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A Point Process Modelling Approach to Raised Incidence of a Rare Phenomenon in the Vicinity of a Prespecified Point

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  • Peter J. Diggle

Abstract

Motivated by the current debate on possible raised incidence of certain types of cancers near nuclear installations, this paper develops a methodology for fitting a class of inhomogeneous Poisson point process models to data consisting of the locations of all occurrences of some phenomenon of interest within a designated planar region. The model is based on a multiplicative decomposition of the intensity function, with separate terms to describe natural spatial variation in intensity and possible raised incidence around a prespecified point. A nonparametric kernel smoothing approach, based on data from a related phenomenon, is used to describe natural spatial variation, while a parametric maximum likelihood approach is used to describe raised incidence near the prespecified point. The methodology is applied to data on the spatial distribution of cancers of the larynx and of the lung in the Chorley‐Ribble area of Lancashire, England.

Suggested Citation

  • Peter J. Diggle, 1990. "A Point Process Modelling Approach to Raised Incidence of a Rare Phenomenon in the Vicinity of a Prespecified Point," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 153(3), pages 349-362, May.
    • Handle: RePEc:bla:jorssa:v:153:y:1990:i:3:p:349-362
    DOI: 10.2307/2982977
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    Cited by:

    1. Davies, Tilman M. & Jones, Khair & Hazelton, Martin L., 2016. "Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 12-28.
    2. Dale L. Zimmerman, 2008. "Estimating the Intensity of a Spatial Point Process from Locations Coarsened by Incomplete Geocoding," Biometrics, The International Biometric Society, vol. 64(1), pages 262-270, March.
    3. Angela L. Riffo-Campos & Guillermo Ayala & Francisco Montes, 2021. "Gene Set Analysis Using Spatial Statistics," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    4. Cucala, Lionel, 2009. "A flexible spatial scan test for case event data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2843-2850, June.
    5. Ronald E. Gangnon & Murray K. Clayton, 2000. "Bayesian Detection and Modeling of Spatial Disease Clustering," Biometrics, The International Biometric Society, vol. 56(3), pages 922-935, September.
    6. Takuo Matsubara & Jeremias Knoblauch & François‐Xavier Briol & Chris J. Oates, 2022. "Robust generalised Bayesian inference for intractable likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 997-1022, July.
    7. Peter J. Diggle & Barry S. Rowlingson, 1994. "A Conditional Approach to Point Process Modelling of Elevated Risk," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(3), pages 433-440, May.
    8. S P Kingham & A C Gatrell & B Rowlingson, 1995. "Testing for Clustering of Health Events within a Geographical Information System Framework," Environment and Planning A, , vol. 27(5), pages 809-821, May.
    9. Alexandre Rodrigues & Peter Diggle & Renato Assuncao, 2010. "Semiparametric approach to point source modelling in epidemiology and criminology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 533-542, May.
    10. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    11. Álvaro Briz‐Redón & Jorge Mateu & Francisco Montes, 2022. "Identifying crime generators and spatially overlapping high‐risk areas through a nonlinear model: A comparison between three cities of the Valencian region (Spain)," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 97-120, February.
    12. Martin L. Hazelton & Tilman M. Davies, 2022. "Pointwise comparison of two multivariate density functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1791-1810, December.
    13. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.
    14. A C Gatrell & C E Dunn & P J Boyle, 1991. "The Relative Utility of the Central Postcode Directory and Pinpoint Address Code in Applications of Geographical Information Systems," Environment and Planning A, , vol. 23(10), pages 1447-1458, October.
    15. Fuqiang Dai & Hao Liu & Xia Zhang & Qing Li, 2021. "Exploring the Emerging Trends of Spatial Epidemiology: A Scientometric Analysis Based on CiteSpace," SAGE Open, , vol. 11(4), pages 21582440211, November.
    16. Carl Schmertmann & Renato Assunção & Joseph Potter, 2010. "Knox meets Cox: Adapting epidemiological space-time statistics to demographic studies," Demography, Springer;Population Association of America (PAA), vol. 47(3), pages 629-650, August.
    17. Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.

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