Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence

  • Brian G. Leroux
  • Xingye Lei
  • Norman Breslow
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 116)


In this paper, a new model is proposed for spatial dependence that includes separate parameters for overdispersion and the strength of spatial dependence. The new dependence structure is incorporated into a generalized linear mixed model useful for the estimation of disease incidence rates in small geographic regions. The mixed model allows for log-linear covariate adjustment and local smoothing of rates through estimation of the spatially correlated random effects. Computer simulation studies compare the new model with the following sub-models: intrinsic autoregression, an independence model, and a model with no random effects. The major finding was that regression coefficient estimates based on fitting intrinsic autoregression to independent data can have very low precision compared with estimates based on the full model. Additional simulation studies demonstrate that penalized quasi-likelihood (PQL) estimation generally performs very well although the estimates are slightly biased for very small counts.

Key words

Random effect log-linear model penalized quasi-likelihood Gaussian intrinsic auto-regression generalized linear mixed model Monte Carlo simulation 


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Brian G. Leroux
    • 1
  • Xingye Lei
    • 1
  • Norman Breslow
    • 1
  1. 1.Department of BiostatisticsUniversity of WashingtonSeattleUSA

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