Low Probability High Consequence Events

1. Low Probability High Consequence Events Farrokh Alemi Ph.D.Professor of Health Administration and PolicyCollege of Health and Human Services, George Mason University4400 University Drive, Fairfax, Virginia 22030 703 993 1929 falemi@gmu.edu

2. Lecture Outline • What is probability? • Probability Distributions • Assessment of rare probabilities • Fault trees • Similarity judgments • Importance sampling • Time to the event • Calculus of probability • Conditional independence • Causal modeling • Case based learning • Validation of risk models • Examples

3. Estimation of Probability of Rare Events • Objective assessments require long data collection periods • Subjective assessments miss orders of magnitude

4. Estimation of Probability of Rare Events • Objective assessments require long data collection periods • Subjective assessments miss orders of magnitude

5. Alternative Approaches • Fault trees • Similarity judgments • Importance sampling • Time to the event

6. Fault Trees • Identify sentinel event • List all possible pathways to sentinel event • Assess probability of each pathway • Use probability calculus to evaluate the probability of rare event

7. Fault Trees

8. Fault Trees

9. Exercise • Assess the risks for privacy violations with estimates from peer students

10. Similarity Judgments • No precedent • Eiffel Tower & Twin Tower attacks

11. Similarity Judgments • No precedent • Children bombed in school .vs. attack on children in pediatric hospital

12. Similarity Judgments Similarity of index case “I” and comparison case “j”

13. Similarity Judgments Features in both index case “I” and comparison case “j” Features in both index case “I” and comparison case “j”

14. Similarity Judgments Features in the index case “I” but not in the comparison case “j”

15. Similarity Judgments Features not in the index case “I” but in the comparison case “j”

16. Similarity Judgments

17. Similarity Judgment • Features in school but not in the hospital • No proximity defense, easy access • No communication system available between rooms allowing terrorist time to collect large number of people • Well and active children • Features in the hospital but not in the school • Difficulty in gathering the population into one central location • Availability of security officers • Features shared in both • Focused on vulnerable population • An ongoing war leading to occupation of the region

18. Similarity Judgment Probability of attack on hospital = (1/10000) * 0.5 ≈ 5 in 100,000

19. Exercise • Calculate the similarity of two Internet sites you are familiar with using their security features

20. Importance Sampling • Purposefully look for the rare events • Adjust the frequency to reflect the true frequency • M narrowly defined samples

21. Example • Loss of data in narrow sample • 1 in 100 computers have virus • 3 computers with virus have loss of data • Loss of data in the organizationP = (1/100) 0.003 + (99/100) 0

22. Correcting for Over-sampling Rare Events Revised count of cause “i” among sentinel event “s”

23. Correcting for Over-sampling Rare Events Count of cause “i” among over sampled sentinel events Revised count of cause “i” among sentinel event “s” Count of over sampled sentinel event

24. Correcting for Over-sampling Rare Events Count of cause “i” among over sampled sentinel events Revised count of cause “i” among sentinel event “s” Count of over sampled sentinel event

25. Correcting for Over-sampling Rare Events Count of cause “i” among over sampled sentinel events Odds of sentinel event Revised count of cause “i” among sentinel event “s” Count of over sampled sentinel event

26. Example of Over Sampling Wrong Blood Transfusion

27. Example of Over Sampling Wrong Blood Transfusion

28. Example of Over Sampling Wrong Blood Transfusion

29. Example of Over Sampling Wrong Blood Transfusion

30. Example of Over Sampling Wrong Blood Transfusion p(Wrong blood transfusion | Understaffed operating room) = 0.004 p(Wrong blood transfusion | No understaffed operating room) = 0.002

31. Exercise • Review the last 10 times that you were not able to keep up with your diet. List the reasons for it. • Estimate the prevalence of these reasons among the last 10 occasions in which you were able to keep with your diet. • Estimate the odds of keeping with your diet • Calculate the probability of missing your diet for each reason identified.

32. Time to the Event • Assumptions • Event either happens or not • Has a constant probability • In repeated trials, probability does not change Probability of event Time toevent

33. Example of Time to the Event

34. Example of Time to the Event • Probability of terrorist attack? • Record Dates of attacks • Calculate time between attacks • Take average of various time between attacks • Use formula to calculate daily probability of attack

35. Example of Time to the Event

36. Exercise • Estimate the daily probability of school shooting from the following recent cases: • March 21, 2005 Red Lake, Minn. Jeff Weise, 16, killed grandfather and companion, then arrived at school where he killed a teacher, a security guard, 5 students, and finally himself, leaving a total of 10 dead. • Nov. 8, 2005 Jacksboro, Tenn. One 15-year-old shot and killed an assistant principal at Campbell County High School and seriously wounded two other administrators. • Aug. 24, 2006 Essex, Vt. Christopher Williams, 27, looking for his ex-girlfriend at Essex Elementary School, shot two teachers, killing one and wounding another. Before going to the school, he had killed the ex-girlfriend's mother. • Sept. 13, 2006 Montreal, CanadaKimveer Gill, 25, opened fire with a semiautomatic weapon at Dawson College. Anastasia De Sousa, 18, died and more than a dozen students and faculty were wounded before Gill killed himself. • Sept. 26, 2006 Bailey, Colo.Adult male held six students hostage at Platte Canyon High School and then shot and killed Emily Keyes, 16, and himself. • Sept. 29, 2006 Cazenovia, Wis.A 15-year-old student shot and killed Weston School principal John Klang. • Oct. 3, 2006 Nickel Mines, Pa.32-year-old Carl Charles Roberts IV entered the one-room West Nickel Mines Amish School and shot 10 schoolgirls, ranging in age from 6 to 13 years old, and then himself. Five of the girls and Roberts died.

37. Exercise • Assess daily probability of medication errors in first and second 6 months

38. Exercise • Assess the time between non-injury accidents by interviewing a peer student

39. Validation • Calibration is not possible • Not enough objective data • Contrary event • NASA

40. Validation • Check validity of assumptions • Check conditional independence • Check accuracy of non-rare parameters

41. Take Home Lesson It is possible to assess probability of very rare events

42. What Do You Know? • Describe three methods of assessing probability of rare events

43. Minute Evaluations • Please use the course web site to ask a question and rate this lecture