GeoInformatics of Hotspot Detection and Prioritization for Emerging Infectious Disease Research, Surveillance, and Early Warning

Transcription

1 GeoInformatics of Hotspot Detection and Prioritization for Emerging Infectious Disease Research, Surveillance, and Early Warning G. P. Patil of Hawaii, March

2 Infectious Diseases Use of remote sensing data and other available geospatial data on a continental scale to help evaluate landscape characteristics that may be precursors for vector-borne diseases leading to early warning systems involving landscape health, ecosystem health, and human health Water-Borne Diseases Air-Borne Diseases Emerging Infectious Diseases 2

3 3

4 Dead Bird Clusters as an Early Warning System for West Nile Virus Activity Mostashari, Kulldorff,, Hartman, Miller, Kulasekara,, Emerging Infectious Diseases 9, Prospective geographic cluster analysis of dead bird reports may provide early warning of increasing viral activity in birds and mosquitoes, allowing jurisdictions to triage limited mosquito-collection and laboratory resources and more effectively prevent human disease caused by the virus We adapted the spatial scan statistic for prospective detection of infectious disease outbreaks in New York City This adaptation of the spatial scan statistic could also be useful in other infectious disease surveillance systems, including those for bioterrorism. 4

5 Geographic Prediction of Human Onset of West Nile Virus Using Dead Crow Clusters: A Quantitative Assessment of Year 2002 Data in New York State Johnson, Eidson, Schmit,, Ellis, Kulldorff (2005) The risk of becoming a West Nile Virus (WNV) case in New York State, excluding New York City, was evaluated for individuals whose town of residence was proximal to spatial clusters of dead American crows (Corvus brachyrhynchos). Weekly clusters were delineated for June-October 2002 by the binomial spatial scan statistic and by kernel density smoothing. Relative risk of a human case was estimated for different spatial-temporal exposure definitions after adjusting for population density and age distribution using Poisson regression, adjusting for week and geographic region, and Cox proportional hazards modeling, where the week of a human case was treated as the failure time and baseline hazard was stratified by region. 5

6 The risk of becoming a WNV case was positively associated with living in towns that are proximal to dead crow clusters. The highest risk was consistently for towns associated with a cluster in the current or prior 1-2 weeks Weaker, but positive, associations were found for towns associated with a cluster in just the 1-2 prior weeks, indicating an ability to predict onset in a timely fashion. These results are relevant to spatial-temporal surveillance for zoonotic diseases in general, including those of bioterrorism concern. 6

7 Multiscale Advanced Raster Map Analysis Geospatial Patterns and Pattern Metrics Landscape patterns, disease patterns, mortality patterns Surface Topology and Spatial Structure Hotspots, outbreaks, critical areas Intrinsic hierarchical decomposition, study areas, reference areas Change detection, change analysis, spatial structure of change 7

8 A 21st Century Scenario What message does a remote sensing- derived land cover land use map have about the large landscape it represents? And at what scale and at what level of detail? Does the spatial pattern of the map reveal any societal, ecological, environmental condition of the landscape? And therefore can it be an indicator of change? 8

9 A 21st Century Scenario How do you automate the assessment of the spatial structure and behavior of change to discover critical areas, hot spots, and their corridors? Is the map accurate? How accurate is it? How do you assess the accuracy of the map? Of the change map over time for change detection? 9

10 A 21st Century Scenario What are the implications of the kind and amount of change and accuracy on what matters, whether climate change, carbon emission, water resources, urban sprawl, biodiversity, indicator species, or early warning, or others. And with what confidence, even with a single map/change- map? 10

11 The needed partnership research is expected to find answers to these questions and a few more that involve multicategorial raster maps based on remote sensing and other geospatial data. It is also expected to design a prototype and user-friendly advanced raster map analysis system for digital governance. 11

12 MARMAP SYSTEM Partnership Research and Outreach Prospectus: spectus8-00.pdf Our web page for raster map analysis: htm Our web page for raster map monographs: Our web page for UNEP HEI 12

13 Geoinformatic Surveillance System Geoinformatic spatio-temporal data from a variety of data products and data sources with agencies, academia, and industry Spatially distributed response variables Hotspot analysis Prioritization Decision support systems Masks, filters Masks, filters Indicators, weights 13

14 Homeland Security Disaster Management Public Health Ecosystem Health Other Case Studies Statistical Processing: Hotspot Detection, Prioritization, etc. Arbitrary Data Model, Data Format, Data Access Application Specific De Facto Data/Information Standard Standard or De Facto Data Model, Data Format, Data Access Data Sharing, Interoperable Middleware Agency Databases Thematic Databases Other Databases National Applications Biosurveillance Carbon Management Coastal Management Community Infrastructure Crop Surveillance Disaster Management Disease Surveillance Ecosystem Health Environmental Justice Environmental Management Environmental Policy Homeland Security Invasive Species Poverty Policy Public Health Public Health and Environment Robotic Networks Sensor Networks Social Networks Syndromic Surveillance Tsunami Inundation Urban Crime Water Management 14

15 Examples of Hotspot Analysis Spatial Disease surveillance Biodiversity: species-rich and species-poor areas Geographical poverty analysis Network Water resource impairment at watershed scales Water distribution systems, subway systems, and road transport systems Social Networks/Terror Networks 15

16 Issues in Hotspot Analysis Estimation: Identification of areas having unusually high (or low) response Testing: Can the elevated response be attributed to chance variation (false positive) or is it statistically significant? Explanation: Assess explanatory factors that may account for the elevated response 16

