Bayesian Biosurveillance Using Causal Networks

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Bayesian Biosurveillance Using Causal Networks
Greg Cooper RODS Laboratory and the
Laboratory for Causal
Modeling and Discovery Center for Biomedical
Informatics University of Pittsburgh
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Outline

• Biosurveillance goals
• Biosurveillance as diagnosis of a population
• Introduction to causal networks
• Examples of using causal networks for
  biosurveillance
• Summary and challenges

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Biosurveillance Detection Goals

• Detect an unanticipated biological disease
  outbreak in the population as rapidly and as
  accurately as possible
• Determine the people who already have the disease
• Predict the people who are likely to get the
  disease

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Biosurveillance as Diagnosis of a Population
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The Similarity of Patient Diagnosis and
Population Diagnosis
Patient risk factors
Population risk factors
Patient disease
Population disease
Patient symptom 1
Patient symptom 2
Symptoms of patient 1
Symptoms of patient 2
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Simple Examples of Patient Diagnosis and
Population Diagnosis
smoking
threats of bioterrorism
lung cancer
aerosolized release of anthrax
weight loss
fatigue
Patient 1 has respiratory symptoms
Patient 2 has respiratory symptoms
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Population Diagnosis with a More Detailed Patient
Model
threats of bioterrorism
aerosolized release of anthrax
?
?
?
patient 1 disease status
patient 2 disease status
respiratory symptoms
respiratory symptoms
wide mediastinum on X-ray
wide mediastinum on X-ray
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Population-Level Symptoms
threats of bioterrorism
aerosolized release of anthrax
local sales of over-the-counter (OTC) cough
medications
patient 1 disease status
patient 2 disease status
respiratory symptoms
respiratory symptoms
wide mediastinum on X-ray
wide mediastinum on X-ray
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An Alternative Way of Modeling OTC Sales
threats of bioterrorism
aerosolized release of anthrax
patient 1 disease status
patient 2 disease status
wide mediastinum on X-ray
respiratory symptoms
wide mediastinum on X-ray
respiratory symptoms
local sales of over-the-counter (OTC) cough
medications
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threats of bioterrorism
aerosolized release of anthrax
sales of over-the-counter (OTC) cough medications
patient 1 disease status
patient 2 disease status
respiratory symptoms
respiratory symptoms
wide mediastinum on X-ray
wide mediastinum on X-ray
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An Introduction to Causal Networks

• A causal network has two components
• Structure A diagram in which nodes represent
  variables and arcs between nodes represent causal
  influence
• Parameters A probability distribution for each
  effect given its direct causes

The diagram (graph) is not allowed to contain
directed cycles, which conveys that an effect
cannot cause itself.
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An Example of a Causal Network
Causal network structure
aerosolized release of anthrax (ARA)
patient disease status (PDS)
respiratory symptoms (RS)
Causal network parameters
P(ARA true) 0.000001 P(PDS respiratory
anthrax ARA true) 0.001 P(PDS respiratory
anthrax ARA false) 0.00000001 P(RS
present PDS respiratory anthrax) 0.8 P(RS
present PDS other) 0.1
These parameters are for illustration only.
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A Previous Example of a Causal Network
threats of bioterrorism
aerosolized release of anthrax
sells of over-the-counter (OTC) cough medications
patient 1 disease status
patient 2 disease status
respiratory symptoms
respiratory symptoms
wide mediastinum on X-ray
wide mediastinum on X-ray
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The Causal Markov Condition

• The Causal Markov Condition
• Let D be the direct causes of a variable X in a
  causal network.
• Let Y be a variable that is not causally
  influenced by X (either directly or indirectly).
• Then X and Y are independent given D.

Example
aerosolized release of anthrax
Y
patient disease status
D
respiratory symptoms
X
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A Key Intuition Behind the Causal Markov
Condition

• An effect is independent of its distant causes,
  given its immediate causes

Example
aerosolized release of anthrax
Y
patient disease status
D
respiratory symptoms
X
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Joint Probability Distributions

• For a model with binary variables X and Y, the
  joint probability distribution is
• P(X t, Y t), P(X t, Y f), P(X f, Y
  t), P(X f, Y f)
• We can use the joint probability distribution to
  derive any conditional probability of interest on
  the model variables.
• Example P(X t Y t)

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A Causal Network Specifies a Joint Probability
Distribution

• The causal Markov condition permits the joint
  probability distribution to be factored as
  follows
• Example
• P(RS, PDS, ARA) P(RS PDS) P(PDS ARA)
  P(ARA)

ARA
PDS
RS
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Causal Network Inference

