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

Motivation

Primary Key

Date Time Hospital ICD9 Prodrome Gender Age Home Location

Work Location

Many more…

100 6/1/03 9:12 1 781 Fever M 20s NE ? …

101 6/1/03 10:45 1 787 Diarrhea F 40s NE NE …

102 6/1/03 11:03 1 786 Respiratory F 60s NE N …

103 6/1/03 11:07 2 787 Diarrhea M 60s E ? …

104 6/1/03 12:15 1 717 Respiratory M 60s E NE …

105 6/1/03 13:01 3 780 Viral F 50s ? NW …

106 6/1/03 13:05 3 487 Respiratory F 40s SW SW …

107 6/1/03 13:57 2 786 Unmapped M 50s SE SW …

108 6/1/03 14:22 1 780 Viral M 40s ? ? …

: : : : : : : : : : :

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

The ProblemFrom this data, can we detect if a disease outbreak is happening?

The ProblemFrom this data, can we detect if a disease outbreak is happening?

We’re talking about a non-specific disease detection

The ProblemFrom this data, can we detect if a disease outbreak is happening? How early can we detect it?

The ProblemFrom 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?

Traditional ApproachesWhat 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

Traditional Approaches

– Time series algorithms– Regression techniques– Statistical Quality Control methods

• Need to know apriori which attributes to form daily aggregates for!

Number of ED Visits per Day

0

10

20

30

40

50

1 10 19 28 37 46 55 64 73 82 91 100

Day Number

Num

ber o

f ED

Vis

its

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:

Traditional ApproachesWhat 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?

Traditional ApproachesWe need to build a univariate detector to monitor each interesting

combination of attributes:

Diarrhea cases among children

Respiratory syndrome cases among females

Viral syndrome cases involving senior citizens from eastern part of city

Number of children from downtown hospital

Number of cases involving people working in southern

part of the city

Number of cases involving teenage girls living in thewestern part of the city

Botulinic syndrome cases

And so on…

Traditional ApproachesWe need to build a univariate detector to monitor each interesting

combination of attributes:

Diarrhea cases among children

Respiratory syndrome cases among females

Viral syndrome cases involving senior citizens from eastern part of city

Number of children from downtown hospital

Number of cases involving people working in southern

part of the city

Number of cases involving teenage girls living in thewestern part of the city

Botulinic syndrome cases

And so on…

You’ll need hundreds of univariate detectors!We would like to identify the groups with the strangest

behavior in recent events.

One Possible ApproachPrimary

KeyDate Time Gender Age Hospital Many

more…

100 8/24/03 9:12 M 20s 1 …

101 8/24/03 10:45 F 40s 1 …

: : : : : : :

2243 8/17/03 11:07 M 60s 2 …

2244 8/17/03 12:15 M 60s 1 …

: : : : : : :

12567 8/24/02 13:05 F 40s 3 …

12568 8/24/02 13:57 M 50s 2 …

: : : : : : :

Today’s Records

Yesterday’s Records

Last Year’s Records

One Possible ApproachPrimary

KeyDate Time Gender Age Hospital Many

more…

100 8/24/03 9:12 M 20s 1 …

101 8/24/03 10:45 F 40s 1 …

: : : : : : :

2243 8/17/03 11:07 M 60s 2 …

2244 8/17/03 12:15 M 60s 1 …

: : : : : : :

12567 8/24/02 13:05 F 40s 3 …

12568 8/24/02 13:57 M 50s 2 …

: : : : : : :

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

One Possible ApproachPrimary

KeyDate Time Gender Age …

100 8/24/03 9:12 M Child …

101 8/24/03 10:45 M Senior …

: : : : : :

Primary Key

Date Time Gender Age …

2164 8/17/03 13:05 F Senior …

2165 8/17/03 13:57 F Senior …

: : : : : :

Recent records ( from today )

Baseline records ( from 7 days ago )

Primary Key

Date Time … Source

100 8/24/03 9:12 … Recent

101 8/24/03 10:45 … Recent

: : : : :

2164 8/17/03 13:05 … Baseline

2165 8/17/03 13:57 … Baseline

: : : : :

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

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

CountRecent CountBaseline

Home Location = NW 48 45

Home Location NW

86 220

Problems with the Approach

1. Multiple Hypothesis Testing

2. A Changing Baseline

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

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.

