What’s Strange About Recent Events (WSARE)

1. What’s Strange About Recent Events (WSARE) Weng-Keen Wong (University of Pittsburgh) Andrew Moore (Carnegie Mellon University) Gregory Cooper (University of Pittsburgh) Michael Wagner (University of Pittsburgh) This work funded by DARPA, the State of Pennsylvania, and NSF

2. Motivation Suppose we have real-time access to Emergency Department data from hospitals around a city (with patient confidentiality preserved)

3. The Problem From this data, can we detect if a disease outbreak is happening?

4. The Problem From this data, can we detect if a disease outbreak is happening? We’re talking about a non-specific disease detection

5. The Problem From this data, can we detect if a disease outbreak is happening? How early can we detect it?

6. The Problem From this data, can we detect if a disease outbreak is happening? How early can we detect it? The question we’re really asking: What’s strange about recent events?

7. Traditional Approaches What about using traditional anomaly detection? • Typically assume data is generated by a model • Finds individual data points that have low probability with respect to this model • These outliers have rare attributes or combinations of attributes • Need to identify anomalous patterns not isolated data points

8. Traditional Approaches What about monitoring aggregate daily counts of certain attributes? • We’ve now turned multivariate data into univariate data • Lots of algorithms have been developed for monitoring univariate data: • Time series algorithms • Regression techniques • Statistical Quality Control methods • Need to know apriori which attributes to form daily aggregates for!

9. Traditional Approaches What if we don’t know what attributes to monitor? What if we want to exploit the spatial, temporal and/or demographic characteristics of the epidemic to detect the outbreak as early as possible?

10. Traditional Approaches Diarrhea cases among children Number of cases involving people working in southern part of the city We need to build a univariate detector to monitor each interesting combination of attributes: Respiratory syndrome cases among females Number of cases involving teenage girls living in the western part of the city Viral syndrome cases involving senior citizens from eastern part of city Botulinic syndrome cases Number of children from downtown hospital And so on…

11. Traditional Approaches Diarrhea cases among children Number of cases involving people working in southern part of the city We need to build a univariate detector to monitor each interesting combination of attributes: Respiratory syndrome cases among females Number of cases involving teenage girls living in the western part of the city You’ll need hundreds of univariate detectors! We would like to identify the groups with the strangest behavior in recent events. Viral syndrome cases involving senior citizens from eastern part of city Botulinic syndrome cases Number of children from downtown hospital And so on…

12. One Possible Approach Today’s Records Yesterday’s Records Last Year’s Records

13. One Possible Approach Today’s Records Yesterday’s Records Last Year’s Records Idea: Can use association rules to find patterns in today’s records that weren’t there in past data

14. One Possible Approach Recent records ( from today ) Baseline records ( from 7 days ago ) Find which rules predict unusually high proportions in recent records when compared to the baseline eg. 52/200 records from “recent” have Gender = Male AND Age = Senior 90/180 records from “baseline” have Gender = Male AND Age = Senior

15. Which rules do we report? • Search over all rules up to a maximum number of components • For each rule, form a 2x2 contingency table eg. • Perform Fisher’s Exact Test to get a p-value for each rule (call this the score) • Report the rule with the lowest score

16. Problems with the Approach • Multiple Hypothesis Testing 2. A Changing Baseline

17. Problem #1: Multiple Hypothesis Testing • Can’t interpret the rule scores as p-values • Suppose we reject null hypothesis when score < , where  = 0.05 • For a single hypothesis test, the probability of making a false discovery =  • Suppose we do 1000 tests, one for each possible rule • Probability(false discovery) could be as bad as: 1 – ( 1 – 0.05)1000 >> 0.05

18. Randomization Test • Take the recent cases and the baseline cases. Shuffle the date field to produce a randomized dataset called DBRand • Find the rule with the best score on DBRand.

19. Randomization Test Repeat the procedure on the previous slide for 1000 iterations. Determine how many scores from the 1000 iterations are better than the original score. If the original score were here, it would place in the top 1% of the 1000 scores from the randomization test. We would be impressed and an alert should be raised. Corrected p-value of the rule is: # better scores / # iterations

20. Reporting Multiple Rules on each Day • But reporting only the best scoring rule can hide other more interesting anomalous patterns! • For example: • The best scoring rule is statistically significant but not a public health concern • The top 5 scoring rules indicate anomalous patterns in 5 neighboring zip codes but individually their p-values do not cause an alarm to be raised

21. Our Solution: FDR False Discovery Rate [Benjamini and Hochberg] • Can determine which of these p-values are significant • Specifically, given an αFDR, FDR guarantees that • Given an αFDR, FDR produces a threshold below which any p-values in the history are considered significant

22. Our Solution: FDR Once we have the set of all possible rules and their scores, use FDR to determine which ones are significant

23. Problem #2: A Changing Baseline From: Goldenberg, A., Shmueli, G., Caruana, R. A., and Fienberg, S. E. (2002). Early statistical detection of anthrax outbreaks by tracking over-the-counter medication sales. Proceedings of the National Academy of Sciences (pp. 5237-5249)

24. Problem #2: A Changing Baseline • Baseline is affected by temporal trends in health care data: • Seasonal effects in temperature and weather • Day of Week effects • Holidays • Etc. • Choosing the wrong baseline distribution can affect the detection time and false positives rate

25. Generating the Baseline… • “Taking into account that today is a public holiday…” • “Taking into account that this is Spring…” • “Taking into account recent heatwave…” • “Taking into account recent flu levels…” • “Taking into account that there’s a known natural Food-borne outbreak in progress…”

