VISUALIZING SPACE-TIME

UNCERTAINTY OF DENGUE

FEVER OUTBREAKS

Dr. Eric Delmel le

Geography & Earth Sciences

University of North Carolina at Charlotte

Objectives

• Evaluate the impact of positional and temporal

inaccuracies on identifying outbreaks of dengue

fever

• Implement Space-Time Kernel Density Estimation

(STKDE) on both observed and simulated datasets

• Monte-Carlo simulations for statistical significance

• Parallel computing approach to reduce effort

• Visualize results in a 3D framework

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Delmelle, E., Dony, C., Casas, I., Jia, M., & Tang, W. (2014). Visualizing the impact of space-time uncertainties on dengue fever patterns. International Journal of Geographical Information Science, (ahead-of-print), 1-21.

Introduction

• Vector-borne diseases (malaria, dengue fever)

spread very quickly under suitable conditions

• Prompt and accurate space-time analyses are necessary

to detect outbreaks in a timely manner and take

appropriate steps to curb expansion of the disease

• Accurate information should be disseminated among the

public to limit the risk of further contagion.

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Duncombe, J., et al., 2012. Review: geographical information systems for dengue surveillance. American Journal of Tropical Medicine and Hygiene, 86 (5), 753.

Eisen, L. and Eisen, R., 2011. Using geographic information systems and decision support systems for the prediction, prevention, and control of vector-borne diseases. Annual Review of Entomology, 56 (1), 41–61

Gubler, D.J. and Clark, G.G., 1995. Dengue/dengue hemorrhagic fever: the emergence of a global health problem. Emerging Infectious Diseases, 1 (2), 55..

Existing work on space-time modeling

• Space-time clustering and geosurveillance are critical

research areas when spatial epidemiological data have a

temporal signature.

• Significant research dedicated to the mapping of disease

intensities across an area and associated clusters.

• Exploratory (KDE) and confirmatory approaches

• Space-time clustering is a more recent research thread

• Computational and visualization issues

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• Aldstadt, J. and Getis, A., 2006. Using AMOEBA to create a spatial weights matrix and identify spatial clusters. Geographical Analysis, 38 (4), 327–343.

Bailey, T. and Gatrell, Q., 1995. Interactive spatial data analysis. Edinburgh Gate, England: Pearson Education Limited.

• Delmelle, E., et al., 2011. H.E.L.P: a GIS-based health exploratory analysis tool for practitioners. Applied Spatial Analysis and Policy, 4 (2), 113–137.

Knox, G.E., 1964. The detection of space-time iterations. Journal of the Royal Statistical Society,13, 25–29.

• Kulldorff, M., et al., 2005. A space–time permutation scan statistic for disease outbreak detection. PLoS Medicine, 2 (3), e59.

• Rogerson, P. and Yamada, I., 2008. Statistical detection and surveillance of geographic clusters. Boca Raton, FL: CRC Press.

Modeling space-time uncertainty

• Spat ia l and tempora l e r ro r

• Errors introduced during data collection and geocoding

will propagate in analysis, impact clustering tests

• Underestimation of local risk

• Misplacement of high-risk areas of a disease

• Misevaluation of spatial association

• Biased evidence for policy makers

• How does space-time uncertainty affect exploratory tests,

and how can space-time uncertainty be visualized?

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• Jacquez, G.M., 1999. Spatial statistics when locations are uncertain. Annals of GIS, 5 (2), 77–87. 600

• Jacquez, G., 2012. A research agenda: does geocoding positional error matter in health GIS studies? Spatial and Spatio-Temporal Epidemiology, 3 (1), 7–16.

• Malizia, N., 2012. The effect of data inaccuracy on tests of space-time interaction. Transactions in GIS. 630

• Malizia, N., 2013. Inaccuracy, uncertainty and the space-time permutation scan statistic. PLoS One, 8 (2), e52034.

• Zimmerman, D.L., et al., 2007. Modeling the probability distribution of positional errors incurred by residential address geocoding. International Journal of Health Geographics, 6 (1).

Framework

• Space-Time Kernel Density Estimation (STKDE)

• Summarizes space-time patterns of the underlying data sets

• Data collection on dengue fever outbreaks

• Geocoding approach and estimation of space-time uncertainty

• Monte-Carlo simulations to perturb datasets under

different uncertainty regimes

• Parallel computing approach and visualization

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Framework

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Space-time kernel density estimation

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• Delmelle, E., Dony, C., Casas, I., Jia, M., & Tang, W. (2014). Visualizing the impact of space-time uncertainties on dengue fever patterns. International Journal of Geographical Information

Science, (ahead-of-print), 1-21.

Collecting data on dengue fever

• Dengue fever data from SIVIGILA (Public Health

Surveillance System). Implicit geographic information.

• Data for the year 2010

• n=11760 (9606)

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• Delmelle, E., Casas, I., Rojas, J. H., & Varela, A. (2013). Spatio-temporal patterns of Dengue Fever in Cali, Colombia. International Journal of Applied Geospatial Research, 4(4), 58-75.

What does the data look like?

• Cumulative presence

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• Demonstration in a

3D environment

Space-time kernel density estimation

• Extension of the kernel density through time.

