Research article
A poisson regression approach for modelling spatial autocorrelation between geographically referenced observations
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* Corresponding author: Mohammadreza Mohebbi Mohammadreza.Mohebbi@monash.edu
Department of Epidemiology and Preventive Medicine, Faculty of Medicine, Nursing and Health Sciences, Monash University, Melbourne, Australia
BMC Medical Research Methodology 2011, 11:133 doi:10.1186/1471-2288-11-133
Published: 3 October 2011Abstract
Background
Analytic methods commonly used in epidemiology do not account for spatial correlation between observations. In regression analyses, omission of that autocorrelation can bias parameter estimates and yield incorrect standard error estimates.
Methods
We used age standardised incidence ratios (SIRs) of esophageal cancer (EC) from the Babol cancer registry from 2001 to 2005, and extracted socioeconomic indices from the Statistical Centre of Iran. The following models for SIR were used: (1) Poisson regression with agglomeration-specific nonspatial random effects; (2) Poisson regression with agglomeration-specific spatial random effects. Distance-based and neighbourhood-based autocorrelation structures were used for defining the spatial random effects and a pseudolikelihood approach was applied to estimate model parameters. The Bayesian information criterion (BIC), Akaike's information criterion (AIC) and adjusted pseudo R2, were used for model comparison.
Results
A Gaussian semivariogram with an effective range of 225 km best fit spatial autocorrelation in agglomeration-level EC incidence. The Moran's I index was greater than its expected value indicating systematic geographical clustering of EC. The distance-based and neighbourhood-based Poisson regression estimates were generally similar. When residual spatial dependence was modelled, point and interval estimates of covariate effects were different to those obtained from the nonspatial Poisson model.
Conclusions
The spatial pattern evident in the EC SIR and the observation that point estimates and standard errors differed depending on the modelling approach indicate the importance of accounting for residual spatial correlation in analyses of EC incidence in the Caspian region of Iran. Our results also illustrate that spatial smoothing must be applied with care.