1 Tests for Spatial Clustering zglobal statistic yaggregate / points xk-function xGrimsons method xCuzick & Edwards method xJoin Count yaggregate data.

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Tests for Spatial Clustering

global statistic aggregate / points

k-function Grimson’s method Cuzick & Edward’s method Join Count

aggregate data Geary’s C Moran’s I

local statistic spatial scan statistic LISA statistic geographical analysis machine (GAM)

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K - Function

summary of local dependence of spatial process -> second order process

expresses number of expected events within given distance of randomly chosen event

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Example: k – Function for Newcastle Disease Outbreak

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TB Case-Control Study in Central North Island of NZ

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Cuzick and Edward’s Test applied to TB Case-Control Study

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Legend0 - 0.690.69 - 2.032.03 - 3.583.58 - 5.85.8 - 10.18

Local Spatial Autocorrelation

Local MoranLocal Geary

Legend-0.59 - -0.21-0.21 - 0.120.12 - 0.60.6 - 2.12.1 - 6.75

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Spatial Scan Statistic

no pre-specified cluster sizecan take confounding into accountalso does time - space clusteringmethod

increasing circles (cylinders if including time) compare risk within with outside circle most likely cluster -> circle with maximum

likelihood (more than expected number of cases)

SaTScan software (public domain)

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Example - SaTScan

locations of den sites of tuberculous and non-tuberculous possums

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Example - SaTScan cont.

MOST LIKELY CLUSTER1. Coordinates / radius..: (348630,708744) / 126.65 Population............: 56 Number of cases.......: 34 (16.44 expected) Overall relative risk.: 2.07 Log likelihood ratio..: 15.86 P-value...............: 0.001SECONDARY CLUSTERS2. Coordinates / radius..: (348491,708496) / 33.35 Population............: 5 Number of cases.......: 5 (1.47 expected) Overall relative risk.: 3.41 Log likelihood ratio..: 6.25 P-value...............: 0.3373. Coordinates / radius..: (348369,708453) / 80.55 Population............: 8 Number of cases.......: 7 (2.35 expected) Overall relative risk.: 2.98 Log likelihood ratio..: 6.13 P-value...............: 0.365

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Example - SaTScan cont.

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Space-Time Scan Statistic

MOST LIKELY CLUSTER

1.Census areas included.: 75, 26, 77, 76, 29, 32

Coordinates / radius..: (389631,216560) / 59840.47

Time frame............: 1997/1/1 - 1999/12/31

Population............: 4847

Number of cases.......: 1507 (632.85 expected)

Overall relative risk.: 2.38

Log likelihood ratio..: 509.4

Monte Carlo rank......: 1/1000

P-value...............: 0.001

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Framework for Spatial Data Analysis

Visualization

Exploration

Modelling

Attribute data

Feature data

Databases

Maps

Describe patterns

Test hypothese

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GISDBMS

StatisticalSoftware

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Modelling

explain and predict spatial structure hypothesis testing

methods data mining statistical and simulation modelling multi-criteria/multi-objective decision

modellingproblem -> spatial dependence

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3D Risk Map for FMD Outbreak Occurrence in Thailand(based on random effects logistic regression analysis)

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Recent Developments in Spatial Regression Modelling

generalised linear mixed models (GLMM) use random effect term to reflect spatial

structureimpose spatial covariance structuresBayesian estimation, Markov chain Monte

Carlo (MCMC), Gibbs sampling

autologistic regression include spatial covariate MCMC estimation

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Bayesian Regression Modelling

Bayesian inference combines

information from data (likelihood)prior distributions for unknown parameters

to generateposterior distribution of dependent variable

allows modelling of data heterogeneity, addresses multiplicity issues

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TB Reactor Risk Modelling

dependent variable -> observed TB reactors per county in 1999 in GB

Poisson regression model MCMC estimation expected no. TB reactors two random effects (convolution prior)

spatial – conditionally autoregressive (CAR) prior

non-spatial – exchangeable normal prior

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Raw Standardised Morbidity Ratio

BUGS softwarewith GeoBUGS extension

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Example – Kernel Density Plots

RR[25] sample: 5000

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Raw SMR and Posterior Relative Risk Maps

raw SMR Bayes’ RRestimates

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Medians and 95% CI of Posterior Relative Risks

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Model Residuals and RR Significance

RR[31] sample: 10000

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Relative Importance of Structured versus Unstructured Random Effect

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Multi-Criteria Decision Making using GIS

decision -> choice between alternatives vaccinate wildlife or not

criterion -> evidence used to decide on decision factors and constraints

presence of wildlife reservoircattle stocking densityaccess to wildlife for vaccine delivery

decision rule -> procedure for selection and combination of criteria

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Multi-Criteria Decision Making in GIS cont.

evaluation -> application of decision rules multi-criteria evaluations

boolean overlaysweighted linear combinations

uncertainty database uncertainty decision rule uncertainty -> fuzzy versus crisp

setsdecision risk -> likelihood of decision being

wrong -> Bayesian probability theory, Dempster-Shafer Theory

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Dempster - Shafer Theory

extension of Bayesian probability theorydata uncertainty included in calculation ->

belief in hypothesis not complement of belief in negation (sensitivity of diagnosis)

collect different sources of evidence for presence/absence (data, expert knowledge) re-express as probability

combine evidence as mass of support for particular hypothesis

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More about Dempster-Shafer Theory

belief total support for hypothesis degree of hard evidence supporting hypothesis

plausibility degree to which hypothesis cannot be

disbelieved degree to which conditions appear to be right

for hypothesis, even though hard evidence is lacking

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Even more about Dempster-Shafer Theory

belief interval range between belief and plausibility degree of uncertainty in establishing

presence/absence of hypothesis areas with high belief interval suitable for

collection of new data

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Example – East Coast Fever Occurrence in Zimbabwe

Belief in T.parva Presence

Belief interval for T.parva Presence(Degree of uncertainty)

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Landscape Structure

quantify landscape structure/composition

habitat features as a whole

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TB Infected Herds around Hauhungaroa Ranges in NZ

Vegetation classespasturepasture/scrubscrublandforest

Farm boundaries

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Framework for Spatial Data Analysis

Visualization

Exploration

Modelling

Attribute data

Feature data

Databases

Maps

Describe patterns

Test hypothese

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GISDBMS

StatisticalSoftware

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Conclusion

spatial analysis essential component of epidemiological analysis

key ideas visualization -> extremely effective for

analysis and presentation exploration -> cluster detection

methods (beware of type I error) modelling -> Bayesian modelling and

decision analysis techniques