• Input: set of space-time explicit data points

• Ouput: set of voxels where each voxel is a density

• 𝑥, 𝑦, 𝑡 : discretized set of voxels

• 𝑥𝑖 , 𝑦𝑖 , 𝑡𝑖 : location of space-time points

• 𝑘𝑠, 𝑘𝑡: kernel density function

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• Delmelle, E., Dony, C., Casas, I., Jia, M., & Tang, W. (2014). Visualizing the impact of space-time uncertainties on dengue fever patterns. International Journal of Geographical Information

Science, (ahead-of-print), 1-21.

• Demšar, U. and Virrantaus, K., 2010. Space–time density of trajectories: exploring spatio-temporal patterns in movement data. International Journal of Geographical Information Science, 24

(10), 1527–1542.

• Nakaya, T., and Yano, K., 2010. Visualising crime clusters in a space-time cube: an exploratory data-analysis approach using space-time kernel density estimation and scan statistics.

Transactions in GIS, 14 (3), 223–239.

𝑓 (𝑥, 𝑦, 𝑡) =1

𝑛ℎ𝑠2ℎ𝑡

𝐼(𝑑𝑖 < ℎ𝑠, t𝑖 < ℎt)𝑘𝑠𝑥−𝑥𝑖

ℎ𝑠,𝑦−𝑦𝑖

ℎ𝑠 𝑘𝑡(

𝑡−𝑡𝑖

ℎ𝑡)𝑖

Impact of parameters

• Impact of STKDE parameters on computational effort

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Visualization

• The kernel density volume is rendered by estimating a

density value for each of the voxels

• Color-coding each voxel based on its density value (rainbow)

• Voxels with lower kernel density values are assigned a higher level

of transparency whereas higher densities are kept opaque

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Visualization

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Temporal cross section Cross-sectional cuts

Estimating spatial uncertainty

• We measures GPS-based location of dengue fever cases

that were geocoded and estimate the error in the data

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• Jacquez, G.M., 1999. Spatial statistics when locations are uncertain. Annals of GIS, 5 (2), 77–87. 600

• Jacquez, G., 2012. A research agenda: does geocoding positional error matter in health GIS studies? Spatial and Spatio-Temporal Epidemiology, 3 (1), 7–16.

• Zimmerman, D.L., et al., 2007. Modeling the probability distribution of positional errors incurred by residential address geocoding. International Journal of Health Geographics, 6 (1).

mean error length=66.4m;

median=56.4m,

min-max=0-273.6m.

Monte-Carlo simulations

• Space-time data is perturbed according to uncertainty

around the estimates

• Spatial coordinates are perturbed by a ∆d factor, and

temporal coordinates by ∆t.

• The new coordinates are given by:

• {xi′, yi

′, ti′} = {xi ± α, yi ± β, ti ± ∆t}

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• This process is similar to geomasking.

{xi′, yi

′}

{xi, yi}

Parallel computation approach

• The derivation of STKDE of a point pattern consumes

considerable computing resources

• Conduct STKDE for each voxel

• Conduct STKDE on observed and simulated datasets

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• Armstrong, M. P., and P. J. Densham. 1992. Domain decomposition for parallel processing of spatial problems. Computers, environment and urban systems 16 (6):497-513.

• Ding, Y., and P. J. Densham. 1996. Spatial strategies for parallel spatial modelling. IJGIS 10 (6):669-698.

Visualization on simulated sets

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Demonstration in Voxel

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• Observed dataset

• Simulated dataset

Discussion and Conclusions

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• Dengue fever can take dramatic proportions when conditions (e.g. population, climate, behavior) are optimal.

• We develop a spatial and temporal extension of the KDE algorithm to map spacetime clusters of dengue fever.

• We perturb each geocoded dengue fever case following a spatial and temporal error (Monte Carlo simulations).

• We conduct STKDE on both observed and simulated sets.

• We use a parallelized computation approach

Discussion and Conclusions

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• Significant clusters appear different from one another

• Compactness, length, reoccurrence, eradication

• Maximum and minimum extent of clusters are generated

from the STKDE on simulated sets.

• Non spatially overlapping envelopes indicate a sensitivity to

geocoding error, while non temporal overlapping envelopes

indicate sensitivity to temporal error, for instance around the

diagnosis.

• Mapping uncertainty allows decision makers to build

confidence around their actions.

Future research

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• Data structure needs to be accounted for in parallel

processing to prevent workload imbalance

• How to optimally partition space-time regions?

1

2

3

Blind decomposition

Quadtree approach

Workload imbalances

Future research

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• Comparing 2D to 3D approaches

• Compare outputs at different times

1 Is KDE better than STKDE? (Effectiveness, efficacy)

2 Can I generate STKDE output for these time intervals where something happened. We could take the derivative or the PDF and identify time where the phenomenon varies the most?

Team

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• Dr. Eric Meijuan

Delmelle Jia

• Dr Wenwu Alexander

Tang Hohl

• Coline Dr. Irene

Dony Casas

2013+ recent research trends

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Mapping vulnerability to dengue fever

3D mapping of cell phone strength and associated SOM trajectories

On-line tools for the mapping of disease patterns

1 2

4 3 Optimal school location planning