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Statistical Modeling of Right-Censored Spatial Data Using Gaussian Random Fields

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  • Fathima Z. Sainul Abdeen

    (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA)

  • Akim Adekpedjou

    (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA)

  • Sophie Dabo Niang

    (Laboratoire Paul Painvelé UMR CNRS 8524, INRIA-MODAL, University of Lille, F-59000 Lille, France)

Abstract

Consider a fixed number of clustered areas identified by their geographical coordinates that are monitored for the occurrences of an event such as a pandemic, epidemic, or migration. Data collected on units at all areas include covariates and environmental factors. We apply a probit transformation to the time to event and embed an isotropic spatial correlation function into our models for better modeling as compared to existing methodologies that use frailty or copula. Composite likelihood technique is employed for the construction of a multivariate Gaussian random field that preserves the spatial correlation function. The data are analyzed using counting process and geostatistical formulation that led to a class of weighted pairwise semiparametric estimating functions. The estimators of model parameters are shown to be consistent and asymptotically normally distributed under infill-type asymptotic spatial statistics. Detailed small sample numerical studies that are in agreement with theoretical results are provided. The foregoing procedures are applied to the leukemia survival data in Northeast England. A comparison to existing methodologies provides improvement.

Suggested Citation

  • Fathima Z. Sainul Abdeen & Akim Adekpedjou & Sophie Dabo Niang, 2024. "Statistical Modeling of Right-Censored Spatial Data Using Gaussian Random Fields," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1521-:d:1393912
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    References listed on IDEAS

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