Whats Strange About Recent Events (WSARE) Weng-Keen Wong (Carnegie Mellon University) Andrew Moore...

What’s Strange About Recent Events (WSARE)

Weng-Keen Wong (Carnegie Mellon University)

Andrew Moore (Carnegie Mellon University)

Gregory Cooper (University of Pittsburgh)

Michael Wagner (University of Pittsburgh)

DIMACS Tutorial on Statistical and Other Analytic Health Surveillance Methods

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 access to Emergency Department data from hospitals around a city (with patient confidentiality preserved)

The Problem

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

The Problem

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

We’re talking about a non-specific disease detection

The Problem

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

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: In the last n hours, has anything strange happened?

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

Nu

mb

er o

f E

D V

isit

s

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:


What if we don’t know what attributes to monitor?


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?

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.

Our Approach• We use Rule-Based Anomaly Pattern Detection• Association rules used to characterize anomalous

patterns. For example, a two-component rule would be:

Gender = Male AND 40 Age < 50• Related work:

– Market basket analysis [Agrawal et. al, Brin et. al.]

– Contrast sets [Bay and Pazzani]

– Spatial Scan Statistic [Kulldorff]

– Association Rules and Data Mining in Hospital Infection Control and Public Health Surveillance [Brossette et. al.]

WSARE v2.0

“Last 24 hours”“Ignore key”

Primary Key


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 …


: : : : : : : : : : :

• Inputs: 1. Multivariate date/time-indexed biosurveillance-relevant data stream

2. Time Window Length

3. Which attributes to use?

“Emergency Department Data”

WSARE v2.0

• Outputs: 1. Here are the records that most surprise me

2. Here’s why3. And here’s how seriously you should take it

Primary Key


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 …


: : : : : : : : : : :

• Inputs: 1. Multivariate date/time-indexed biosurveillance-relevant data stream

2. Time Window Length

3. Which attributes to use?

WSARE v2.0 Overview

2. Search for rule with best score

3. Determine p-value of best scoring rule through randomization test

All Data

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

RecentData

Baseline

1. Obtain Recent and Baseline datasets

Step 1: Obtain Recent and Baseline Data

RecentData

Baseline

Data from last 24 hours

Baseline data is assumed to capture non-outbreak behavior. We use data from 35, 42, 49 and 56 days prior to the current day

Step 2. Search for Best Scoring RuleFor each rule, form a 2x2 contingency table eg.

• Perform Fisher’s Exact Test to get a p-value for each rule => call this p-value the “score”

• Take the rule with the lowest score. Call this rule RBEST.

• This score is not the true p-value of RBEST because we are performing multiple hypothesis tests on each day to find the rule with the best score

CountRecent CountBaseline

Age Decile = 3 48 45

Age Decile 3 86 220

The Multiple Hypothesis Testing Problem

• 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

Step 3: 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.

June 4, 2002 C2

June 5, 2002 C3

June 12, 2002 C4

June 19, 2002 C5

June 26, 2002 C6

June 26, 2002 C7

July 2, 2002 C8

July 3, 2002 C9

July 10, 2002 C10

July 17, 2002 C11

July 24, 2002 C12

July 30, 2002 C13

July 31, 2002 C14

July 31, 2002 C15

June 4, 2002 C2

June 12, 2002 C3

July 31, 2002 C4

June 26, 2002 C5

July 31, 2002 C6

June 5, 2002 C7

July 2, 2002 C8

July 3, 2002 C9

July 10, 2002 C10

July 17, 2002 C11

July 24, 2002 C12

July 30, 2002 C13

June 19, 2002 C14

June 26, 2002 C15

Step 3: 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.

Estimated p-value of the rule is:

# better scores / # iterations

Two Kinds of AnalysisDay by Day• If we want to run WSARE

just for the current day…

…then we end here.

Historical Analysis• If we want to review all

previous days and their p-values for several years and control for some percentage of false positives……then we’ll once again run into overfitting problems…we need to compensate for multiple hypothesis testing because we perform a hypothesis test on each day in the history

We only need to do this for historical analysis!

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

FDRrejected washyp nullin which tests#

positives false#

WSARE v3.0

WSARE v2.0 Review



All Data


RecentData

Baseline


Obtaining the Baseline

Recall that the baseline was assumed to be captured by data that was from 35, 42, 49, and 56 days prior to the current day.

Baseline

Obtaining the Baseline

Recall that the baseline was assumed to be captured by data that was from 35, 42, 49, and 56 days prior to the current day.

Baseline

We would like to determine the baseline automatically!

What if this assumption isn’t true? What if data from 7, 14, 21 and 28

days prior is better?

