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Modeling Longitudinal Spatial Periodontal Data: A Spatially Adaptive Model with Tools for Specifying Priors and Checking Fit

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  • Brian J. Reich
  • James S. Hodges

Abstract

Summary Attachment loss (AL), the distance down a tooth's root that is no longer attached to surrounding bone by periodontal ligament, is a common measure of periodontal disease. In this article, we develop a spatiotemporal model to monitor the progression of AL. Our model is an extension of the conditionally autoregressive (CAR) prior, which spatially smooths estimates toward their neighbors. However, because AL often exhibits a burst of large values in space and time, we develop a nonstationary spatiotemporal CAR model that allows the degree of spatial and temporal smoothing to vary in different regions of the mouth. To do this, we assign each AL measurement site its own set of variance parameters and spatially smooth the variances with spatial priors. We propose a heuristic to measure the complexity of the site‐specific variances, and use it to select priors that ensure parameters in the model are well identified. In data from a clinical trial, this model improves the fit compared to the usual dynamic CAR model for 90 of 99 patients' AL measurements.

Suggested Citation

  • Brian J. Reich & James S. Hodges, 2008. "Modeling Longitudinal Spatial Periodontal Data: A Spatially Adaptive Model with Tools for Specifying Priors and Checking Fit," Biometrics, The International Biometric Society, vol. 64(3), pages 790-799, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:790-799
    DOI: 10.1111/j.1541-0420.2007.00956.x
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    References listed on IDEAS

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    1. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, December.
    2. Reich, Brian J. & Hodges, James S. & Carlin, Bradley P., 2007. "Spatial Analyses of Periodontal Data Using Conditionally Autoregressive Priors Having Two Classes of Neighbor Relations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 44-55, March.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    5. James S. Hodges & Bradley P. Carlin & Qiao Fan, 2003. "On the Precision of the Conditionally Autoregressive Prior in Spatial Models," Biometrics, The International Biometric Society, vol. 59(2), pages 317-322, June.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Brian J. Reich & James S. Hodges & Vesna Zadnik, 2006. "Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease-Mapping Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1197-1206, December.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Chiranjit Mukherjee & Prasad Kasibhatla & Mike West, 2014. "Spatially varying SAR models and Bayesian inference for high-resolution lattice data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 473-494, June.
    2. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    3. Lee, Duncan, 2013. "CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i13).
    4. Alastair Rushworth & Duncan Lee & Christophe Sarran, 2017. "An adaptive spatiotemporal smoothing model for estimating trends and step changes in disease risk," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 141-157, January.
    5. Lin Zhang & Veerabhadran Baladandayuthapani & Hongxiao Zhu & Keith A. Baggerly & Tadeusz Majewski & Bogdan A. Czerniak & Jeffrey S. Morris, 2016. "Functional CAR Models for Large Spatially Correlated Functional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 772-786, April.

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