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A Conditional Approach to Point Process Modelling of Elevated Risk

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  • Peter J. Diggle
  • Barry S. Rowlingson

Abstract

We consider the problem of investigating the elevation in risk for a specified disease in relation to possible environmental factors. Our starting point is an inhomogeneous Poisson point process model for the spatial variation in the incidence of cases and controls in a designated geographic region, as proposed by Diggle. We develop a conditional approach to inference which converts the point process model to a non‐linear binary regression model for the spatial variation in risk. Simulations suggest that the usual asymptotic approximations for likelihood‐based inference are more reliable in this conditional setting than in the original point process setting. We present an application to some data on the spatial distribution of asthma in relation to three industrial locations.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:157:y:1994:i:3:p:433-440
    DOI: 10.2307/2983529
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    References listed on IDEAS

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    1. Colin Muirhead & Sarah Darby, 1989. "Royal Statistical Society Meeting on Cancer Near Nuclear Installations," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 152(3), pages 305-305, May.
    2. 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.
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    Cited by:

    1. Cucala, Lionel, 2009. "A flexible spatial scan test for case event data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2843-2850, June.
    2. Lawson, Andrew B. & Simeon, Silvia & Kulldorff, Martin & Biggeri, Annibale & Magnani, Corrado, 2007. "Line and point cluster models for spatial health data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6027-6043, August.
    3. Nelson B. Walker & Trevor J. Hefley & Daniel P. Walsh, 2020. "Bias correction of bounded location error in binary data," Biometrics, The International Biometric Society, vol. 76(2), pages 530-539, June.
    4. 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.
    5. Xiaojian Yi & Peng Hou & Haiping Dong, 2020. "A Novel Risk-Based Prioritization Approach for Wireless Sensor Network Deployment in Pipeline Networks," Energies, MDPI, vol. 13(6), pages 1-15, March.
    6. Davidson, Marty, 2024. "Strategic Point Processes," OSF Preprints g5r9t, Center for Open Science.
    7. Hui Huang & Xiaomei Ma & Rasmus Waagepetersen & Theodore R. Holford & Rong Wang & Harvey Risch & Lloyd Mueller & Yongtao Guan, 2014. "A New Estimation Approach for Combining Epidemiological Data From Multiple Sources," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 11-23, March.
    8. 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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