17 The Spatial Scan Statistic Move a circular window across the map. Use a variable circle radius, from zero up to a maximum where 50 percent of the population is included. 17

18 A small sample of the circles used 18

19 Detecting Emerging Clusters Instead of a circular window in two dimensions, we use a cylindrical window in three dimensions. The base of the cylinder represents space, while the height represents time. The cylinder is flexible in its circular base and starting date, but we only consider those cylinders that reach all the way to the end of the study period. Hence, we are only considering alive clusters. 19

20 West Nile Virus Surveillance in New York City 2000 Data: Simulation/Testing of Prospective Surveillance System 2001 Data: Real Time Implementation of Daily Prospective Surveillance 20

21 West Nile Virus Surveillance in New York City Major epicenter on Staten Island Dead bird surveillance system: June 14 Positive bird report: July 16 (coll. July 5) Positive mosquito trap: July 24 (coll. July 7) Human case report: July 28 (onset July 20) 21

22 22

23 Hospital Emergency Admissions in New York City Hospital emergency admissions data from a majority of New York City hospitals. At midnight, hospitals report last 24 hour of data to New York City Department of Health A spatial scan statistic analysis is performed every morning If an alarm, a local investigation is conducted 23

24 Issues 24

25 Geospatial Surveillance 25

26 Spatial Temporal Surveillance 26

27 Syndromic Surveillance Symptoms of disease such as diarrhea, respiratory problems, headache, etc Earlier reporting than diagnosed disease Less specific, more noise 27

28 Syndromic Crisis-Index Surveillance 28

29 Hotspot Prioritization 29

30 30

31 You Are Invited NSF DGP PROJECT Geoinformatic Surveillance: Hotspot Detection and Prioritization Across Geographic Regions and Networks for Digital Government in the 21st Century Geoinformatic surveillance for spatial and temporal hotspot detection and prioritization is a critical need for the 21st century Digital Government. A hotspot can mean an unusual phenomenon, anomaly, aberration, outbreak, elevated cluster, or critical area. The declared need may be for monitoring, etiology, management, or early warning. The responsible factors may be natural, accidental or intentional, with relevance to both infrastructure and homeland security. This project describes a multi-disciplinary research program based on novel methods and tools for hotspot detection and prioritization, driven by a wide variety of case studies of direct interest to several government agencies. These case studies deal with critical societal issues, such as carbon budgets, water resources, ecosystem health, public health, drinking water distribution system, persistent poverty, environmental justice, crop pathogens, invasive species, biosecurity, biosurveillance, remote sensor networks, early warning and homeland security. The geosurveillance provides an excellent opportunity, challenge, and vehicle for synergistic collaboration of computational, technical, and social scientists. Our methodology involves an innovation of the popular circle-based spatial scan statistic methodology. In particular, it employs the notion of an upper level set and is accordingly called the upper level set scan statistic, pointing to the next generation of a sophisticated analytical and computational system, effective for the detection of arbitrarily shaped hotspots along spatio-temporal dimensions. We also propose a novel prioritization scheme based on multiple indicator and stakeholder criteria without having to integrate indicators into an index, using revealing Hasse diagrams and partially ordered sets. Responding to the Government s role and need, we propose a cross-disciplinary collaboration among federal agencies and academic researchers to design and build the prototype system for surveillance infrastructure of hotspot detection and prioritization. The methodological toolbox and the software toolkit developed will support and leverage core missions of federal agencies as well as their interactive counterparts in the society. The research advances in the allied sciences and technologies necessary to make such a system work are the thrust of this five year project. The project will have a dual disciplinary and cross-disciplinary thrust. Dialogues and discussions will be particularly welcome, leading potentially to well considered synergistic case studies. The collaborative case studies are expected to be conceptual, structural, methodological, computational, applicational, developmental, refinemental, validational, and/or visualizational in their individual thrust. For additional information, see the webpages: (1) (4) http: // (2) (5) (3) (6) Project address: Penn State Center for Statistical Ecology and Environmental Statistics 421 Thomas Building, Penn State University, University Park, PA Telephone: (814) ; gpp@stat.psu.edu 31

32 Geographical Disease Surveillance Discrete response Hotspot detection and upper level set scan Hotspot delineation and hot-spot rating Multiple hotspot detection and delineation Hotspot prioritization and poset ranking Space-time detection and early warning Continuous response User friendly software and downloadable website 32

33 Hotspot Detection Innovation Upper Level Set Scan Statistic Attractive Features Identifies arbitrarily shaped clusters Data-adaptive adaptive zonation of candidate hotspots Applicable to data on a network Provides both a point estimate as well as a confidence set for the t hotspot Uses hotspot-membership rating to map hotspot boundary uncertainty Computationally efficient Applicable to both discrete and continuous syndromic responses Identifies arbitrarily shaped clusters in the spatial-temporal temporal domain Provides a typology of space-time hotspots with discriminatory surveillance potential 33

34 Poor Hotspot Delineation by Circular Zones Hotspot Circular zone approximations Circular zones may represent single hotspot as multiple hotspots 34

35 Scan Statistic Zonation for Circles and Space-Time Cylinders Time Cholera outbreak along a river flood-plain Small circles miss much of the outbreak Large circles include many unwanted cells Space Outbreak expanding in time Small cylinders miss much of the outbreak Large cylinders include many unwanted cells 35