Temporal Trends• But health care data has many different

trends due to – Seasonal effects in temperature and weather– Day of Week effects– Holidays– Etc.

• Allowing the baseline to be affected by these trends may dramatically alter the detection time and false positives of the detection algorithm

Temporal Trends

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)

WSARE v3.0 Generate the baseline…• “Taking into account recent flu levels…”• “Taking into account that today is a public holiday…”• “Taking into account that this is Spring…”• “Taking into account recent heatwave…”• “Taking into account that there’s a known natural Food-

borne outbreak in progress…”

Bonus: More efficient use of historical data

Conditioning on observed environment: Well understood for Univariate Time Series

Time

Sig

nal

Example Signals:• Number of ED visits today• Number of ED visits this hour• Number of Respiratory Cases Today• School absenteeism today• Nyquil Sales today

An easy case

Time

Sig

nal

Dealt with by Statistical Quality Control

Record the mean and standard deviation up the the current time.

Signal an alarm if we go outside 3 sigmas

Mean

Upper Safe Range

Conditioning on Seasonal Effects

Time

Sig

nal

Time

Sig

nal

Fit a periodic function (e.g. sine wave) to previous data. Predict today’s signal and 3-sigma confidence intervals. Signal an alarm if we’re off.

Reduces False alarms from Natural outbreaks.

Different times of year deserve different thresholds.

Conditioning on Seasonal Effects

Weekly counts of P&I from week 1/98 to 48/00

Example [Tsui et. Al]

From: “Value of ICD‑9–Coded Chief Complaints for Detection of Epidemics”, Fu-Chiang Tsui, Michael M. Wagner, Virginia Dato, Chung-Chou Ho Chang, AMIA 2000

Seasonal Effects with Long-Term Trend

Weekly counts of IS from week 1/98 to 48/00.


Fit a periodic function (e.g. sine wave) plus a linear trend:

E[Signal] = a + bt + c sin(d + t/365)

Good if there’s a long term trend in the disease or the population.

Weekly counts of IS from week 1/98 to 48/00.


Called the Serfling Method [Serfling, 1963]

Seasonal Effects with Long-Term Trend

Day-of-week effects


Day-of-week effects


Fit a day-of-week component

E[Signal] = a + deltaday

E.G: deltamon= +5.42, deltatue= +2.20, deltawed= +3.33, deltathu= +3.10, deltafri= +4.02, deltasat= -12.2, deltasun= -23.42

Another simple form of ANOVA

Analysis of variance (ANOVA)

• Good news:If you’re tracking a daily aggregate (univariate

data)…then ANOVA can take care of many of these effects.

• But…What if you’re tracking a whole joint distribution

of events?

Idea: Bayesian Networks

“On Cold Tuesday Mornings the folks coming in from the North

part of the city are more likely to have respiratory problems”

“Patients from West Park Hospital are less likely to be young”

“On the day after a major holiday, expect a boost in the morning followed by a lull in

the afternoon”

Bayesian Network: A graphical model representing the joint probability distribution of a set of random variables

“The Viral prodrome is more likely to co-occur with a Rash

prodrome than Botulinic”

WSARE Overview



All Data


RecentData

Baseline


Obtaining Baseline Data

Baseline

All HistoricalData

Today’s Environment

1. Learn Bayesian Network

2. Generate baseline given today’s environment

Obtaining Baseline Data

Baseline

All HistoricalData

Today’s Environment

1. Learn Bayesian Network

2. Generate baseline given today’s environment

What should be happening today given today’s environment

Step 1: Learning the Bayes Net StructureInvolves searching over DAGs for the structure that maximizes a scoring function. Most common algorithm is hillclimbing.

Initial Structure

Add an arc Delete an arc Reverse an arc

3 possible operations:

Step 1: Learning the Bayes Net StructureInvolves searching over DAGs for the structure that maximizes a scoring function. Most common algorithm is hillclimbing.

Initial Structure

Add an arc Delete an arc Reverse an arc

3 possible operations:

But hillclimbing is too slow and single link modifications may not find the correct structure (Xiang, Wong and Cercone 1997). We use Optimal Reinsertion (Moore and Wong 2002).

T

1. Select target node in current graph

T

2. Remove all arcs connected to T

Optimal Reinsertion

Optimal Reinsertion

T

3. Efficiently find new in/out arcs

T

4. Choose best new way to connect T

??

?? ?

?

?

?

The Outer Loop

Until no change in current DAG:

• Generate random ordering of nodes

• For each node in the ordering, do Optimal Reinsertion

The Outer Loop

For NumJolts:

• Begin with randomly corrupted version of best DAG so far




For NumJolts:

• Begin with randomly corrupted version of best DAG so far

The Outer Loop




Conventional hill-climbing without maxParams restriction

How is Optimal Reinsertion done efficiently?

