Bayesian Biosurveillance Using Causal Networks

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

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

3. 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

4. Biosurveillance as Diagnosis of a Population

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.

12. Causal network structure: An Example of a Causal Network 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.

13. 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

14. 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

15. 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

16. 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)

17. 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

18. 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 (RS) respiratory symptoms wide mediastinum on X-ray (WM) wide mediastinum on X-ray

19. 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

20. Basic Population Model

21. Prior Risk of Release of Agent X

22. Basic Patient Model

23. A Model with One Patient Case

24. A Model with One Abstracted Patient Case

25. 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

26. A Model with One Abstracted Patient Case

27. An Example in Which a Single Patient Case Is Inadequate to Detect a Release Data: A patient who presents with respiratory symptoms today

28. 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.

29. A Model with Two Patient Cases

30. A Model with Three Patient Cases

31. A Model with Ten Patient Cases

32. 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

33. Posterior Probability of a Release of X Among the Population of Ten People Being Modeled

34. Adding Population-Based Data Data: Increased OTC sales of cough medications today

35. 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%

36. Modeling the Frequency Distribution Over the Number of Infected People

37. The Frequency Distribution Over the Number of Infected People in the Example

38. A More Detailed Patient Model

39. 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

40. 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.

41. 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).

42. Challenges Include ...

43. 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.

44. 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)

45. 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

46. Suggested Reading R.E. Neapolitan, Learning Bayesian Networks (Prentice Hall, 2003).

47. A Sample of Causal Network Commercial Software Hugin: www.hugin.com Netica: www.norsys.com Bayesware: www.bayesware.com