36 Candidate Zones Z Tessellated study area Want zones to be connected Allowable zone Ω= collection of all (allowable) zones Not a zone = collection of all connected unions of cells Maximize L(Z) for Z in Ω 36

37 ULS Scan Statistic -- 1 Tessellation of a geographic region c k j a b e h f i d g a, b, c, are cell labels Region R, Tessellation T = {a} of R Cell a, Response Y a, Cell Size A a Two distributional settings: Y a is Binomial ( N a, p a ), A a = N a, p a = cell rate/intensity Y a is Poisson ( λ a A a ), λ a = cell rate/intensity Cell sizes A a are known and fixed Cell responses Y a, a A, are independent 37

38 ULS Scan Statistic -- 2 G a = Y a / A a empirical cell intensity determines a cellular (piece-wise constant) surface defined over the tessellated region Zones Z are connected unions of cells from tessellation Ω = collection of all possible zones SatScan hotspot model: Zone Z such that p a = p 1 for all a Z p a = p 0 for all a R - Z p 1 > p 0 38

39 ULS Scan Statistic 3 Hotspot Detection Hypothesis testing approach: H 0 : There is no hotspot; p a constant for all cells a H 1 : There is a hotspot Z Ω; Z unknown Parameter space for full model: { (Z, p 1, p 0 ) : Z Ω, 0 < p 0 p 1 < 1 } For fixed Z, expression for likelihood and MLE for p 1, p 0 are straightforward Profile likelihood for Z : L(Z) = Max {L (Z, p 1, p 0 ) : 0 < p 0 p 1 < 1 }, Z Ω 39

40 Ω is finite but large Maximizing L(Z), Z Ω, by exhaustive search impractical Possible optimization methods: ULS Scan Statistic 4 Hotspot Estimation Stochastic optimization (annealing, GA, etc. ) Reduction of Ω to Ω 0 with Ω 0 Ω and Ω 0 small enough for exhaustive search Possible reductions of Ω to Ω 0 : Expanding circles An a priori reduction which depends only on the tessellation and not on the data Upper level sets of empirical intensity surface (Tree-Structured SATScan) An adaptive, data-dependent, reduction allowing flexible shapes for zones in Ω 0. Data dependence must be incorporated into simulations. 40

41 ULS Scan Statistic 5 Hotspot Testing Test H 0 versus H 1 for significance of hotspot Use reduced parameter space Ω 0 Zˆ = hotspot MLE, maximizes L( Z), Z Ω Likelihood ratio test Test statistic: LR = L(H ˆ 0) / L( Z) Reject H when LR is small 0 Nonstandard likelihood situation ( Ω 0 is finite discrete; parameter Z is non-identifiable under H 0 ) Asymptotic chi-squared not applicable Null distribution of LR to be determined by simulation Eliminate nuisance parameters p 1, p 0 under H 0 by conditioning on the total response a Y a 0 41

42 ULS Scan Statistic 6 Goal: Identify geographic zone(s) in which a response is significantly elevated relative to the rest of a region A list of candidate zones Z is specified a priori. This list becomes part of the parameter space and the zone must be estimated from within this list. Each candidate zone should generally be spatially connected, e.g., a union of contiguous spatial units or cells. Longer lists of candidate zones are usually preferable Expanding circles or ellipses about specified centers are a common method of generating the list 42

43 ULS Scan Statistic 7 Question: Are there data-driven (rather than a priori) ways of selecting the list of candidate zones? Motivation for the question: A human being can look at a map and quickly determine a reasonable set of candidate zones and eliminate many other zones as obviously uninteresting. Can the computer do the same thing? A data-driven proposal: Candidate zones are the connected components of the upper level sets of the response surface. The candidate zones have a tree structure, which may assist in automated detection of multiple, but geographically separate, elevated zones. Null distribution: If the list is data-driven (i.e., random), its variability must be accounted for in the null distribution. A new list must be developed for each simulated data set. 43

44 Upper Level Set (ULS) of Intensity Surface Intensity G g Z1 Z Z 2 3 Region R Hotspot zones at level g (Connected Components of upper level set) 44

45 Changing Connectivity of ULS as Level Drops Intensity G g g Z1 Z2 Z3 Z Z Z Region R 45

46 ULS Connectivity Tree -- 1 Ingredients: Tessellation of a geographic region: c k j a b e Intensity value G on each cell. Determines a cellular (piece-wise constant) surface with G as elevation. Imagine surface initially inundated with water Water evaporates gradually exposing the surface which appears as islands in the sea How does connectivity (number of connected components) of the exposed surface change with h f i d g a, b, c, are cell labels 46

47 ULS Connectivity Tree -- 2 Think of the tessellated surface as a landform Initially the entire surface is under water As the water level recedes, more and more of the landform is exposed At each water level, cells are colored as follows: Green for previously exposed cells (green = vegetated) Yellow for newly exposed cells (yellow = sandy beach) Blue for unexposed cells (blue = under water) For each newly exposed cell, one of three things happens: New island emerges. Cell is a local maximum. Morse index=2. Connectivity increases. Existing island increases in size. Cell is not a critical point. Connectivity unchanged. Two (or more) islands are joined. Cell is a saddle point Morse index=1. Connectivity decreases. 47

48 ULS Connectivity Tree -- 3 Newly exposed island c k j a b e h f i d g ULS Tree a Island grows j c a b e k h f i d g a b,c 48

