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Modelling spatial disease rates using maximum likelihood.

B G Leroux1

  • 1Department of Biostatistics, Box 357232, University of Washington, Seattle WA 98195, USA. leroux@biostat.washington.edu

Statistics in Medicine
|August 29, 2000
PubMed
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Maximum likelihood (ML) estimation for generalized linear mixed models (GLMMs) in spatial disease modeling showed mixed results. ML provided less biased intercept estimates but was more variable than penalized quasi-likelihood (PQL) for small samples.

Area of Science:

  • Biostatistics
  • Epidemiology
  • Spatial Statistics

Background:

  • Generalized linear mixed models (GLMMs) are crucial for analyzing complex disease rate data.
  • Modeling spatial disease rates requires accounting for both covariate effects and spatial autocorrelation.
  • Accurate estimation methods are vital for reliable public health insights.

Purpose of the Study:

  • To evaluate maximum likelihood (ML) estimation for GLMMs in spatial disease rate modeling.
  • To compare the performance of ML with penalized quasi-likelihood (PQL) estimation.
  • To investigate the impact of a novel covariance structure on parameter estimation.

Main Methods:

  • Developed a GLMM incorporating log-linear covariates and spatially correlated random effects.

Related Experiment Videos

  • Utilized a recently proposed covariance structure parameterizing spatial dependence via the inverse covariance matrix.
  • Implemented a Markov chain Monte Carlo (MCMC) algorithm for ML estimation.
  • Conducted a computer simulation study to compare ML and PQL estimators.

    • Main Results:

    • ML yielded less biased intercept estimates compared to PQL, though with slightly higher variability.
    • Estimates for other regression coefficients were unbiased and comparable between ML and PQL.
    • ML estimators for random effects standard deviation and spatial correlation showed greater bias than PQL estimators.
    • Performance differences were most pronounced in small sample scenarios.

    Conclusions:

    • Maximum likelihood estimation for GLMMs in spatial disease modeling may not outperform PQL for small sample sizes.
    • The choice between ML and PQL depends on the specific parameters of interest and sample size.
    • Further research may be needed to refine ML methods for improved small-sample performance in spatial analyses.