On the convenience of heteroscedasticity in highly multivariate disease mapping

Abstract

Highly multivariate disease mapping has recently been proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential since it integrates the information of many diseases into a single model yielding richer and more accurate risk maps. In this paper we show how some of the proposals already put forward in this area display some particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. In this paper we propose two new models to deal with the variance-adaptivity problem in multivariate disease mapping studies and give some theoretical insights on their interpretation.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3

References

  1. Barnard J, McCulloch R, Meng XL (2000) Modeling covariance matrices in terms of standard deviations and correlations, with applications to shrinkage. Stat Sin 10:1281–1311

    MathSciNet  MATH  Google Scholar 

  2. Bernardinelli L, Clayton D, Montomoli C (1995) Bayesian estimates of disease maps: How important are priors? Stat Med 14:2411–2431

    Article  Google Scholar 

  3. Besag J, York J, Mollié A (1991) Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 43:1–21

    MathSciNet  Article  Google Scholar 

  4. Botella-Rocamora P, Martinez-Beneito MA, Banerjee S (2015) A unifying modeling framework for highly multivariate disease mapping. Stat Med 34(9):1548–1559

    MathSciNet  Article  Google Scholar 

  5. Congdon P (2008) A spatially adaptive conditional autoregressive prior for area health data. Stat Methodol 5:552–563

    MathSciNet  Article  Google Scholar 

  6. Gelman A, Carlin JB, Stern HS, Dunson D B, Vehtari A, Rubin D B (2014) Bayesian data analysis, 3rd edn. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  7. Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge

    Google Scholar 

  8. Gentle J E (2007) Matrix algebra. Theory, computations, and applications in statistics. Springer, Berlin

    Google Scholar 

  9. Lunn D, Thomas A, Best N, Spiegelhalter D (2000) WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Stat Comput 10:325–337

    Article  Google Scholar 

  10. MacNab Y, Kemetic A, Gustafson P, Sheps S (2006) An innovative application of Bayesian disease mapping methods to patient safety research: a Canadian adverse medical event study. Stat Methods Med Res 25:3960–3980

    MathSciNet  Article  Google Scholar 

  11. MacNab YC (2016a) Linear models of coregionalization for multivariate lattice data: a general framework for coregionalized multivariate CAR models. Stat Med 35:3827–3850

    MathSciNet  Article  Google Scholar 

  12. MacNab YC (2016b) Linear models of coregionalization for multivariate lattice data: Order-dependent and order-free cMCARs. Stat Methods Med Res 25(4):1118–1144

    MathSciNet  Article  Google Scholar 

  13. MacNab YC (2018) Some recent work on multivariate Gaussian Markov random fields. TEST 27(3):497–541

    MathSciNet  Article  Google Scholar 

  14. Martinez-Beneito MA (2013) A general modelling framework for multivariate disease mapping. Biometrika 100(3):539–553

    MathSciNet  Article  Google Scholar 

  15. Martinez-Beneito MA, Botella-Rocamora P, Banerjee S (2017) Towards a multidimensional approach to Bayesian disease mapping. Bayesian Anal 12:239–259

    MathSciNet  Article  Google Scholar 

  16. Schrodle B, Held L (2011) A primer on disease mapping and ecological regression using INLA. Comput Stat 26:241–258

    MathSciNet  Article  Google Scholar 

  17. Scott JG, Berger JO (2010) Bayesian and empirical-Bayes multiplicity adjustment in the variable-selection problem. Ann Stat 38(5):2587–2619

    Article  Google Scholar 

  18. Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc Ser B (Stat Methodol) 64:583–641

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support of the research Grant PI16/01004 (co-funded with FEDER grants) of Instituto de Salud Carlos III and predoctoral contract UGP-15-156 of FISABIO.

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. A. Martinez-Beneito.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Corpas-Burgos, F., Botella-Rocamora, P. & Martinez-Beneito, M.A. On the convenience of heteroscedasticity in highly multivariate disease mapping. TEST 28, 1229–1250 (2019). https://doi.org/10.1007/s11749-019-00628-8

Download citation

Keywords

  • Gaussian Markov random fields
  • Multivariate disease mapping
  • Bayesian statistics
  • Spatial statistics
  • Mortality studies

Mathematics Subject Classification

  • 62P10-Applications to biology and medical sciences