26. Generating the Baseline… • “Taking into account that today is a public holiday…” • “Taking into account that this is Spring…” • “Taking into account recent heatwave…” • “Taking into account recent flu levels…” • “Taking into account that there’s a known natural Food-borne outbreak in progress…” Use a Bayes net to model the joint probability distribution of the attributes

27. Obtaining Baseline Data All Historical Data • Learn Bayesian Network using Optimal Reinsertion [Moore and Wong 2003] Today’s Environment Baseline 2. Generate baseline given today’s environment

28. Environmental Attributes Divide the data into two types of attributes: • Environmental attributes: attributes that cause trends in the data eg. day of week, season, weather, flu levels • Response attributes: all other non-environmental attributes

29. Environmental Attributes When learning the Bayesian network structure, do not allow environmental attributes to have parents. Why? • We are not interested in predicting their distributions • Instead, we use them to predict the distributions of the response attributes Side Benefit: We can speed up the structure search by avoiding DAGs that assign parents to the environmental attributes Season Day of Week Weather Flu Level

30. Generate Baseline Given Today’s Environment Suppose we know the following for today: Day of Week = Monday Flu Level = High Season = Winter Weather = Snow We fill in these values for the environmental attributes in the learned Bayesian network We sample 10000 records from the Bayesian network and make this data set the baseline Baseline

31. Generate Baseline Given Today’s Environment Suppose we know the following for today: Day of Week = Monday Flu Level = High Season = Winter Weather = Snow We fill in these values for the environmental attributes in the learned Bayesian network Sampling is easy because environmental attributes are at the top of the Bayes Net We sample 10000 records from the Bayesian network and make this data set the baseline Baseline

32. Generate Baseline Given Today’s Environment Suppose we know the following for today: Day of Week = Monday Flu Level = High Season = Winter Weather = Snow We fill in these values for the environmental attributes in the learned Bayesian network An alternate possible technique is to use inference We sample 10000 records from the Bayesian network and make this data set the baseline Baseline

33. What’s Strange About Recent Events (WSARE) 3.0 • Obtain Recent and Baseline datasets 2. Search for rule with best score All Data Recent Data • Determine p-value of best scoring rule Baseline 4. If p-value is less than threshold, signal alert

34. Simulator

35. Simulation • 100 different data sets • Each data set consisted of a two year period • Anthrax release occurred at a random point during the second year • Algorithms allowed to train on data from the current day back to the first day in the simulation • Any alerts before actual anthrax release are considered a false positive • Detection time calculated as first alert after anthrax release. If no alerts raised, cap detection time at 14 days

36. Other Algorithms used in Simulation • Control Chart:Mean + multiplier * standard deviation • Moving Average:7 day window • ANOVA Regression:Linear regression with extra covariates for season, day of week, count from yesterday • WSARE 2.0:Create baseline using raw historical data • WSARE 2.5: Use raw historical data that matches environmental attributes

37. Results on Simulation

38. Results on Actual ED Data from 2001 1. Sat 2001-02-13: SCORE = -0.00000004 PVALUE = 0.00000000 14.80% ( 74/500) of today's cases have Viral Syndrome = True and Encephalitic Prodome = False 7.42% (742/10000) of baseline have Viral Syndrome = True and Encephalitic Syndrome = False 2. Sat 2001-03-13: SCORE = -0.00000464 PVALUE = 0.00000000 12.42% ( 58/467) of today's cases have Respiratory Syndrome = True 6.53% (653/10000) of baseline have Respiratory Syndrome = True 3. Wed 2001-06-30: SCORE = -0.00000013 PVALUE = 0.00000000 1.44% ( 9/625) of today's cases have 100 <= Age < 110 0.08% ( 8/10000) of baseline have 100 <= Age < 110 4. Sun 2001-08-08: SCORE = -0.00000007 PVALUE = 0.00000000 83.80% (481/574) of today's cases have Unknown Syndrome = False 74.29% (7430/10001) of baseline have Unknown Syndrome = False 5. Thu 2001-12-02: SCORE = -0.00000087 PVALUE = 0.00000000 14.71% ( 70/476) of today's cases have Viral Syndrome = True and Encephalitic Syndrome = False 7.89% (789/9999) of baseline have Viral Syndrome = True and Encephalitic Syndrome = False 6. Thu 2001-12-09: SCORE = -0.00000000 PVALUE = 0.00000000 8.58% ( 38/443) of today's cases have Hospital ID = 1 and Viral Syndrome = True 2.40% (240/10000) of baseline have Hospital ID = 1 and Viral Syndrome = True

39. Limitations of WSARE • Works on categorical data • Works on lower dimensional, dense data • Cannot monitor aggregate counts – relies on changes in ratios • Assumes that given the environmental variables, the baseline ratios are fairly stationary over time

40. Related Work • Contrast sets [Bay and Pazzani] • Association Rules and Data Mining in Hospital Infection Control and Public Health Surveillance [Brossette et. al.] • Spatial Scan Statistic [Kulldorff] • WRSARE: What’s Really Strange About Recent Events [Singh and Moore] P( Age = Senior, Gender = Male | Season = Winter, Day of Week = Monday) =

41. Bayesian Biosurveillance of Disease Outbreaks To appear in UAI04 [Cooper, Dash, Levander, Wong, Hogan, Wagner]

42. Conclusion • One approach to biosurveillance: one algorithm monitoring millions of signals derived from multivariate data instead of Hundreds of univariate detectors • WSARE is best used as a general purpose safety net in combination with other detectors • Careful evaluation of statistical significance • Modeling historical data with Bayesian Networks to allow conditioning on unique features of today Software: http://www.autonlab.org/