan
• RODS Laboratory, Center of Biomedical Informatics
• University of Pittsburgh, Pittsburgh, Pennsylvania

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.

• 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

• 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.

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

Assumed amount of anthrax released 0.02 0.13 0.25 0.50 1.0
Estimated upper bound of the expected detection time in days 11.08 6.11 5.50 5.26 5.14
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• Methods
• The 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

• 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.
• P(IAseverity Time)
• P( XrayDone IAseverity)
• P( XRayResult XRayDone, Time, IAseverity)
• P(CultureDone XRayResult, IAseverity)
• P(CultureDone MW, XRayResult, Time)
• P(CulturePositive CultureDone)
• P(MW XRayResult, Time)
• MW Widened mediastinum

• References
• Meselson M, Guillemin J, Hugh-Jones M, Langmuir
  A, Papova I, Shelokov A, Yampolskaya O. The
  Sverdlovsk anthrax outbreak of 1979. Science
  19942661202-1207.
• Inglesby TV, OToole T, Henderson DA, Bartlett
  JG, Ascher MS, Eitzen E, et al. Anthrax as a
  biological weapon, 2002 Updated recommendations
  for management. JAMA 20022872236-2252.
• Brachman PS. Inhalation anthrax. Ann NY Acad Sci.
  198035383-93.
• Penn CC, Klotz SA. Anthrax pneumonia Sem Resp Med
  19971228-30.
• Jernigan JA, Stephens DS, Ashford DA, Omenaca C,
  Topiel MS, Galbraith M, et al. Bioterrorism-relate
  d inhalation anthrax The first 10 cases reported
  in the United States. Emerg Infect Dis.
  20017933-944.
• 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.

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