Upper level set scan statistic for detecting arbitrarily shaped hotspots
Tóm tắt
A declared need is around for geoinformatic surveillance statistical science and software infrastructure for spatial and spatiotemporal hotspot detection. Hotspot means something unusual, anomaly, aberration, outbreak, elevated cluster, critical resource area, etc. The declared need may be for monitoring, etiology, management, or early warning. The responsible factors may be natural, accidental, or intentional. This proof-of-concept paper suggests methods and tools for hotspot detection across geographic regions and across networks. The investigation proposes development of statistical methods and tools that have immediate potential for use in critical societal areas, such as public health and disease surveillance, ecosystem health, water resources and water services, transportation networks, persistent poverty typologies and trajectories, environmental justice, biosurveillance and biosecurity, among others. We introduce, for multidisciplinary use, an innovation of the health-area-popular circle-based spatial and spatiotemporal scan statistic. Our innovation employs the notion of an upper level set, and is accordingly called the upper level set scan statistic, pointing to a sophisticated analytical and computational system as the next generation of the present day popular SaTScan. Success of surveillance rests on potential elevated cluster detection capability. But the clusters can be of any shape, and cannot be captured only by circles. This is likely to give more of false alarms and more of false sense of security. What we need is capability to detect arbitrarily shaped clusters. The proposed upper level set scan statistic innovation is expected to fill this need
Tài liệu tham khảo
Aarts, E. and Korst, J. (1989) Simulated Annealing and Boltzmann Machines, Wiley, Chichester.
Bickel, P.J. and Doksum, K.A. (1977) Mathematical Statistics: Basic Ideas and Selected Topics, Holden-Day, San Francisco.
Bithell, J.F., Dutton, S.J., Neary, N.M., and Vincent, T.J. (1995) Controlling for socioeconomic confounding using regression methods. Community Health, 49, S15-S19.
Cormen, T.H., Leierson, C.E., Rivest, R.L., and Stein, C. (2001) Introduction to Algorithms (second edition), MIT Press, Cambridge, Massachusetts.
Cressie, N. (1991) Statistics for Spatial Data, Wiley, New York.
Davies, R.B. (1977) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 64, 247-54.
Duczmal, L. and Assunçã, R.A. (2004) A simulated annealing strategy for the detection of arbitrarily shaped spatial clusters. Computational Statistics and Data Analysis, in press.
Dwass, M. (1957) Modified randomization tests for nonparametric hypotheses. Annals of Mathematical Statistics, 28, 181-7.
Glaz, J. and Balakrishnan, N. (eds) (1999) Scan Statistics and Applications, Birkhauser, Boston.
Glaz, J., Naus, J., and Wallenstein, S. (2001) Scan Statistics, Springer-Verlag, New York.
Knjazew, D. (2002) OmeGA: A Competent Genetic Algorithm for Solving Permutation and Scheduling Problems, Kluwer Academic Publishers, Boston, Massachusetts.
Knuth, D.E. (1973) The Art of Computer Programming: Volume 1, Fundamental Algorithms, (second edition), Addison-Wesley, Reading, Massachusetts.
Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics: Theory and Methods, 26, 1481-96.
Kulldorff, M. (2001) Prospective time-periodic geographical disease surveillance using a scan statistic. Journal of the Royal Statistical Society, Series A, 164, 61-72.
Kulldorff, M., Feuer, E.J., Miller, B.A., and Freedman, L.S. (1997) Breast cancer clusters in Northeast United States: A geographic analysis. American Journal of Epidemiology, 146, 161-70.
Kulldorff, M., Huang, L., and Pickle, L. (2004) An elliptic spatial scan statistic. Manuscript, to be submitted.
Kulldorff, M. and Nagarwalla, N. (1995) Spatial disease clusters: Detection and inference. Statistics in Medicine, 14, 799-810.
Kulldorff, M., Rand, K., Gherman, G., Williams, G., and DeFrancesco, D. (1998) SaTScan version 2.1: Software for the spatial and space-time scan statistics. National Cancer Institute, Bethesda, MD.
Lehmann, E.L. (1986) Testing Statistical Hypotheses (second edition), Wiley, New York.
Mostashari, F., Kulldorff, M., and Miller, J. (2002) Dead bird clustering: An early warning system for West Nile virus activity. (Manuscript prepared for the New York City West Nile Virus Surveillance Working Group.) Under review.
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992) Numerical Recipes in C (second edition), Cambridge University Press, Cambridge.
Rogerson, P.A. (2001) Monitoring point patterns for the development of space-time clusters. Journal of the Royal Statistical Society, Series A, 164, 87-96.
Waller, L. (2002) Methods for detecting disease clustering in time or space. In Statistical Methods and Principles in Public Health Surveillance, R. Brookmeyer and D. Stroup (eds), Oxford University Press, Oxford.
Walsh, S.J. and DeChello, L.M. (2001) Geographical variation in mortality from systemic lupus erythematosus in the United States. Lupus, 10, 637-46.
Walsh, S.J. and Fenster, J.R. (1997) Geographical clustering of mortality from systemic sclerosis in the Southeastern United States, 1981–1990. The Journal of Rheumatology, 24, 2348-52.
Winkler, G. (1995) Image Analysis, Random Fields and Dynamic Monte Carlo Methods, Springer, New York.