Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

Peter J. Diggle Peter Diggle is Distinguished University Professor, School of Health and Medicine, Lancaster University, Lancaster, U.K. and Adjunct Professor, Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore . Yongtao Guan is Associate Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 and is corresponding author. Fauzia Paize is a Research Fellow, Institute of Child Health, University of Liverpool, Alder Hey Children’s NHS Foundation Trust, Liverpool, U.K. . C. Anthony Hart was Professor of Medical Microbiology, Division of Medical Microbiology, University of Liverpool, Liverpool, U.K. (deceased September 2007). Michelle Stanton is Research Student, School of Health and Medicine, Lancaster University, Lancaster, U.K. . Yongtao Guan’s research was supported in part by NSF grant DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. Michelle Stanton’s research was supported by the award of a research studentship by the U.K. Engineering and Physical Sciences Research Council. Data on childhood meningococcal disease in Merseyside, U.K., were collected by Alistair Thomson, Omnia Marzouk, Andrew Riordan, Paul Baines, Enitan Carrol, Scott Hackett, and Niten Makwana, Alder Hey Children’s Hospital, Merseyside.

Yongtao Guan Peter Diggle is Distinguished University Professor, School of Health and Medicine, Lancaster University, Lancaster, U.K. and Adjunct Professor, Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore . Yongtao Guan is Associate Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 and is corresponding author. Fauzia Paize is a Research Fellow, Institute of Child Health, University of Liverpool, Alder Hey Children’s NHS Foundation Trust, Liverpool, U.K. . C. Anthony Hart was Professor of Medical Microbiology, Division of Medical Microbiology, University of Liverpool, Liverpool, U.K. (deceased September 2007). Michelle Stanton is Research Student, School of Health and Medicine, Lancaster University, Lancaster, U.K. . Yongtao Guan’s research was supported in part by NSF grant DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. Michelle Stanton’s research was supported by the award of a research studentship by the U.K. Engineering and Physical Sciences Research Council. Data on childhood meningococcal disease in Merseyside, U.K., were collected by Alistair Thomson, Omnia Marzouk, Andrew Riordan, Paul Baines, Enitan Carrol, Scott Hackett, and Niten Makwana, Alder Hey Children’s Hospital, Merseyside.

Anthony C. Hart Peter Diggle is Distinguished University Professor, School of Health and Medicine, Lancaster University, Lancaster, U.K. and Adjunct Professor, Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore . Yongtao Guan is Associate Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 and is corresponding author. Fauzia Paize is a Research Fellow, Institute of Child Health, University of Liverpool, Alder Hey Children’s NHS Foundation Trust, Liverpool, U.K. . C. Anthony Hart was Professor of Medical Microbiology, Division of Medical Microbiology, University of Liverpool, Liverpool, U.K. (deceased September 2007). Michelle Stanton is Research Student, School of Health and Medicine, Lancaster University, Lancaster, U.K. . Yongtao Guan’s research was supported in part by NSF grant DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. Michelle Stanton’s research was supported by the award of a research studentship by the U.K. Engineering and Physical Sciences Research Council. Data on childhood meningococcal disease in Merseyside, U.K., were collected by Alistair Thomson, Omnia Marzouk, Andrew Riordan, Paul Baines, Enitan Carrol, Scott Hackett, and Niten Makwana, Alder Hey Children’s Hospital, Merseyside.

Fauzia Paize Peter Diggle is Distinguished University Professor, School of Health and Medicine, Lancaster University, Lancaster, U.K. and Adjunct Professor, Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore . Yongtao Guan is Associate Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 and is corresponding author. Fauzia Paize is a Research Fellow, Institute of Child Health, University of Liverpool, Alder Hey Children’s NHS Foundation Trust, Liverpool, U.K. . C. Anthony Hart was Professor of Medical Microbiology, Division of Medical Microbiology, University of Liverpool, Liverpool, U.K. (deceased September 2007). Michelle Stanton is Research Student, School of Health and Medicine, Lancaster University, Lancaster, U.K. . Yongtao Guan’s research was supported in part by NSF grant DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. Michelle Stanton’s research was supported by the award of a research studentship by the U.K. Engineering and Physical Sciences Research Council. Data on childhood meningococcal disease in Merseyside, U.K., were collected by Alistair Thomson, Omnia Marzouk, Andrew Riordan, Paul Baines, Enitan Carrol, Scott Hackett, and Niten Makwana, Alder Hey Children’s Hospital, Merseyside.

Michelle Stanton Peter Diggle is Distinguished University Professor, School of Health and Medicine, Lancaster University, Lancaster, U.K. and Adjunct Professor, Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore . Yongtao Guan is Associate Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 and is corresponding author. Fauzia Paize is a Research Fellow, Institute of Child Health, University of Liverpool, Alder Hey Children’s NHS Foundation Trust, Liverpool, U.K. . C. Anthony Hart was Professor of Medical Microbiology, Division of Medical Microbiology, University of Liverpool, Liverpool, U.K. (deceased September 2007). Michelle Stanton is Research Student, School of Health and Medicine, Lancaster University, Lancaster, U.K. . Yongtao Guan’s research was supported in part by NSF grant DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. Michelle Stanton’s research was supported by the award of a research studentship by the U.K. Engineering and Physical Sciences Research Council. Data on childhood meningococcal disease in Merseyside, U.K., were collected by Alistair Thomson, Omnia Marzouk, Andrew Riordan, Paul Baines, Enitan Carrol, Scott Hackett, and Niten Makwana, Alder Hey Children’s Hospital, Merseyside.

Abstract

We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk-factors is available at the individual level for cases, but only at a spatially aggregated level for the population at risk. We develop data-driven methods to select the weights used in the estimating equations and show through simulation that the choice of weights can have a major impact on efficiency of estimation. We develop a formal test to detect non-Poisson behavior in the underlying point process and assess the performance of the test using simulations of Poisson and Poisson cluster point processes. We apply our methods to data on the spatial distribution of childhood meningococcal disease cases in Merseyside, U.K. between 1981 and 2007.

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Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

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