West Nile Virus: DYCAST spatial-temporal model. Why spatial is special Modifiable area unit problem...

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, USADiffusion of West Nile Virus in Birds, USA

Jan 1, 1999 to Dec 31, 1999


Jan 1, 2000 to Dec 31, 2000


Jan 1, 2001 to Dec 31, 2001


Jan 1, 2002 to Dec 31, 2002


• Jan 1, 2002 to Dec 31, 2002

Jan 1, 2003 to Dec 31, 2003


Jan 1, 2004 to Dec 31, 2004


Jan 1, 2005 to Dec 31, 2005


Jan 1, 2006 to Dec 31, 2006


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

Source: The Centers for Disease Control and Prevention;

http://www.cdc.gov/ncidod/dvbid/westnile/cycle.htm

Spillover effect hypothesized by some researchers

Birds

• Resident, wild passerine birds act as the principal amplifying hosts of West Nile virus.

• 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

Species Mortality Rate Mean days to death Mean day of highest viremiaAmerican 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)

Order Bird 1 2 3 4 5 6 7Passeriformes BLJA 124 8.8 11.6 12 11 deadPasseriformes BLJA 125 5.6 9.5 12.6 9.7 deadPasseriformes BLJA-910 8.7 10.9 11.4 deadPasseriformes BLJA-911 7.1 7.8 7.5 5 2.2 <1.7 <1.7

Passeriformes COGR 118 5.6 9 10.5 <1.7 <1.7 <1.7 <1.7Passeriformes COGR 119 6.8 9 6.7 <1.7 <1.7 <1.7 <1.7Passeriformes COGR 120 5.4 5.6 11.3 deadPasseriformes COGR 121 5.4 5.4 4.7 <1.7 <1.7 <1.7 <1.7Passeriformes COGR 122 3.3 7.6 9.3 6 <1.7 <1.7 <1.7Passeriformes COGR 123 6 >11 12.5 12.5 dead

Passeriformes HOSP 011 6.3 7.7 5.3 4.5 2 1.7 <1.7Passeriformes HOSP 012 5.3 7.6 4.8 2.4 <1.7 <1.7 <1.7Passeriformes HOSP 016 3.9 8.9 6.5 3.8 2.5 2.1 <1.7Passeriformes HOSP 010 6.3 9 deadPasseriformes HOSP 014 8.6 10.5 >11.0 >11.0 deadPasseriformes HOSP 015 5.7 8.8 8.9 8.9 9 dead

Birds continued

Data Source: Komar, N. unpublished. Used with permission

Mosquitoes

• Culex pipiens:– 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.

Photo source:

Iowa State University online image gallery

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?

• 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.

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.

1

1 1

n

i

n

ijijij stT

2

)1(

nnN

MEASURES OF SPACE TIME INTERACTION

THE KNOX TEST (1963)

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

Where:

N : the total number of pairs that can be formed from:

n data points

SPACE Close Not Close Close T(o11) 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

P(X T) = 1 -

Chi-Square

P(X T) =

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.

1

0

)(

!)(T

X

XTE

XTEe

4

1

2

)()(

ij

ijij

OEOEO

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.

Random Monte Carlo Simulations

1.5 m

21 days

Repeat 5000 times.

Randomly seed the cylinder with X number of points.

i.e. 10

0.25 m 3 days

Sweep the cylinder with a smaller cylinder of closeness in search for close pairs.

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 SurveillanceOverlay 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

Figure 1

0

10

20

30

40

50

60

70

80

90

100

21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1

Days Before Onset

Pe

rce

nt

su

cc

es

ful i

de

nti

fic

ati

on

MONTE CARLO MARGINALS CHI-SQUARED

Days before area was identified as at-risk

Figure 2

0

10

20

30

40

50

60

70

80

90

100

22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Number of Days

Pe

rce

nta

ge

MONTE CARLO MARGINALS CHI-SQUARED

Number of days area was lit.

Kappa

,)*(

)*(ˆ

1

2

1

r

iii

r r

iiiii

xxN

xxx

where: N is the total number of areas considered, and xii, xi+, x+i are the elements of the following

matrix:

Rater 1

Rater 2

Class 1

Class 2

Class 1

x11 x12

Class 2

x21 x22

The sum of which amounts to N.