49 ULS Connectivity Tree -- 4 Second island appears c k j a b e h f i d g a b,c ULS Tree d New leaf node (local maximum) Both islands grow j h c a b e k f i d g a b,c e d f,g 49

50 ULS Connectivity Tree -- 5 Islands join saddle point j h f d c a b e i k a g b,c ULS Tree e h d f,g Junction node Exposed land grows j h c a b e k f i d g a b,c e d f,g h i,j,k Root node 50

51 Comparison of Tree-Structured and Circle-Based SATScan Agreement/Disagreement regarding hotspot locus Pr[ Zˆ I Zˆ ] ULS circles Comparative plausibility and accuracy of hotspot delineation Pr[ LZ ( ˆ ) LZ ( ˆ ) ] ULS circles Execution time and computer efficiency 51

52 ULS Connectivity Tree Intensity G g Z Z Z g A Z4 Z5 Z6 Schematic intensity surface B C N.B. Intensity surface is cellular (piece-wise constant), with only finitely many levels A, B, C are junction nodes where multiple zones coalesce into a single zone 52

53 A confidence set of hotspots on the ULS tree. The different connected components correspond to different hotspot loci while the nodes within a connected component correspond to different delineations of that hotspot Tessellated Region R MLE Junction Node Alternative Hotspot Delineation Alternative Hotspot Locus 53

54 Hotspot Delineation and Hotspot Rating Determine a confidence set for the hotspot Each member of the confidence set is a zone which is a statistically plausible delineation of the hotspot at specified confidence Confidence set lets us rate individual cells a for hotspot membership Rating for cell a is percentage of zones in confidence set that contain a. (More generally, use weighted proportion.) Map of cell ratings: Inner envelope = cells with 100% rating Outer envelope = cells with positive rating 54

55 Estimation Uncertainty in Hotspot Delineation MLE Outer envelope Inner envelope 55

56 Space-Time Detection and Early Warning ULS Scan Statistic The traditional space-time scan statistic employs cylinders as the candidate zones in the reduced parameter space. In many instances, the cylindrical shape may be a poor approximation to actual space-time hotspots, whereas the ULS approach is able to adapt its shape to the actual hotspot. Since the ULS tree is derived from the adjacency matrix, the same software will work once the notion of adjacency has been specified for spacetime cells. 56

57 Some Space-Time Hotspots and Their Cylindrical Approximations Time Hotspot Cylindrical approximation Cylindrical approximation sees single hotspot as multiple hotspots Space 57

58 Hotspot Detection for Continuous Responses Human Health Context: Blood pressure levels for spatial variation in hypertension Cancer survival (censoring issues) Environmental Context: Landscape metrics such as forest cover, fragmentation, etc. Pollutant loadings Animal abundance 58

59 Hotspot Model for Continuous Responses Simplest distributional model: Y a ~ Gamma( k, β ) Additivity with respect to the index parameter k suggests that we model k as proportional to size: k a = / c. Scale parameter β takes one value inside Z and another outside Z Other distribution models (e.g., lognormal) are possible but are computationally more complex and applicable to only a single spatial scale A a 59

60 Circles vs ULS Circles capture only compactly shaped clusters Want to identify clusters of arbitrary shape Circles provide point estimate of hotspot Want to assess estimation uncertainty (hotspot confidence set) Circles handle only synoptic (tessellated) data Want to also handle data on a network 60

61 Multiple Criteria Analysis Multiple Indicators and Choices Health Statistics Disease Etiology, Health Policy, Resource Allocation First stage screening Significant clusters by SaTScan and/or upper level sets Second stage screening Multicriteria noteworthy clusters by partially ordered sets and Hass diagrams Final stage screening Follow up clusters for etiology, intervention based on multiple criteria using Hass diagrams 61

62 Network Analysis of Biological Integrity in Freshwater Streams 62

63 Network-Based Surveillance Subway system surveillance Drinking water distribution system surveillance Stream and river system surveillance Postal System Surveillance Road transport surveillance Syndromic Surveillance 63

64 Syndromic Surveillance Admissions Records Method of ε-machines a 1 a 2 a 3 a 4 M.δαηηλψ. Symbol Stream High dimensional vector LSA v 1 v 2 M Reduced dimensional vector 1. Language Sample 2. Tree of all substrings of length l with transition probabilities abaaabaaababababaaabab. 3. PFSA 0 b, p(b 0) a 2 1 a p(a 1), b p(b 1) 0 b, P(b 0) a, P(a 0) 1 2 a b, P(b 2) a, P(a 2) a, p(a 0) b, P(b 3) a, P(a 3) a a Hospital Behavior Model Formal Language Measure Crisis Behavior Model Crisis Index (left) The overall procedure, leading from admissions records to the crisis index for a hospital. The hotspot detection algorithm is then applied to the crisis index values defined over the hospital network. (right) The -machine procedure for converting an event stream into a parse tree and finally into a probabilistic finite state automaton (PFSA). 64

65 Symbolization: Network Sensor Readings to Symbolic Dynamics Phase-Space Trajectory String of Symbols Sensor Sensor 2 0 α ε β δ φ η χ 0 φ χ γ η δ α δ χ γ Sensor

66 Experimental Validation Pressure sensitive floor Formal Language Events: a green to red or red to green b green to tan or tan to green c green to blue or blue to green d red to tan or tan to red e blue to red or red to blue f blue to tan or tan to blue a Wall following a 8 5 c d 7 6 f d f 12 c 9 f 0 a 10 d 11 c f a 1 2 c d 4 3 f 0 a, b, c, d, e, f Random walk Counter-Clockwise c d a Clockwise Target Behavior Analyze String Rejections 66