Aug 16, 2003 C2

Aug 17, 2003 C3

Aug 17, 2003 C4

Aug 17, 2003 C5

Aug 17, 2003 C6

Aug 17, 2003 C7

Aug 21, 2003 C8

Aug 21, 2003 C9

Aug 22, 2003 C10

Aug 22, 2003 C11

Aug 23, 2003 C12

Aug 23, 2003 C13

Aug 24, 2003 C14

Aug 24, 2003 C15

Aug 16, 2003 C2

Aug 17, 2003 C3

Aug 24, 2003 C4

Aug 17, 2003 C5

Aug 24, 2003 C6

Aug 17, 2003 C7

Aug 21, 2003 C8

Aug 21, 2003 C9

Aug 22, 2003 C10

Aug 22, 2003 C11

Aug 23, 2003 C12

Aug 23, 2003 C13

Aug 17, 2003 C14

Aug 17, 2003 C15

Randomization TestRepeat 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

Reporting Multiple Rules on each Day

But reporting only the best scoring rule can hide other more interesting anomalous patterns!

For example:

1. The best scoring rule is statistically significant but not a public health concern

2. 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

Our Solution: FDRFalse 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

FDRrejected washyp nullin which tests#

positives false#

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

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)

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

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…”

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

Obtaining Baseline Data

Baseline

All HistoricalData

Today’s Environment

1. Learn Bayesian Network using Optimal Reinsertion [Moore and Wong 2003]

2. Generate baseline given today’s environment

Environmental AttributesDivide 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

Environmental AttributesWhen 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

attributesSide 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

Generate Baseline Given Today’s Environment

Season Day of Week Weather Flu Level

Today Winter Monday Snow High

Season = Winter

Day of Week = Monday

Weather = Snow

Flu Level = High

Suppose we know the following for today:

We fill in these values for the environmental attributes in the learned Bayesian network

Baseline

We sample 10000 records from the Bayesian network and make this data set the baseline

Generate Baseline Given Today’s Environment

Season Day of Week Weather Flu Level

Today Winter Monday Snow High

Season = Winter

Day of Week = Monday

Flu Level = High

Suppose we know the following for today:

We fill in these values for the environmental attributes in the learned Bayesian network

Baseline

We sample 10000 records from the Bayesian network and make this data set the baseline

Sampling is easy because

environmental attributes are at the

top of the Bayes Net

Weather = Snow

Generate Baseline Given Today’s Environment

Season Day of Week Weather Flu Level

Today Winter Monday Snow High

Season = Winter

Day of Week = Monday

Flu Level = High

Suppose we know the following for today:

We fill in these values for the environmental attributes in the learned Bayesian network

Baseline

We sample 10000 records from the Bayesian network and make this data set the baseline

An alternate possible technique is to use inference

Weather = Snow

What’s Strange About Recent Events (WSARE) 3.0

2. Search for rule with best score

3. Determine p-value of best scoring ruleAll

Data

4. If p-value is less than threshold, signal alert

RecentData

Baseline

1. Obtain Recent and Baseline datasets

Simulator

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

Other Algorithms used in Simulation

1. Control Chart: Mean + multiplier * standard deviation

2. Moving Average: 7 day window

3. ANOVA Regression: Linear regression with extra covariates for season, day of week, count from yesterday

4. WSARE 2.0: Create baseline using raw historical data

5. WSARE 2.5: Use raw historical data that matches environmental attributes

Results on Simulation

Results on Actual ED Data from 20011. 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

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

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) =

Bayesian Biosurveillance of Disease Outbreaks

To appear in UAI04 [Cooper, Dash, Levander, Wong,

Hogan, Wagner]

Conclusion• One approach to biosurveillance: one algorithm

monitoring millions of signals derived from multivariate data

instead ofHundreds 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/