1. Create an efficient cache of NodeScore(PS->T) values using ADSearch [Moore and Schneider 2002]

2. Restrict PS->T combinations to those with CPTs with maxParams or fewer parameters

3. Additional Branch and Bound is used to restrict space an additional order of magnitude

Scoring functions can be decomposed:P1 P2 P3

T

Efficiency Tricks

))(()(1

iiPSNodeScoreDDagScorem

i

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

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 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

Step 2: Generate Baseline Given Today’s Environment


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

Step 2: Generate Baseline Given Today’s Environment


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

Why not use inference?

• With sampling, we create the baseline data and then use it to obtain the p-value of the rule for the randomization test

• If we used inference, we will not be able to perform the same randomization test and we need to find some other way to correct for the multiple hypothesis testing

• Sampling was chosen for its simplicity

Why not use inference?

• With sampling, we create the baseline data and then use it to obtain the p-value of the rule for the randomization test

• If we used inference, we will not be able to perform the same randomization test and we need to find some other way to correct for the multiple hypothesis testing

• Sampling was chosen for its simplicity

But there may be clever things to do with inference which may help us. File this under future work

SimulationNW

100

N

400

NE

500

W

100

C

200

E

300

SW

200

S

200

SE

600

City with 9 regions and different population in each region

For each day, sample the city’s environment from the following Bayesian Network

Date

Day of Week

PreviousWeather Season

PreviousFlu Level

PreviousRegion Food

Condition

PreviousRegion Anthrax

Concentration

Region FoodCondition

Region Anthrax Concentration

Weather Flu Level

Simulation

DATE

DAY OF WEEK SEASONFLU LEVEL WEATHER

REGION

AGE

GENDER Region Grassiness


Region Food

Condition

ImmuneSystem

OutsideActivity

HasAnthrax

HasFlu

HasAllergy

Has HeartAttack

HasSunburn

HasCold

HeartHealth

Has FoodPoisoning

Disease

ACTION

ActualSymptom

REPORTEDSYMPTOM DRUG

For each person in a region, sample their profile

Visible Environmental Attributes

DATE


REGION

AGE



Region Food

Condition

ImmuneSystem

OutsideActivity

HasAnthrax

HasFlu

HasAllergy

Has HeartAttack

HasSunburn

HasCold

HeartHealth

Has FoodPoisoning

Disease

ACTION

ActualSymptom


Simulation

DATE


REGION

AGE



Region Food

Condition

ImmuneSystem

OutsideActivity

HasAnthrax

HasFlu

HasAllergy

Has HeartAttack

HasSunburn

HasCold

HeartHealth

Has FoodPoisoning

Disease

ACTION

ActualSymptom


Diseases: Allergy, cold, sunburn, flu, food poisoning, heart problems, anthrax (in order of precedence)

Simulation

DATE


REGION

AGE



Region Food

Condition

ImmuneSystem

OutsideActivity

HasAnthrax

HasFlu

HasAllergy

Has HeartAttack

HasSunburn

HasCold

HeartHealth

Has FoodPoisoning

Disease

ACTION

ActualSymptom


Actions: None, Purchase Medication, ED visit, Absent. If Action is not None, output record to dataset.

Simulation Plot

Simulation PlotAnthrax release

(not highest peak)

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

Time

Sig

nal

Mean

Upper Safe Range

1. Standard algorithm

2. WSARE 2.0

3. WSARE 2.5

• Use all past data but condition on environmental attributes

Results on Simulation

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

• Modeling historical data with Bayesian Networks to allow conditioning on unique features of today

• Computationally intense unless we use clever algorithms

Conclusion

• WSARE 2.0 deployed during the past year• WSARE 3.0 about to go online• WSARE now being extended to

additionally exploit over the counter medicine sales

For more informationReferences:

• Wong, W. K., Moore, A. W., Cooper, G., and Wagner, M. (2002). Rule-based Anomaly Pattern Detection for Detecting Disease Outbreaks. Proceedings of AAAI-02 (pp. 217-223). MIT Press.

• Wong, W. K., Moore, A. W., Cooper, G., and Wagner, M. (2003). Bayesian Network Anomaly Pattern Detection for Disease Outbreaks. Proceedings of ICML 2003.

• Moore, A., and Wong, W. K. (2003). Optimal Reinsertion: A New Search Operator for Accelerated and More Accurate Bayesian Network Structure Learning. Proceedings of ICML 2003.

AUTON lab website: http://www.autonlab.org/wsare

Email: [email protected]

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