67 Emergent Surveillance Plexus (ESP) Surveillance Sensor Network Testbed Autonomous Ocean Sampling Network Types of Hotspots Hotspots due to multiple, localized, stationary sources Hotspots corresponding to areas of interest in a stationary mapped field Time-dependent, localized hotspots Hotspots due to moving point sources 67

68 Ocean SAmpling MObile Network OSAMON 68

69 Ocean SAmpling MObile Network OSAMON Feedback Loop Network sensors gather preliminary data ULS scan statistic uses available data to estimate hotspot Network controller directs sensor vehicles to new locations Updated data is fed into ULS scan statistic system 69

70 SAmpling MObile Networks (SAMON) Additional Application Contexts Hotspots for radioactivity and chemical or biological agents to prevent or mitigate the effects of terrorist attacks or to detect nuclear testing Mapping elevation, wind, bathymetry, or ocean currents to better understand and protect the environment Detecting emerging failures in a complex networked system like the electric grid, internet, cell phone systems Mapping the gravitational field to find underground chambers or tunnels for rescue or combat missions 70

71 Scalable Wireless Geo-Telemetry with Miniature Smart Sensors Geo-telemetry enabled sensor nodes deployed by a UAV into a wireless ad hoc mesh network: Transmitting data and coordinates to TASS and GIS support systems 71

72 Architectural Block Diagram of Geo-Telemetry Enabled Sensor Node with Mesh Network Capability 72

73 Data Fusion Hierarchy for Smart Sensor Network with Scalable Wireless Geo-Telemetry Capability 73

74 Wireless Sensor Networks for Habitat Monitoring 74

75 Video Surveillance and Data Streams 75

76 Crop Attack Decision Support System Site Identification Module Crops Key Crop Areas NOAA Weather Threat Locations Hyperspectral Imagery Signature Development Module Plants Infected Non-infected Sentinel Ground Cameras Air/Space Platforms Data Processing Signature Library Anomaly Report Ground Truthing 76

77 Crop Biosurveillance/Biosecurity 77

78 Crop Biosurveillance/Biosecurity Data Processing Module Hyperspectral Imagery Image Segmentation (hyperclustering) Tessellation (segmentation) of raster grid Proxy Signal (per segment) Signature Similarity Map Signature Library Disease Signature Similarity Index (per segment) Hotspot/ Anomaly Detection 78

79 Prioritization Innovation Partial Order Set Ranking We also present a prioritization innovation. It lies in the ability for prioritization and ranking of hotspots based on multiple indicator and stakeholder criteria without having to integrate indicators into an index, using Hasse diagrams and partial order sets. This leads us to early warning systems, and also to the selection of investigational areas. 79

80 HUMAN ENVIRONMENT INTERFACE LAND, AIR, WATER INDICATORS for land - % of undomesticated land, i.e., total land area-domesticated (permanent crops and pastures, built up areas, roads, etc.) for air - % of renewable energy resources, i.e., hydro, solar, wind, geothermal for water - % of population with access to safe drinking water RANK COUNTRY 1 Sweden 2 Finland 3 Norway 5 Iceland 13 Austria 22 Switzerland 39 Spain 45 France 47 Germany 51 Portugal 52 Italy 59 Greece 61 Belgium 64 Netherlands 77 Denmark 78 United Kingdom 81 Ireland LAND AIR WATER

81 Hasse Diagram (all countries)

82 Hasse Diagram (Western Europe) Norway Sweden Finland Austria Switz. Ireland Italy Portugal Greece Spain Den. France UK Germany Belgium Neth. 82

83 83 83 Ranking Partially Ordered Sets Ranking Partially Ordered Sets 5 Linear extension decision tree a b d c e f a c e b b d f f d e d f e e f c f d e d f e e f d f e e f c f e e f c c f d e d f e e f d f e e f c b a b a d Jump Size: Poset (Hasse Diagram)

84 Cumulative Rank Frequency Operator 5 An Example of the Procedure In the example from the preceding slide, there are a total of 16 linear extensions, giving the following cumulative frequency table. Rank Element a b c d e f Each entry gives the number of linear extensions in which the element (row 84 label) receives a rank equal to or better that the column heading

85 Cumulative Rank Frequency Operator 6 An Example of the Procedure Cumulative Frequency Rank The curves are stacked one above the other and the result is a 85 linear ordering of the elements: a > b > c > d > e > f a b c d e f

86 Cumulative Rank Frequency Operator 7 An example where F must be iterated F F 2 Original Poset (Hasse Diagram) b a f e c g d g a f e b ad a f e b ad h c h g c h 86

87 Incorporating Judgment Poset Cumulative Rank Frequency Approach Certain of the indicators may be deemed more important than the others Such differential importance can be accommodated by the poset cumulative rank frequency approach Instead of the uniform distribution on the set of linear extensions, we may use an appropriately weighted probability distribution π, e.g., π ( 2 ω) = w 0 + w1n 1( ω) + w2n ( ω) + L+ w p np ( ω) 87

88 88

89 Space-Time Poverty Hotspot Typology Federal Anti-Poverty Programs have had little success in eradicating pockets of persistent poverty Can spatial-temporal temporal patterns of poverty hotspots provide clues to the causes of poverty and lead to improved location-specific anti- poverty policy? 89

