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.
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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
For example, HMO data concerning:
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.
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
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.
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
Let cst = # cases in the cylinder covering
location s and time interval t.
2. For each cylinder, calculate the Poisson likelihood Tst =
[cst / μst ]cstx [(C-cst)/(C- μst)] C-cst
if cst / μst > 1, Tst = 1 otherwise
3. Test statistic T = maxst log [ Tst ]
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)
For each cylinder, add the Poisson log likelihoods: Tst =
log[ Tst ] +log[ Tst ] +log[ Tst ]
Test statistic T = maxst Tst
Multiple contacts by the same person removed.
Tele:0.001< 1 / 1000 days
Urgent0.91~ every day
Regular:0.84 ~ every day
Multiple DS:0.001< 1 / 1000 days
Tele:0.031 / 32 days
Urgent0.71~ every day
Regular:0.0031 / 333 days
Multiple DS:0.0021 / 500 days
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,
Tele:0.071 / 14 days
Urgent0.85~ every day
Regular:0.18 1 / 6 days
Combined:0.0071 / 142 days
Research Funded By
Alfred P Sloan Foundation
Data, National Bioterrorism Syndromic Surveillance Demonstration Program:
National Center for Infectious Diseases, Centers for Disease Control and Prevention
SaTScan v 5.1