The Space-Time Scan Statistic for
Multiple Data Streams
Martin Kulldorff, Katherine Yih, Ken Kleinman,
Richard Platt, Harvard Medical School and
Harvard Pilgrim Health Care
Farzad Mostashari, New York City Department
of Health and Mental Hygiene
Luiz Duczmal, Univ Fed Minas Gerais, Brazil
Different Data Sources
For example:
• OTC Drug Sales, from pharmacy chains
• Nurses Hotline Calls, from Optum
• Regular Physician Visits, from HMOs/VA
• Emergency Department Visits, from hospitals
• Ambulance Dispatches, from 911 call centers
• Lab Test Results, from laboratories
Different Types of Data from
the Same Data Source
For example, HMO data concerning:
• Telephone Calls to Physicians
• Regular Physician Visits
• Emergency Department Visits
• Lab Test Requests
• Lab Test Results
• Drug Prescriptions
Different Groupings in the
Same Type of Data
• Children, Young Adults, Adults age 65+
• Male, Female
• Diarrhea, Vomiting
Early Work
Burkom HS, Biosurveillance Applying Scan
Statistics with Multiple, Disparates Data
Sources, Journal of Urban Health, 80i:57-65,
2003
Wong WK, Moore A, Cooper G, Wagner M.
WSARE: What’s strange about recent
events? Journal of Urban Health, 80i:66-75,
2003.
Why Multivariate Detection
Methods?
• We do not know whether an outbreak will
create a signal in one or more data streams.
• The informational content is different in
different data streams.
Outline
• Method: Space-Time Permutation Scan Statistic
• Example: Gastrointestinal telephone calls,
urgent care visits and regular physician visits in
Boston
The Spatial Scan Statistic
Create a regular or irregular grid of centroids
covering the whole study region.
Create an infinite number of circles around each
centroid, with the radius anywhere from zero up
to a maximum so that at most 50 percent of the
population is included.
A small sample of the circles used
Space-Time Scan Statistic
Use a cylindrical window, with the
circular base representing space and the
height representing time.
We will only consider cylinders that
reach the present time.
Space-Time Permutation Scan Statistic
1. For each cylinder, calculate the expected
number of cases conditioning on the marginals
μst = Cs Ct / C
where
Cs = # cases in location s
Ct = # cases in time interval t
C = total number of cases
Space-Time Permutation Scan Statistic
Let cst = # cases in the cylinder covering
location s and time interval t.
Space-Time Permutation Scan Statistic
2. For each cylinder, calculate the Poisson
likelihood Tst
=
cst
C-cst
[cst / μst ] x [(C-cst)/(C- μst)]
if cst
/ μst > 1, Tst = 1 otherwise
3. Test statistic T = maxst log [ Tst ]
Statistical Inference
4. Generate random replicas of the data
set conditioned on the marginals, by
permuting the pairs of spatial locations
and times.
5. Compare test statistic in real and
random data sets using Monte Carlo
hypothesis testing (Dwass, 1957):
p = rank(Treal) / (1+#replicas)
Multiple Data Streams
For each cylinder, add the Poisson log
Tst =
[1]
[2]
[3]
log[ T st ] +log[ T st ] +log[ T st ]
likelihoods:
Test statistic T = maxst Tst
Syndromic Surveillance in Boston:
Upper and Lower GI
• Harvard Pilgrim Health Care HMO members
cared for by Harvard Vanguard Medical
Associates
• Historical Data from Jan 1 to Dec 31, 2002
• Mimicking Surveillance from Sept 1 to Dec 31,
2002
Three Data Streams
• Telephone Calls ( ~ 20 / day)
• Urgent Care Visits ( ~ 9 / day)
• Regular Physician Visits ( ~ 22 / day)
Multiple contacts by the same person removed.
Strongest Signal: October 18
p=
Recurrence Int.
Tele:
0.001
< 1 / 1000 days
Urgent
0.91
~ every day
Regular:
0.84
~ every day
Multiple DS: 0.001
< 1 / 1000 days
October 18 Signal
•
•
•
•
•
Friday
Number of Cases: 5
Expected Cases: 0.04
Location: Zip Code 01740
Time Length: One Day
October 18 Signal
•
•
•
•
•
•
Friday
Number of Cases: 5
Expected Cases: 0.04
Location: Zip Code 01740
Time Length: One Day
Diagnosis: Pinworm Infestation (all 5)
October 18 Signal
•
•
•
•
•
•
•
Friday
Number of Cases: 5
(all tele)
Expected Cases: 0.04
Location: Zip Code 01740
Time Length: One Day
Diagnosis: Pinworm Infestation (all 5)
Same Family: Mother, Father, 3 Kids
2nd Strongest Signal:
December 20
p=
Recurrence Int.
Tele:
0.03
1 / 32 days
Urgent
0.71
~ every day
Regular:
0.003
1 / 333 days
Multiple DS: 0.002
1 / 500 days
December 20 Signal
• Number of Cases: 16 (7 tele, 7 regular, 2
urgent)
• Expected Cases: 3.5
• Location: Zips 01810,26,45,50,52,76
• Time Length: Two Days (Thu, Fri)
• Strong signals on the two following days.
December 20 Signal
Mostly diverse vague GI diagnoses:
Esophageal Reflux (3), Nausea (2),
Abdominal Pain (2), Noninfectious GI (2),
Acute pharyngitis, Mastodynia, Diarrhea,
Anemia, Hypertension, Blood in stool,
Holiday parties?
3rd Strongest Signal:
October 26
p=
Recurrence Int.
Tele:
0.07
1 / 14 days
Urgent
0.85
~ every day
Regular:
0.18
1 / 6 days
Combined:
0.007
1 / 142 days
October 26 Signal
•
•
•
•
•
•
Saturday
Number of Cases: 8 ( 5 tele, 3 regular)
Expected Cases: 0.9
Location: Zip Codes 01902,07,15,45,70
Time Length: Two Days (Fri, Sat)
Various specific diagnoses.
Research Funded By
Methods:
Alfred P Sloan Foundation
Data, National Bioterrorism Syndromic
Surveillance Demonstration Program:
National Center for Infectious Diseases,
Centers for Disease Control and Prevention
Free Software
SaTScan v 5.1
www.satscan.org