90 Dimensions of Tract Poverty in Four Metropolitan Areas Shifting Growing Persistent Concentrated Oakland, CA Detroit, MI Camden, NJ Memphis, TN 90

91 Growing poverty 91

92 Persistent poverty 92

93 Shifting poverty Oakland 1970 Poverty data Oakland 1980 Poverty data Oakland 1990 Poverty data 93

94 Camden 1970 Poverty data Camden 1980 Poverty data Concentrated poverty Camden 1990 Poverty data 94

95 Hotspot Persistence Persistence is a property of space-time hotspots Persistence can be assessed by the projection of the space-time hotspot onto the time axis Time (census year) Persistent Hotspot Space (census tract) Long Duration Time (census year) One-shot Hotspot Short Duration Space (census tract) 95

96 Typology of Persistent Space-Time Hotspots-1 Time (census year) Stationary Hotspot Time (census year) Expanding Hotspot Space (census tract) Space (census tract) Time (census year) Shifting Hotspot Time (census year) Contracting Hotspot Space (census tract) Space (census tract) 96

97 Typology of Persistent Space-Time Hotspots-2 These hotspots are connected in space-time However, certain time slices of the hotspot are disconnected in space Spatially disconnected time slice Time (census year) Time (census year) Bifurcating Hotspot Space (census tract) Merging Hotspot Space (census tract) 97

98 Trajectory of a Persistent Space-Time Hotspot A space-time hotspot is a three-dimensional object Visualization can be done by displaying the sequence of time slices---called the trajectory of the hotspot Time slices of space-time hotspot Time (census year) Merging Hotspot Space (census tract) 98

99 Trajectory of a Merging Hotspot

100 Trajectory of a Shifting Hotspot

101 Covariate Adjustment Known Covariate Effects (age, population size, etc.) Y a = count in cell a Y Poisson( λ A ) where λ = unknown relative risk for cell a a a a a A a = known numerical covariate adjustment Hotspot Hypothesis Testing Model H H 0 1 : λ are equal for all cells a (constant relative risk) a : λ take two distinct values, an elevated value in an unknown zone a and a smaller value outside Z Z List of candidate zones Z (ULS approach) All connected components of upper level sets of the adjuste cellular surface Y / A d a a 101

102 Covariate Adjustment Given Covariates, Unknown Effects Y Poisson( λ A ) where λ = unknown relative risk for cell a a a a a 0 A a = unknown covariate adjustment GLM Model Xa = vector of known covariate values for cell a β = vector of unknown covariate effects T T Model: log( A ) = X β or log( λ A ) η = log( λ ) + X β a a a a a a a Hotspot Hypothesis Testing Model H H 1 : λ are equal for all cells a (constant relative a rs i k) : λ take two distinct values, an elevated value in an unknown zone a and a smaller value outside Z List of candidate zones Z (ULS approach) All connected components of upper level sets of the adjusted cellular surface Y / A Here the model must be fitted under the null hypothesis before determining the adjustments a a A and the candidate zones Z a Z 102

103 Incorporating Spatial Autocorrelation Ignoring autocorrelation typically results in: under-assessment of variability over-assessment of significance (H 0 rejected too frequently) How can we account for possible autocorrelation? GLMM (SAR) Model Y a = count in cell a Y a distributed as Poisson η a = log(e[y a ]) The Y a are conditionally independent given the η a The η a are jointly Gaussian with a Simultaneous AutoRegressive (SAR) specification Here, µ = E[ η ] a a 2 a are iid N(0, σ ) η µ = ρ W ( η µ ) + ε a a ab a a a b ε Wab is a spatial weight expressing the "degree of association" between cells a and b (Take Waa = 0 and Wa = 1) Thus, the residual ηa µ a for cell a is a deflated (by ρ) weighted average of the residuals for neighboring cells plus a disturbance term ε a 103

104 Incorporating Spatial Autocorrelation SAR Model: Matrix Form: η µ = ρ W ( η µ ) + ε a a ab a a a b η µ = ρw( η µ ) + ε = ( ρ ) 1 η µ I W ε ( 1 ) 2 T σ ( ρ ) ( ρ ) η MVN µ, I W I W 2 Unknown Parameters: µ, ρ, σ a 2 Special Cases: σ = 0 classical (iid) spatial scan ( ρ is not identifiable here) ρ = σ 2 0, 0 overdispersed classical scan 104

105 Incorporating Spatial Autocorrelation GLMM (SAR) Model Y Poisson(exp( η )) = Poisson(exp( µ )exp( η µ )) = Poisson( λ A ) a a a a a a a ( 1 ) 2 T σ ρ ) ( ρ ) where η MVN µ, ( I W I W Hotspot Hypothesis Testing Model H0 : µ a are equal (to µ ) for all cells a (constant relative risk) H1 : µ a take two distinct values, an elevated value in an unknown zone Z and a smaller value outside Z List of candidate zones Z (ULS approach) All connected components of upper level sets of the adjusted cellular surface Ya / Aa where Aa = exp( η a µ ) Here the model must be fitted under the null hypothesis ( µ = µ ) before determining the adjustments Aa and the candidate zones a Z 105

106 Spatial Autocorrelation Plus Covariates In the SAR model, Y Poisson(exp( η )) a ( 1 ) 2 T E σ ρ ρ where η MVN [ η], ( I W) ( I W), express the mean of η as E[ η ] = µ + Xβ and formulate the Hotspot Hypothesis Testing Model in terms of the constant term µ in this expression. a 106

