Bayesian Biosurveillance
Using Causal Networks
Greg Cooper
RODS Laboratory and the
Laboratory for Causal Modeling and Discovery
Center for Biomedical Informatics
University of Pittsburgh
Outline
• Biosurveillance goals
• Biosurveillance as diagnosis of a population
• Introduction to causal networks
• Examples of using causal networks for
biosurveillance
• Summary and challenges
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
Biosurveillance as Diagnosis
of a Population
The Similarity
of Patient Diagnosis and
Population Diagnosis
Patient risk
factors
Population risk
factors
Patient disease
Patient
Patient
symptom 1 symptom 2
Population disease
Symptoms of
patient 1
Symptoms of
patient 2
Simple Examples of Patient Diagnosis and
Population Diagnosis
smoking
threats of
bioterrorism
lung cancer
weight loss
fatigue
aerosolized release
of anthrax
Patient 1 has
respiratory
symptoms
Patient 2 has
respiratory
symptoms
Population Diagnosis with a More Detailed
Patient Model
threats of
bioterrorism
aerosolized release
of anthrax
patient 1 disease status
respiratory
symptoms
?
?
?
wide
mediastinum
on X-ray
respiratory
symptoms
patient 2 disease status
wide
mediastinum
on X-ray
Population-Level “Symptoms”
threats of
bioterrorism
aerosolized release
of anthrax
local sales of over-thecounter (OTC) cough
medications
patient 1 disease status
respiratory
symptoms
patient 2 disease status
wide
mediastinum
on X-ray
respiratory
symptoms
wide
mediastinum
on X-ray
An Alternative Way of Modeling OTC Sales
threats of
bioterrorism
aerosolized release
of anthrax
patient 1 disease status
respiratory
symptoms
patient 2 disease status
wide
mediastinum
on X-ray
respiratory
symptoms
wide
mediastinum
on X-ray
local sales of over-thecounter (OTC) cough
medications
threats of
bioterrorism
aerosolized release
of anthrax
sales of over-the-counter
(OTC) cough medications
patient 1 disease status
respiratory
symptoms
patient 2 disease status
wide
mediastinum
on X-ray
respiratory
symptoms
wide
mediastinum
on X-ray
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.
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.
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
respiratory
symptoms
patient 2 disease status
wide
mediastinum
on X-ray
respiratory
symptoms
wide
mediastinum
on X-ray
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
patient disease status
respiratory
symptoms
X
D
Y
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
patient disease status
respiratory
symptoms
X
D
Y
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)
A Causal Network Specifies
a Joint Probability Distribution
• The causal Markov condition permits the joint
probability distribution to be factored as follows:
n
P( X 1 , X 2 ,..., X n )   P( X i | direct _ causes _ of _ X i )
i 1
• Example:
P(RS, PDS, ARA) = P(RS | PDS) P(PDS | ARA) P(ARA)
ARA
PDS
RS
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 = )
+
aerosolized release
of anthrax (ARA)
patient 1 (Pt1)
disease status
threats of
bioterrorism (TOB)
sales of over-the-counter
(OTC) cough medications
?
?
?
+
respiratory
wide mediastinum
symptoms (RS) on X-ray (WM)
patient (Pt2)
disease status
+
respiratory
symptoms
wide mediastinum
on X-ray
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
Basic Population Model
Prior Risk of Release of Agent X
Basic Patient Model
A Model with One Patient Case
A Model with One Abstracted Patient Case
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
A Model with One Abstracted Patient Case
An Example in Which a Single Patient Case Is Inadequate
to Detect a Release
Data: A patient who presents with respiratory symptoms today
How Might We Distinguish Anticipated
Diseases (e.g., Influenza) from Unanticipated
Diseases (e.g., Respiratory Anthrax)?
Differences in their expected spatiotemporal patterns over the population may
be very helpful.
A Model with Two Patient Cases
A Model with Three Patient Cases
A Model with Ten Patient Cases
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
Posterior Probability of a Release of X
Among the Population of Ten People Being Modeled
Adding Population-Based Data
Data: Increased OTC sales of cough medications today
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
< 1%
5
area 1
no visit to ED
NA
< 1%
6
area 1
today
respiratory
27%
7
area 2
today
non-respiratory
11%
8
area 1
today
respiratory
27%
9
area 1
no visit to ED
NA
< 1%
10
area 2
no visit to ED
NA
< 1%
Modeling the Frequency Distribution Over
the Number of Infected People
The Frequency Distribution Over
the Number of Infected People in the Example
A More Detailed Patient Model
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
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)
P(dx X | evidence)
U(alarm, no dx X)
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.
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).
Challenges Include ...
One Challenge: Modeling Contagious Diseases
One approach: Include arcs among the diseasestatus nodes of individuals who were in close
proximity of each other during the period of
concern being modeled.
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)
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
Suggested Reading
R.E. Neapolitan, Learning Bayesian Networks
(Prentice Hall, 2003).
A Sample of Causal Network
Commercial Software
Hugin: www.hugin.com
Netica: www.norsys.com
Bayesware: www.bayesware.com