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Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

Author

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  • Mohammadreza Mohebbi

    (Biostatistics Unit, Faculty of Health, Deakin University, Melbourne 3125, Australia
    Department of Epidemiology and Preventive Medicine, Faculty of Medicine, Nursing and Health Sciences, Monash University, Melbourne 3000, Australia)

  • Rory Wolfe

    (Department of Epidemiology and Preventive Medicine, Faculty of Medicine, Nursing and Health Sciences, Monash University, Melbourne 3000, Australia)

  • Andrew Forbes

    (Department of Epidemiology and Preventive Medicine, Faculty of Medicine, Nursing and Health Sciences, Monash University, Melbourne 3000, Australia)

Abstract

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

Suggested Citation

  • Mohammadreza Mohebbi & Rory Wolfe & Andrew Forbes, 2014. "Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach," IJERPH, MDPI, vol. 11(1), pages 1-20, January.
  • Handle: RePEc:gam:jijerp:v:11:y:2014:i:1:p:883-902:d:32039
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    References listed on IDEAS

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    Cited by:

    1. Chawarat Rotejanaprasert & Andrew B. Lawson, 2018. "A Bayesian Quantile Modeling for Spatiotemporal Relative Risk: An Application to Adverse Risk Detection of Respiratory Diseases in South Carolina, USA," IJERPH, MDPI, vol. 15(9), pages 1-15, September.
    2. Chien-Chou Chen & Guo-Jun Lo & Ta-Chien Chan, 2022. "Spatial Analysis on Supply and Demand of Adult Surgical Masks in Taipei Metropolitan Areas in the Early Phase of the COVID-19 Pandemic," IJERPH, MDPI, vol. 19(11), pages 1-12, May.
    3. I. Gede Nyoman Mindra Jaya & Budhi Handoko & Yudhie Andriyana & Anna Chadidjah & Farah Kristiani & Mila Antikasari, 2023. "Multivariate Bayesian Semiparametric Regression Model for Forecasting and Mapping HIV and TB Risks in West Java, Indonesia," Mathematics, MDPI, vol. 11(17), pages 1-23, August.

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