107 CAR Model The entire formulation is similar for Conditional AutoRegressive (CAR) specs except that the form of the variance-covariance matrix of η is changes. In the CAR model, Poisson(exp( η )) where η Y a a ( * E η σ ( I ρw ) 1 A ) 2 * * MVN [ ], and is diagonal However, parameters in CAR and SAR have very different interpretations. In CAR, the conditional variances are 2 * Var( ηa ηb, b a) = σ Aaa which (strangely) do not depend on the autocorrelation parameter ρ. In SAR, the conditional variances are Var( ηa ηb, b a) = σ ( 1+ ρ W b ba) This expression is intuitively appealing since the conditional variances 2 are decreasing functions of and are smallest for cells with many ρ 2 strongly associated neighbors (relatively large W for many b). ba A a. 107

108 Application of the Scan Statistic to Wetland and Stream Monitoring: Testing the Method in the Upper Juniata Watershed, Pennsylvania, USA Denice Heller Wardrop, Charles Taillie, Kristen Hychka,, G.P. Patil, and Wayne Myers Penn State University, University Park, PA Penn State Cooperative Wetlands Center 108

109 This presentation will.. Provide background on the resource to be monitored (wetland condition and restoration) Provide a description of the data set (the Upper Juniata watershed) Illustrate how the scan statistic was applied Recommend future enhancements of the scan statistic for environmental problem solving (surveillance and early warning) Penn State Cooperative Wetlands Center 109

110 Necessary Context Wetlands are a valuable ecological resource We are interested in their condition One way in which we assess condition is by the plant community We seek to relate land cover characteristics to wetland condition (e.g., plant community) Since we cannot identify hotspots of condition, can we identify hotspots of stress? Penn State Cooperative Wetlands Center 110

111 Why use the Scan Statistic? Identify critical areas of stress as an indicator of wetlands in potentially poor condition (condition assessment) Target restoration areas (restoration) Narrow down an overwhelming management problem (1300 square miles) into a manageable one Penn State Cooperative Wetlands Center 111

112 Which factors are good predictors of condition? Exhaustive assessment of landscape factors shows that agricultural activity on steep slopes (>8%) is an important factor in determining physical and biological condition Management of practices on steep agricultural lands is feasible, and current restoration programs have targeted these areas (USDA) Penn State Cooperative Wetlands Center 112

113 Penn State Cooperative Wetlands Center 113

114 Necessary Elements of the Scan Statistic Observed rate versus expected rate Contiguous coverage of elements Spatial independence Constraint on maximum hotspot size Penn State Cooperative Wetlands Center 114

115 Factors to consider when using SatScan for ecological data Size constraint placed on critical areas must be adjusted to the landscape of concern Circular shape of critical areas may not agree with ecological knowledge Penn State Cooperative Wetlands Center 115

116 Potential advantages of critical areas as Delineation of contributing areas is labor intensive Can critical areas give us a first cut as to wetlands in poor condition? Can they serve as an early warning? an indicator of stress Penn State Cooperative Wetlands Center 116

117 Penn State Cooperative Wetlands Center 117

118 Penn State Cooperative Wetlands Center 118

119 Restoration Targeting with SaTScan Can effectively target areas for restoration activities or best management practices Can be scaled so that critical area matches management area Penn State Cooperative Wetlands Center 119

120 Agricultural Use Sedimentation Plant Community Turbidity Amphibian Comm. Urbanization Bird Community Eutrophication Are there warnings? Macroinvertebrates Pollutant Trans. Hydroperiod Mining Hydrologic Modif. Fragmentation Organic Matter Soil Acidification Microtopography Penn State Cooperative Wetlands Center 120

121 Conclusions When using SaTScan,, assess appropriateness of circular critical areas and size constraints Can be used for condition assessment Highly useful for restoration targeting Use of scan statistic methods in an ecological context raises three future needs: Non-circular critical areas Ability to include spatial dependency (e.g., critical areas of condition, infectious disease) Continuous response variable (e.g., fertilizer loadings, livestock density) Penn State Cooperative Wetlands Center 121

122 Spatial-Temporal Surveillance for Infectious Disease: Where are we and where can we go? Glen D. Johnson, PhD,MS, MA Zoonoses Program Bureau of Communicable Disease Control New York State Department of Health and The State University of New York University at Albany School of Public Health Department of Environmental Health and Toxicology 122

123 Public Health Professionals Analysts & Researchers & Policy Makers Intended Users Law Enforcement & National Security Agencies Canadian & Mexican Public Health Partners General Public & Other Users Web-based Access User Interface Layer Data Management and Business Logic Layer Data Source Layer The WNV-BOT Portal Bi-directional Information Exchange NYSDOH WNV human cases Dead bird surveillance data Reports on mammals Mosquito surveillance data Vector control data CADHS Detailed WNV/BOT human cases Dead bird surveillance data Mosquito surveillance data Chicken sera data Information Sources Other Sources USGS/NWHC/NBII Epizoo data Canadian & Mexican public health data CDC WNV/BOT data NOAA and NASA data US Census Bureau NY GIS clearing house 123

124 West Nile Virus Surveillance through the HIN Written summary report of lab results ed internally within NYSDOH daily Public website map and summary report of lab results updated daily during WNV season Map of dead crow density by county posted to public website weekly Maps of prediction analysis results (SaTScan, kernel density estimation) posted to Secure Discussion Forum (requires HIN access) weekly 124

