Transcript A Prospective and Dynamic Spatio

West Nile Virus: DYCAST spatial-temporal model
Why spatial is special
• Modifiable area unit problem (MAUP)
– Results of statistical analysis are sensitive to the zoning
system used to report aggregated data
– Results of statistical analysis are sensitive to the scale at
which the analysis are performed
– Examine sensitivity of results to MAUP
• Boundary problem
– Study areas are bounded and results just outside the study
are can affect results.
– Size and shape can affect results
• Migration
– Rhode Island (xs)
– Tennessee (xl)
– Ohio (jr)
Why spatial is special (cont.)
• Spatial sampling
– Space can be used as a means of stratification
• Spatial autocorrelation
– Refers to the fact that values of phenomena close in space
are related
• Problem: Implication for sampling is that samples close
in space may not be independent
– Spatial autocorrelation can be calculated and variances
can be adjusted accordingly
• Prospects: spatial autocorrelation can be used to
estimate values at unknown locations based on
surrounding know points (interpolation).
Why spatial is special (cont.)
• Data management
– Editing
• Editing of spatial data is a long transaction
– User needs to “check out” a region for extended periods of
time
– Other users need access
• Spatial databases are version managed to permit
multiple long-transaction editing
– Access
• Indexes are spatially based
– Quad-tree recursive algorithm
• Addition of temporal dimension requires a second index.
Optimization of spatial-temporal searching is still a topic
under research
Map to Geographic Information Systems (GIS)
• Maps as layers of geographic information
• Desire to ‘automate’ map
• Evolution of GIS
– Create automated mapping systems
– Analyze geographic relationships
– Model real-world phenomena
What is GIS?
• Component definition: set of subsystems for the
input, storage, transformation and retrieval of
geographic data.
• Tool definition: measuring and analyzing aspects
of geographic phenomena and processes.
• Model definition: a model of the real world.
GIS: It’s about
• Modeling and analyzing relationships and processes that
occur across space, time and different scales.
• New tools for modeling
– Geo-statistical procedures (Dead Crows)
– Object-based GIS (Tiger model)
– Seamless geographic databases (Big Apple)
Global issues and motivation
•Hundreds Dead
•Thousands Infected and Sick. Sickness can last for
months and result in long term neurological problems.
•Threatening the blood supply. One of the most common
pathogens.
•Kills wildlife and threatens ecological balance.
•Remediation can cause problems.
Diffusion of West Nile Virus in Birds, USA
Jan 1, 1999 to Dec 31, 1999
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2000 to Dec 31, 2000
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2001 to Dec 31, 2001
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2002 to Dec 31, 2002
Diffusion of West Nile Virus in Birds, USA
• Jan 1, 2002 to Dec 31, 2002
Jan 1, 2003 to Dec 31, 2003
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2004 to Dec 31, 2004
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2005 to Dec 31, 2005
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2006 to Dec 31, 2006
Diffusion of West Nile Virus in Birds, USA
Jan 1, 2007 to Sept. 25, 2007
Confronting the problem at hand
• Newly introduced infectious agent arrives in New
York City
• Observations
– Wildlife are killed especially birds
– Individuals become sick in close geographic
proximity
– Seasonal effect
Synthesizing a hypothesis: literature review
• What do we know about this disease from other
parts of the world?
– Outbreaks have been observed for decades in the
Middle East, Africa and Europe
– Mosquitoes are the vectors
• These mosquitoes tend to be ornithophilic
– Birds play a primary role as the reservoir host
• Amplification cycle and spillover
Synthesizing a hypothesis: local observations and
experience
• Many birds die prior to human onset
• Most are resident Passerines particularly
Corvids
• Patterns of birds deaths tend to be highly
localized and dynamic
• Human infections tend to follow these patterns of
bird deaths
Spillover effect hypothesized by some researchers
Source: The Centers for Disease Control and Prevention;
http://www.cdc.gov/ncidod/dvbid/westnile/cycle.htm
Birds
• Resident, wild passerine birds act as
the principal amplifying hosts
of West Nile virus.
•
Species
Mortality Rate Mean days to death Mean day of highest viremia
American Crow
100%
5.1 4 (10.2)
Fish Crow
55%
9.6 4 (8.9)
Blue Jay
75%
4.7 3 (12.1)
House Sparrow
50%
4.7 3, 4 (10.3)
Ring-Billed Gull
100%
9 3 (8.0)
Ring-Billed Magpie
100%
6 3 (8.8)
Common Grackle
33%
4.5 3, 4 (11.8)
Data from Komar (2003)
• Crows suffer highest casualties. 82% dead in
Illinois, by 2003.
• The nature of the bird as a reservoir for WNV
transmission is still! under investigation.
Photo Source: Ornithology and Mammalogy Department, Cornell University
Birds continued
Order
Passeriformes
Passeriformes
Passeriformes
Passeriformes
Bird
BLJA 124
BLJA 125
BLJA-910
BLJA-911
1
8.8
5.6
8.7
7.1
2
11.6
9.5
10.9
7.8
3
12
12.6
11.4
7.5
4
11
9.7
dead
5
5
dead
dead
6
7
2.2
<1.7
<1.7
Passeriformes
Passeriformes
Passeriformes
Passeriformes
Passeriformes
Passeriformes
COGR 118
COGR 119
COGR 120
COGR 121
COGR 122
COGR 123
5.6
6.8
5.4
5.4
3.3
6
9
9
5.6
5.4
7.6
>11
10.5
6.7
11.3
4.7
9.3
12.5
<1.7
<1.7
dead
<1.7
6
12.5
<1.7
<1.7
<1.7
<1.7
<1.7
<1.7
<1.7
<1.7
dead
<1.7
<1.7
<1.7
<1.7
Passeriformes
Passeriformes
Passeriformes
Passeriformes
Passeriformes
Passeriformes
HOSP 011
HOSP 012
HOSP 016
HOSP 010
HOSP 014
HOSP 015
6.3
5.3
3.9
6.3
8.6
5.7
7.7
7.6
8.9
9
10.5
8.8
5.3
4.8
6.5
dead
>11.0
8.9
4.5
2.4
3.8
2
<1.7
2.5
1.7
<1.7
2.1
<1.7
<1.7
<1.7
Data Source: Komar, N. unpublished. Used with permission
>11.0
8.9
dead
9
dead
Mosquitoes
•
Culex pipiens:
Photo source:
Iowa State University online image gallery
– The most common pest mosquito in urban and suburban
settings.
– An indicator of polluted water in the immediate vicinity.
– Recognized as the primary vector of St. Louis encephalitis
(SLE).
– Is normally considered to be a bird feeder but some urban
strains have a predilection for mammalian hosts and feed
readily on humans. (American Hybrids?).
– Extrinsic incubation period of 4-12 days.
•
Species identified in transmission in NYC include: Culex pipiens, Culex
restuans, Culex salinarius and Aedes vexans.
Hypotheses
• Primary Hypothesis: Dead birds are an integral part
of the process that results in human infection.
• Sub goals
– How do we quantify dead bird activity?
– How can we establish the relationship between
dead birds and human infection?
– Is there a statistical procedure that mirrors the
process governing this relationship?
– Are the statistical measures adequate?
Quantifying WNV dead bird activity.
• Point Indicators of WNV
– Laboratory Confirmation in Birds-Mosquitoes
• Temporal lag between laboratory detection of positives
and actual presence of virus in the wild.
• Does not allow for early identification of amplification
cycle.
• Point data, no continuity in space.
Quantifying WNV dead bird activity.
•Area estimates of WNV infection
–Density of Dead Crows and Blue Jays
•Arbitrary thresholds.
•Surveillance bias.
•Modifiable Areal Unit Problem (MAUP).
•Data regarding the ecology of the disease ignored.
Quantifying WNV dead bird activity.
DYCAST Analysis (Dynamic Continuous Area Space Time Analysis)
• Assumptions:
– Good surveillance design and adequate public participation in
reporting.
– Persons are infected at place of residence.
– Non-random space-time interaction of bird deaths attributed to
WNV.
– WNV is continuous across space.
Quantifying WNV dead bird activity.
DYCAST Analysis (contd.)
• Model Components
– Space-time correspondence of the death of birds as
amplification measure.
• Knox method (statistical)
– Run Knox as an interpolation function to estimate a surface
of WNV activity .
– Calibrate the model using ecological information and
statistical analysis.
– Dynamic: Use a moving window for the temporal domain.
Quantifying WNV dead bird activity.
Statistical Approach.
MEASURES OF SPACE TIME INTERACTION
THE KNOX TEST (1963)
n ( n  1)
N 
2
Where:
N : the total number of pairs that can be formed from:
n data points
n 1
n
T    tij sij
i 1 j i 1
Where:
T: the test statistic
tij: the distance between points i and j: 0 if greater than the critical distance, 1
otherwise
sij: the time between points i and j: 0 if greater than the critical time, 1 otherwise
SPACE
Close
Close
T(o11)
Not Close
Time Only (o12)
TIME
Not Close
Space Only(o21)
Not Close(o22)
Where:
cell o11 is T, close in space and time
cell o21 are the pairs close in space only (not in space and
time)
cell o12 are the pairs close in time only (not in space and
time)
cell O22 are pairs not close in space nor time
Quantifying WNV dead bird activity.
Significance Testing
Poisson
T 1
E(T)
P(X T) = 1 - 
e
X 0
Chi-Square

4
P(X  T) =
1
E(T)
X!
X
O E(O )
2
ij
ij
E(Oij)
where: Oij = O11, O12, O21, O22 of the Knox matrix
Monte Carlo: Space-Time Label switching.
Monte Carlo: Completely random seeding in space and
time.
Random Monte Carlo
Simulations
Randomly seed the
cylinder with X number
of points.
i.e. 10
1.5 m
Sweep the cylinder
with a smaller cylinder
of closeness in search
for close pairs.
0.25 m
21 days
3 days
Count the number of pairs
that can be formed from the
points that fall in the smaller
cylinder of closeness. Also
keep track of close-space,
close-time pairs.
Repeat 5000 times.
Methodology
• Calibration Methodology
– Home address of humans testing positive considered the most
definitive location of WNV existence.
– Calibration date assumed to be 7 days before symptoms onset for
each case.
– Spatial and temporal domains of 1.5 miles and 21 days were chosen
based on ecological factors.
– Close space/time values were chosen from an ecologically relevant
range (.25-.75 miles/3-7 days).
Methodology
Spatial Design-Prospective Surveillance
Overlay Grid (0.5 x 0.5 miles ) across NYC and Chicago and run
Knox test at centroid of grid cells (each as a potential human
case) on a daily basis for the year 2001 season, using all birds
except pigeons.
Result evaluation
• Ran for NYC in 2001
•not sufficient number of human cases to quantify.
•Chicago: 215 human cases.
•Rate of success.
•Kappa index of agreement.
•Chi-Squared test.
Publication
CHICAGO 2002
• Unconditional Monte Carlo
Days before area was identified as at-risk
Figure 1
100
90
Percent succesful identification
80
70
60
50
40
30
20
10
0
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
Days Before Onset
MONTE CARLO MARGINALS
CHI-SQUARED
6
5
4
3
2
1
0
-1
Number of days area was lit.
Figure 2
100
90
80
70
Percentage
60
50
40
30
20
10
0
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
Number of Days
MONTE CARLO MARGINALS
CHI-SQUARED
7
6
5
4
3
2
1
0
Kappa
Measures inter-rater agreement excluding chance:
ˆ 
r
r
 
i 1
  xii   ( xi  * x i )
r
N 2   ( xi  * x i )
,
i 1
Rater 1
Rat
er 2
Class
1
Class
2
Class
1
x11
x12
Class
2
x21
x22
where:
N is the total number of areas considered,
and xii, xi+, x+i are the elements of the following
matrix:
The sum of which amounts to N.
Space-Time Application of kappa:
Run for a selected combination of windows and days prior
Monte Carlo kappa table
Windows
19
18
17
16
15
14
13
12
Days
21
-0 0.01 0.03 0.04 0.06 0.08 0.1 0.11
Prior
20 0.04 0.05 0.07 0.09 0.11 0.13 0.14 0.16
19 0.08 0.1 0.12 0.13 0.15 0.17 0.19 0.21
18 0.12 0.14 0.16 0.18 0.19 0.22 0.24 0.26
17 0.17 0.18 0.2 0.22 0.24 0.26 0.28 0.3
16 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34
15 0.24 0.26 0.27 0.3 0.32 0.34 0.36 0.38
14 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.42
13 0.3 0.32 0.34 0.36 0.38 0.41 0.43 0.45
12 0.33 0.35 0.37 0.4 0.42 0.44 0.46 0.48
11 0.36 0.38 0.4 0.42 0.44 0.47 0.49 0.5
10 0.39 0.41 0.43 0.45 0.47 0.49 0.51 0.52
9 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.53
8 0.43 0.45 0.47 0.49 0.5 0.52 0.53 0.54
7 0.45 0.47 0.49 0.5 0.51 0.52 0.53 0.54
6 0.47 0.49 0.5 0.51 0.52 0.53 0.53 0.54
5 0.48 0.49 0.51 0.51 0.52 0.53 0.53 0.54
4 0.49 0.5 0.51 0.51 0.52 0.53 0.53 0.53
3 0.49 0.5 0.5 0.51 0.52 0.52 0.52 0.52
2 0.49 0.5 0.5 0.51 0.51 0.51 0.51 0.5
1 0.49 0.49 0.5 0.5 0.5 0.5 0.49 0.49
0 0.48 0.49 0.49 0.49 0.49 0.48 0.47 0.47
Table 1. Kappa values for Windows and Days prior
11
0.13
0.18
0.23
0.28
0.32
0.36
0.4
0.44
0.47
0.5
0.52
0.53
0.54
0.54
0.55
0.55
0.54
0.53
0.52
0.5
0.48
0.46
10
0.14
0.2
0.25
0.3
0.34
0.38
0.42
0.46
0.49
0.51
0.52
0.54
0.54
0.55
0.55
0.55
0.54
0.53
0.51
0.49
0.47
0.45
9
0.16
0.22
0.27
0.31
0.36
0.41
0.44
0.47
0.5
0.52
0.53
0.54
0.55
0.55
0.55
0.55
0.54
0.53
0.51
0.48
0.46
0.44
8
0.18
0.23
0.29
0.33
0.38
0.43
0.46
0.49
0.51
0.53
0.54
0.55
0.56
0.56
0.55
0.55
0.54
0.52
0.5
0.48
0.46
0.43
7
0.19
0.25
0.31
0.36
0.41
0.45
0.47
0.5
0.52
0.54
0.55
0.56
0.56
0.56
0.55
0.55
0.53
0.52
0.49
0.47
0.45
0.42
6
0.2
0.27
0.34
0.39
0.43
0.46
0.48
0.51
0.53
0.55
0.56
0.57
0.57
0.56
0.55
0.54
0.53
0.51
0.49
0.46
0.44
0.41
5
0.22
0.3
0.37
0.4
0.44
0.47
0.49
0.52
0.54
0.56
0.57
0.58
0.57
0.56
0.55
0.54
0.52
0.51
0.48
0.45
0.43
0.4
4
0.26
0.33
0.39
0.42
0.45
0.48
0.5
0.53
0.55
0.57
0.58
0.58
0.57
0.56
0.55
0.53
0.52
0.5
0.47
0.44
0.41
0.38
3
0.29
0.35
0.41
0.42
0.45
0.48
0.51
0.54
0.56
0.58
0.58
0.58
0.57
0.56
0.54
0.53
0.51
0.49
0.46
0.42
0.39
0.37
2
0.32
0.38
0.41
0.43
0.45
0.5
0.53
0.56
0.58
0.59
0.59
0.58
0.56
0.54
0.53
0.52
0.5
0.47
0.43
0.39
0.37
0.36
1
0.36
0.38
0.41
0.42
0.46
0.5
0.53
0.56
0.58
0.58
0.57
0.56
0.53
0.53
0.5
0.49
0.47
0.44
0.39
0.36
0.37
0.33
Figure 3: Kappa value surface
21
19
17
k = 0.59
15
12
Days Before
9
6
4
2
0
0.6
0.5
0.4
0.3 Kappa
0.2
0.1
21
01
18
3
15
5
12
7
9
9
Days Before
11
6
13
15
3
17
0
19
Windows
Interpreting the results
• The maximum kappa value is for a 2 day window
for 12 days prior
– With a 1 day reporting lag and lag for maximum
viremia 1-2 days prior to death we have maximum
viremia occurring on days 15 and 16 prior to onset
of human illness.
– Given that extrinsic incubation period in
mosquitoes averages 9 days and intrinsic
incubation in humans averages 7 days, the above
results are consistent with this pathology.
Comparison of statistical analysis and epidemiology
Figure 1 Illustration of temporal windows and days prior to onset
and model prediction: most likely time maximum viremia exist in
environment
Figure 2. Time: mosquito infection to onset date of human infection.
Interpreting the results
• Maximum kappa is followed by a gradual drop of
30% by 7 days prior to infection.
– This can be explained by a reduction in avian
hosts which may be causing mosquitoes to search
for other sources of blood meals perhaps humans
– This coincides with the likely infection of humans
by mosquitoes and may explain the so called “spill
over effect”.
• Maximum kappa occurred for window size 2, 3
and 1 respective
– Maximum viremia in birds occurs between 1-3
days
Chi-Square Surface
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
19
-0.02
1
15
4
7
11
10
7
13
3
16
19
Monte Carlo-Chi-Square comparison
Monte Carlo
ChiSquare
Risk
Risk
No Risk
Significant at < 0.001 level.
No Risk
7134
47
10866
97691
Broader implications of results
• Proved the role of dead-birds in human
infections. Important for control.
• Supported hypothesis concerning the
amplification cycle and spillover effect in WNV
• Identified a weakness of the Knox statistic and
proposed a way of resolving it.
• First space-time implementation of the Kappa
statistic.
Publication
DYCAST Implementation in California
DYCAST Implementation in California
Implementation
DYCAST Implementation in California
DYCAST Implementation in California
• For 2006/07 the entire state of California (every ½
by ½ mile grid cell) is being run every day
beginning May 1, 2006/07 and ending October 1 of
each year
Alert to Mosquito control boards in California
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Dave,
Here is an update on the DYCAST risk in Sacramento and Yolo counties, in case you may find it useful in advance of the aerial spraying scheduled
for next week. The risk has continued to rise sharply in Sacramento County, with a new, large cluster appearing in the Citrus Heights/Foothill
Farms/North Highlands area (Attachment A). As you can see from Attachment B, the level of DYCAST risk in Sacramento County is at the exact same
level as it was on this date last year (199 lit tiles, 49.75 square miles). Sacramento County also has the highest level of risk (i.e., the largest combined
square mileage of high risk areas) of any county in California at this time (Attachment C).
A:
current DYCAST risk map
B:
comparative DYCAST risk profiles from 2006-2007
C:
comparative DYCAST risk profiles (top 6 high risk counties), 2007
D:
animation of the DYCAST high risk areas from June 16 to July 26, 2007
DYCAST high risk areas in 2007:
Sacramento
Yolo
date*
# tiles sq. mi.
# tiles sq. mi.
6/17/2007
2
0.5
0
0
7/1/2007
24
6
2
0.5
7/2/2007
34
8.5
3
0.75
7/3/2007
35
8.75
4
1
7/4/2007
31
7.75
4
1
7/5/2007
44
11
5
1.25
7/6/2007
33
8.25
4
1
7/7/2007
40
10
6
1.5
7/8/2007
42
10.5
6
1.5
7/9/2007
60
15
6
1.5
7/10/2007
52
13
4
1
7/11/2007
72
18
13
3.25
7/12/2007
70
17.5
1
0.25
7/13/2007
61
15.25
7
1.75
7/14/2007
64
16
9
2.25
7/15/2007
72
18
10
2.5
7/16/2007
71
17.75
12
3
7/17/2007
92
23
18
4.5
7/18/2007
102
25.5
18
4.5
7/19/2007
111
27.75
48
12
7/20/2007
128
32
53
13.25
7/21/2007
134
33.5
49
12.25
7/22/2007
141
35.25
49
12.25
7/23/2007
152
38
54
13.5
7/24/2007
152
38
55
13.75
7/25/2007
158
39.5
55
13.75
7/26/2007
199 49.75
55
13.75
Ryan M. Carney
Coordinator, West Nile Virus
Dead Bird Surveillance Program
Associate Public Health Biologist
California Department of Public Health
Vector-Borne Disease Section
850 Marina Bay Parkway
Richmond, CA 94804
Deriving Cellular Automata Rules for Areas at Risk of West Nile Virus Infection
G. Green, PhD student, CARSI, Hunter College – City University of New York; S. Ahearn, CARSI, Hunter College – CUNY;
R. Carney, California Department of Health Services; and A. McConchie, CARSI, Hunter College - CUNY
ArcEngine Model with Daily Sacramento Area DYCAST Output Raster
24-Bit Encoding Schemes (Master Templates)
Selection of master template and sub-templates via mutual
information and genetic algorithm based on accuracy of CA output:
2005 Sacramento Season
Sacramento CA Accuracy
Data: California Department of Health Services