• Inference algorithms exist for deriving a
  conditional probability of interest from the
  joint probability distribution defined by a
  causal network.
• Example P(ARA TOB , Pt1_RS ,
  Pt2_WM , OTC )

threats of bioterrorism (TOB)

aerosolized release of anthrax (ARA)
sales of over-the-counter (OTC) cough medications
?
?
patient 1 (Pt1) disease status
?
patient (Pt2) disease status


respiratory symptoms
respiratory symptoms (RS)
wide mediastinum on X-ray (WM)
wide mediastinum on X-ray
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Examples of Using Bayesian Inference on Causal
Networks for Biosurveillance

• The following models are highly simplified and
  serve as simple examples that suggest a set of
  research issues
• They are intended only to illustrate basic
  principles
• These models were implemented using Hugin
  (version 6.1) www.hugin.com

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Basic Population Model
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Prior Risk of Release of Agent X
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Basic Patient Model
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A Model with One Patient Case
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A Model with One Abstracted Patient Case
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Where do the probabilities come from?

• Databases of prior cases
• Case studies in the literature
• Animal studies
• Computer models (e.g., particle dispersion
  models)
• Expert assessments

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A Model with One Abstracted Patient Case
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An Example in Which a Single Patient Case Is
Inadequate to Detect a Release
Data A patient who presents with respiratory
symptoms today
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How Might We Distinguish Anticipated Diseases
(e.g., Influenza) from Unanticipated Diseases
(e.g., Respiratory Anthrax)?

• Differences in their expected spatio-temporal
  patterns over the population may be very helpful.

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A Model with Two Patient Cases
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A Model with Three Patient Cases
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A Model with Ten Patient Cases
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A Hypothetical Population of Ten People (not all
of whom are patients)
Person Home Location Day of ED Visit ED
Symptoms 1 area 1 yesterday respiratory 2 area
1 yesterday non-respiratory 3 area
2 yesterday non-respiratory 4 area 2 no
visit to ED NA 5 area 1 no visit to
ED NA 6 area 1 today respiratory 7 area
2 today non-respiratory 8 area
1 today respiratory 9 area 1 no visit to
ED NA 10 area 2 no visit to ED NA
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Posterior Probability of a Release of X Among the
Population of Ten People Being Modeled
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Adding Population-Based Data
Data Increased OTC sales of cough medications
today
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For Each Person in the Population a Probability
of Current Infection with Disease X Can be
Estimated
Person Home Location Day of ED Visit ED
Symptoms Risk for Disease X 1 area
1 yesterday respiratory 26 2 area
1 yesterday non-respiratory 9 3 area
2 yesterday non-respiratory 6 4 area 2 no
visit to ED NA lt 1 5 area 1 no visit to
ED NA lt 1 6 area 1 today respiratory 27 7 are
a 2 today non-respiratory 11 8 area
1 today respiratory 27 9 area 1 no visit to
ED NA lt 1 10 area 2 no visit to ED NA lt 1
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Modeling the Frequency Distribution Over
the Number of Infected People
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The Frequency Distribution Over
the Number of Infected People in the
Example
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A More Detailed Patient Model
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Incorporating Heterogeneous Patient Models
Data Same as before, except patient 1 is now
known to have a chest X-ray result that is
consistent with Disease X
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We Can Use the Derived Posterior Probabilities in
a Computer-Based Ongoing Decision Analysis
P(dx X evidence)
U(alarm, dx X)
sound an alarm
P(no dx X evidence)
U(alarm, no dx X)
P(dx X evidence)
U(silent, dx X)
keep silent
P(no dx X evidence)
U(silent, no dx X)
The probabilities in blue can be derived using a
causal network.
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Summary of Bayesian Biosurveillance Using Causal
Networks

• Biosurveillance can be viewed as ongoing
  diagnosis of an entire population.
• Causal networks provide a flexible and expressive
  means of coherently modeling a population at
  different levels of detail.
• Inference on causal networks can derive the type
  posterior probabilities needed for
  biosurveillance.
• These probabilities can be used in a decision
  analytic system that determines whether to raise
  an alarm (and that can recommend which additional
  data to collect).

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Challenges Include ...
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One Challenge Modeling Contagious Diseases

• One approach Include arcs among the
  disease-status nodes of individuals who were in
  close proximity of each other during the period
  of concern being modeled.

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Another Challenge Achieving Tractable Inference
on Very Large Causal Networks

• Possible approaches include
• Aggregating individuals into equivalence classes
  to reduce the size of the causal network
• Use sampling methods to reduce the time of
  inference (at the expense of deriving only
  approximate posterior probabilities)

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Some Additional Challenges

• Constructing realistic outbreak models
• Constructing realistic decision models about when
  to raise an alert
• Developing explanations of alerts
• Evaluating the detection system

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Suggested Reading

• R.E. Neapolitan, Learning Bayesian Networks
  (Prentice Hall, 2003).

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A Sample of Causal Network Commercial Software

• Hugin www.hugin.com
• Netica www.norsys.com
• Bayesware www.bayesware.com