125 Ability of Dead Crow Clusters to Predict Human WNV 2002 data in NYS, excluding NYC exposed if town of residence within one mile of spatial cluster of crows within previous two weeks Estimate risk of exposed vs. unexposed by - Poisson regression, using cases within town/week units as response and adjusting for region, week, town population density, density squared and proportion of town > 50 years old - Proportional Hazards modelling, using week until onset as the response, stratifying by region and adjusting for town population density, density squared and proportion of town > 50 years old 125

126 So, What Next? Much data not currently being exploited - geo-spatial and spatial-temporal - much is free and readily available - some that may require development How use such data? -via GIS, compile with respect to geographic units of concern, such as townships -via Generalized Linear Mixed Models (GLMM), model outcome (i.e. # dead crows or human cases) as a function of predictors obtained across multiple spatial-temporal scales 126

127 Data Current: Monitor outcome variable only, such as - dead crows, positive mosquitoes, human cases for WNV - ER visits, pharmaceutical sales, syndromes, etc. proposed for BT-motivated surveillance Proposed: Incorporate predictive covariate data, such as - human population characteristics - climatic variables - season/day identifiers and for vectored diseases: - elevation / topography - wetland proximity - ecoregions - land cover / vegetation characteristics 127

128 128

129 How to combine all these data for purposes of surveillance? If risk is desired at, say, the town/township level, then modelling may be applied using towns as observational units. So for i = 1,, n towns, each town is represented by the outcome and covariates (as discussed). Models may then be used to predict risk, which may serve different purposes: - providing a basis for comparison of future observations - use risk predictions themselves to identify hot spots 129

130 Predicting WNV activity through adjusted dead crow counts Currently, dead crow counts provide weekly indication of WNV activity prior to obtaining lab results. Subject to extreme observation bias, as counts are directly proportional to human population density. 130

131 2002 dead crow locations 131

132 Breeding Bird Atlas indicates more uniform distribution 132

133 133

134 Although the risk of at least one person getting infected is also proportional to population density, the risk of any one individual in a rural area may be no less than an individual in a more populated area but dead crow clusters alone may not indicate this. So, how do we go beyond just identifying dead crows clusters in order to predict risk within small geographic areas (i.e. towns) in a way that adjusts for other variables related to crow and mosquito habitat? 134

135 Once the baseline dataset is established, from associating each area (say, town) with fundamental geo-spatial data, then a WNV risk map may be updated weekly by running the model for current week s crow counts and other covariates that change weekly, like rainfall. 135

136 Atlantic Slope Consortium Watershed Classification Modeling ecological condition in upstream watersheds and downstream estuaries in the Atlantic Slope Region D.H. Wardrop,, R.P. Brooks, G.P. Patil, W. Myers, M.M. Easterling,, and C. Taille

137 Penn State University Smithsonian Environmental Research Center Virginia Institute of Marine Science East Carolina University Environmental Law Institute FTN Associates Atlantic Slope Project 137

138 What s s the question? How do we develop a useful, relevant, and defensible set of indicators for the Atlantic Slope? We know how to do defensible This story is all about combining defensible ecology with relevant and useful in the Atlantic Slope Tools: watershed and estuarine segment classification for experimental design and identification of critical areas 138

139 Ecosystem State Ecosystem State Stress Stress Ecosystem State F 1 F 2 Ecosystem State F 2 Stress Stress Schematic representation of four possible responses of ecosystems to stress. Reproduced from Panarchy, 2002, Island Press. 139

140 Vision Statement Using a universe of watersheds and estuarine segments, covering a range of social choices, we ask two questions: How good can the environment be, given those social choices? What is the intellectual model of condition within those choices, i.e., what are the causes of condition and what are the steps for improvement? 140

141 Indicator Taxonomy Social Choices Assess condition Diagnose condition Measure management performance Communicate condition to the public and stakeholders Using a universe of watersheds, covering a range of social choices, we ask two questions: How good can the environment be, given those social choices? What is the intellectual model of condition within those choices, i.e., what are the causes of condition and what are the steps for improvement? 141

142 Resulting Process Define Watershed Types Compile Frequency Distributions Designate Sampling Design Distribute Candidate Watersheds 142

143 Ternary Plot Description Require a fuller pct_urban description of departure.2 from reference than.8 disturbed.4.6 Describes land use via the three main land.6.4 cover types.2 Can be used at any spatial extent (as can land cover %) pct_forest.8 pct_ag 143

144 Allegheny Plateau pct_urban pct_ag pct_forest

145 Ridge and Valley Watersheds pct_urban pc t_ag pc t_forest

146 Piedmont Watersheds pct_urban pct_ag pct_forest

147 Coastal Plain Watersheds pct_urban pct_ag pct_forest

148 Clustering Analysis should follow vision statement Clustered first on land uses (social choices) and slope (susceptibility of resource to land use) Binned on research question (many ways to be a mixed watershed) Other binning possible 148

149 High Slope High Forest Low Slope Low Forest, High Ag Low Slope High Urban Low Slope Moderate Forest Moderate Ag Moderate Slope High Nodal Var Low Nodal Var 149

150 Results Six watershed classes identified: 1. Forested, high slope 2. Forested, low slope 3. Agricultural 4. Urban 5. Mixed, low nodal variance 6. Mixed, high nodal variance 150

151 151

152 152

153 153

154 154

155 155

156 Logo for Statistics, Ecology, Environment, and Society 156