Measures inter-rater agreement excluding chance:

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 11 10 9 8 7 6 5 4 3 2 1Days 21 -0 0.01 0.03 0.04 0.06 0.08 0.1 0.11 0.13 0.14 0.16 0.18 0.19 0.2 0.22 0.26 0.29 0.32 0.36Prior 20 0.04 0.05 0.07 0.09 0.11 0.13 0.14 0.16 0.18 0.2 0.22 0.23 0.25 0.27 0.3 0.33 0.35 0.38 0.38

19 0.08 0.1 0.12 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.34 0.37 0.39 0.41 0.41 0.4118 0.12 0.14 0.16 0.18 0.19 0.22 0.24 0.26 0.28 0.3 0.31 0.33 0.36 0.39 0.4 0.42 0.42 0.43 0.4217 0.17 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.41 0.43 0.44 0.45 0.45 0.45 0.4616 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.41 0.43 0.45 0.46 0.47 0.48 0.48 0.5 0.515 0.24 0.26 0.27 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.47 0.48 0.49 0.5 0.51 0.53 0.5314 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.42 0.44 0.46 0.47 0.49 0.5 0.51 0.52 0.53 0.54 0.56 0.5613 0.3 0.32 0.34 0.36 0.38 0.41 0.43 0.45 0.47 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.58 0.5812 0.33 0.35 0.37 0.4 0.42 0.44 0.46 0.48 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.5811 0.36 0.38 0.4 0.42 0.44 0.47 0.49 0.5 0.52 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.58 0.59 0.5710 0.39 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.53 0.54 0.54 0.55 0.56 0.57 0.58 0.58 0.58 0.58 0.569 0.41 0.43 0.45 0.47 0.49 0.51 0.52 0.53 0.54 0.54 0.55 0.56 0.56 0.57 0.57 0.57 0.57 0.56 0.538 0.43 0.45 0.47 0.49 0.5 0.52 0.53 0.54 0.54 0.55 0.55 0.56 0.56 0.56 0.56 0.56 0.56 0.54 0.537 0.45 0.47 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.54 0.53 0.56 0.47 0.49 0.5 0.51 0.52 0.53 0.53 0.54 0.55 0.55 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.495 0.48 0.49 0.51 0.51 0.52 0.53 0.53 0.54 0.54 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.51 0.5 0.474 0.49 0.5 0.51 0.51 0.52 0.53 0.53 0.53 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.5 0.49 0.47 0.443 0.49 0.5 0.5 0.51 0.52 0.52 0.52 0.52 0.52 0.51 0.51 0.5 0.49 0.49 0.48 0.47 0.46 0.43 0.392 0.49 0.5 0.5 0.51 0.51 0.51 0.51 0.5 0.5 0.49 0.48 0.48 0.47 0.46 0.45 0.44 0.42 0.39 0.36

1 0.49 0.49 0.5 0.5 0.5 0.5 0.49 0.49 0.48 0.47 0.46 0.46 0.45 0.44 0.43 0.41 0.39 0.37 0.370 0.48 0.49 0.49 0.49 0.49 0.48 0.47 0.47 0.46 0.45 0.44 0.43 0.42 0.41 0.4 0.38 0.37 0.36 0.33

Table 1. Kappa values for Windows and Days prior

21

18

15

12

9

6

3

0 19

17

15

13

11

97

53

10

0.1

0.2

0.3

0.4

0.5

0.6

Kappa

Days BeforeWindows

Figure 3: Kappa value surface

12

0

2119

1715

9

24

6

Days Before

k = 0.59

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

19

15

11

7

3

19

16

13

10

7

4

1-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Chi-Square Surface

Monte Carlo-Chi-Square comparison

Monte Carlo

Chi-Square

Risk No Risk

Risk 7134 47

No Risk 10866 97691

Significant at < 0.001 level.

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


Implementation


• 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

• 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 VirusDead Bird Surveillance ProgramAssociate Public Health BiologistCalifornia Department of Public HealthVector-Borne Disease Section850 Marina Bay ParkwayRichmond, CA 94804Phone: (510) 412-6254Fax: (510) [email protected]

mailto:[email protected]

24-Bit Encoding Schemes (Master Templates)ArcEngine Model with Daily Sacramento Area DYCAST Output Raster

2005 Sacramento Season

Sacramento CA Accuracy

Deriving Cellular Automata Rules for Areas at Risk of West Nile Virus InfectionG. 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

Selection of master template and sub-templates via mutual information and genetic algorithm based on accuracy of CA output:

Data: California Department of Health Services

West Nile Virus: DYCAST spatial-temporal model. Why spatial is special Modifiable area unit problem...

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