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 disease Patient symptom 1 Patient symptom 2 Patient risk factors Population disease Symptoms of patient 1 Population risk factors Symptoms of patient 2

Simple Examples of Patient Diagnosis and Population Diagnosis lung cancer weight lossfatigue smoking aerosolized release of anthrax Patient 1 has respiratory symptoms threats of bioterrorism Patient 2 has respiratory symptoms

Population Diagnosis with a More Detailed Patient Model aerosolized release of anthrax threats of bioterrorism patient 1 disease status patient 2 disease status respiratory symptoms wide mediastinum on X-ray respiratory symptoms wide mediastinum on X-ray ? ? ?

Population-Level “Symptoms” aerosolized release of anthrax threats of bioterrorism patient 1 disease status patient 2 disease status respiratory symptoms wide mediastinum on X-ray respiratory symptoms wide mediastinum on X-ray local sales of over-the- counter (OTC) cough medications

An Alternative Way of Modeling OTC Sales aerosolized release of anthrax threats of bioterrorism patient 1 disease status patient 2 disease status respiratory symptoms wide mediastinum on X-ray respiratory symptoms wide mediastinum on X-ray local sales of over-the- counter (OTC) cough medications

aerosolized release of anthrax threats of bioterrorism patient 1 disease status patient 2 disease status respiratory symptoms wide mediastinum on X-ray respiratory symptoms wide mediastinum on X-ray sales of over-the-counter (OTC) cough medications

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: Causal network parameters: * aerosolized release of anthrax (ARA) patient disease status (PDS) respiratory symptoms (RS) P(ARA = true) = P(PDS = respiratory anthrax | ARA = true) = P(PDS = respiratory anthrax | ARA = false) = 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 aerosolized release of anthrax threats of bioterrorism patient 1 disease status patient 2 disease status respiratory symptoms wide mediastinum on X-ray respiratory symptoms wide mediastinum on X-ray sells of over-the-counter (OTC) cough medications

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. aerosolized release of anthrax patient disease status respiratory symptoms D X Y Example:

A Key Intuition Behind the Causal Markov Condition An effect is independent of its distant causes, given its immediate causes aerosolized release of anthrax patient disease status respiratory symptoms D X Y Example:

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: Example: P(RS, PDS, ARA) = P(RS | PDS) P(PDS | ARA) P(ARA) ARA PDS RS

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 = ) Causal Network Inference aerosolized release of anthrax (ARA) threats of bioterrorism (TOB) respiratory symptoms wide mediastinum on X-ray respiratory symptoms (RS) wide mediastinum on X-ray (WM) sales of over-the-counter (OTC) cough medications patient 1 (Pt1) disease status patient (Pt2) disease status ? ? ?

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)

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 spatio- temporal 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) PersonHome LocationDay of ED VisitED Symptoms 1area 1yesterdayrespiratory 2area 1yesterdaynon-respiratory 3area 2yesterdaynon-respiratory 4area 2no visit to EDNA 5area 1no visit to EDNA 6area 1todayrespiratory 7area 2todaynon-respiratory 8area 1todayrespiratory 9area 1no visit to EDNA 10area 2no visit to EDNA

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 PersonHome LocationDay of ED VisitED SymptomsRisk for Disease X 1area 1yesterdayrespiratory26% 2area 1yesterdaynon-respiratory9% 3area 2yesterdaynon-respiratory6% 4area 2no visit to EDNA< 1% 5area 1no visit to EDNA< 1% 6area 1todayrespiratory27% 7area 2todaynon-respiratory11% 8area 1todayrespiratory27% 9area 1no visit to EDNA< 1% 10area 2no visit to EDNA< 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 sound an alarm keep silent P(dx X | evidence) P(no dx X | evidence) P(dx X | evidence) P(no dx X | evidence) U(alarm, dx X) U(alarm, no dx X) U(silent, dx X) 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 disease- status 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: Netica: Bayesware: