A More Robust Random Effects Model for Disease Mapping
American Journal of Theoretical and Applied Statistics
Volume 7, Issue 1, January 2018, Pages: 29-34
Received: Dec. 20, 2017; Accepted: Jan. 8, 2018; Published: Jan. 19, 2018
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Authors
Tonui Benard Cheruiyot, Department of Mathematics & Computer Science, University of Kabianga, Kericho, Kenya; Department of Statistics & Actuarial Science, Jomo Kenyatta University of Science & Technology, Juja, Kenya
Mwalili Samuel, Department of Statistics & Actuarial Science, Jomo Kenyatta University of Science & Technology, Juja, Kenya; Kenya Medical Research Institute/Centre for Disease Control, Nairobi, Kenya
Wanjoya Anthony, Department of Statistics & Actuarial Science, Jomo Kenyatta University of Science & Technology, Juja, Kenya
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Abstract
Disease mapping studies have found wide applications within geographical epidemiology and public health and are typically analysed within a Bayesian hierarchical model formulation. The most popular disease mapping model is the Besag-York-Molli´e model. A distinguishing feature of this model is the use of two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual unstructured heterogeneity. Very often the spatially unstructured random effect is assumed to be normally distributed. Under practical situations, this normality assumption is found to be over restrictive. In this study, we investigate a more robust spatially unstructured random effect distribution by considering the Inverse Gaussian (IG) distribution in the disease mapping problem. The distribution has the normal distribution as special case. The inferences under this model are carried out within a bayesian hierarchical model formulation implemented in WinBUGS. The IG distribution is introduced in WinBUGS using zero tricks. The usefulness of the proposed model is investigated with a simulation study and applied in real data; mapping HIV in Kenya. In this work we showed that the IG distribution can produce better results when the normality assumption is violated due to the skewness of the data. For the case of data in which the random effects are truly normal, the IG distribution adjusts to a normal distribution as dictated by the data itself. On the other hand, the spatially structured random effect is normally modelled using the intrinsic conditional autoregressive (iCAR) prior. This prior is improper and has the undesirable large scale property of leading to a negative pairwise correlation for regions located further apart. In addition, the BYM model presents some identifiability problems of the spatial and non-spatial effects. In this work, we consider Leroux CAR (named lCAR hereafter) prior, a less widely used prior in disease mapping, as the prior distribution for the spatially structured random effects.
Keywords
Disease Mapping, Spatial Analysis, Random Effects, Bayesian Analysis, Markov Chain Monte Carlo, Inverse Gaussian Distribution
To cite this article
Tonui Benard Cheruiyot, Mwalili Samuel, Wanjoya Anthony, A More Robust Random Effects Model for Disease Mapping, American Journal of Theoretical and Applied Statistics. Vol. 7, No. 1, 2018, pp. 29-34. doi: 10.11648/j.ajtas.20180701.14
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Lawson, AB. (2013). Bayesian disease mapping: Hierarchical modelling in spatial Epidemiology. Chapman and Hall/CRC press.
[2]
Elliott, P. and Wartenberg, D. (2004). Spatial epidemiology: Current Approaches and Future Challenges. Environmental Health Perspectives; 112, 998.1006.
[3]
Clayton D. and Bernardinelli L. (1992). Bayesian methods for mapping disease risk: Geographical and environmental epidemiology, methods for small-area studies. Oxford University Press, Oxford.
[4]
Bithell J. (2000). A classification of disease mapping methods. Statistics in Medicine; 19: 2203-2215.
[5]
Diggle PJ. (2000). Overview of statistical methods for disease mapping and its relationship to cluster detection. In: Spatial Epidemiology: Methods and Applications; Edited by: Elliot P, Wakefield JC, Best NG, Briggs DJ. Oxford, Oxford University Press; 87-103.
[6]
Lawson AB. (2001). Tutorial in Biostatistics: Disease map reconstruction. Statistics in Medicine; 20: 2183-2203.
[7]
Wakefield J. (2007). Disease mapping and spatial regression with count data. Biostatistics; 8 (2): 158-183.
[8]
Besag J, York J and Molli´e A. (1991). Bayesian image restoration with two applications in spatial statistics (with discussion). Ann Inst Stat Math., 43, 1.59.
[9]
Ngesa O, Achia T and Mwambi H. (2014). A Flexible Random Effects Distribution in Disease Mapping Models. South African Statistical Journal; 48 (1), 83-93.
[10]
Box G. and Tiao G. (1973). Bayesian inference in statistical analysis. Addison-Wesley Pub. Co.
[11]
MacNab YC. (2011). On Gaussian Markov random fields and Bayesian disease mapping. Statistical Methods in Medical Research; 20: 49–68.
[12]
Botella-Rocamora P, Lo´ pez-Quı´lez A and Martı´nez-Beneito MA. (2013). Spatial Moving Average Risk Smoothing. Statistics in Medicine; 32: 2595. 2612.
[13]
MacNab YC. (2014). On identification in Bayesian disease mapping and ecological-spatial regression models. Statistical Methods in Medical Research; 23 (2) 134–155; Originally published online 8 May 2012 DOI: 10.1177/0962280212447152. Available at: http://smm.sagepub.com/content/23/2/134.
[14]
Rampaso RC, de Souza ADP & Flores EF (2016). Bayesian analysis of spatial data using different variance and neighbourhood structures, Journal of Statistical Computation and Simulation, 86:3, 535-552, DOI: 10.1080/00949655.2015.1022549.
[15]
Leroux BG, Lei X and Breslow N. (1999). Estimation of disease rates in small areas: A new mixed model for spatial dependence. In Statistical models in epidemiology, the environment and clinical trials. New York: Springer-Verlag; pp.135–178.
[16]
Lee, D. (2011). A comparison of conditional autoregressive models used in Bayesian disease mapping. Spatial and Spatio-temporal Epidemiology; 2 (2): 79–89.
[17]
Rue H and Held L. (2005). Gaussian Markov random …fields: theory and applications. CRC Press.
[18]
Bernardinelli L, Clayton D and Montomoli C. (1995). Bayesian estimates of disease maps: How important are priors? Statistics in Medicine; 14 (21-22): 2411. 2431.
[19]
Best N., Thomas A., Waller L., Conlon E., and Arnold R. (1999). Bayesian models for spatially correlated disease and exposure data. In Bayesian Statistics 6: Proceedings of the Sixth Valencia International Meeting, volume 6. Oxford University Press, USA, pp. 131. 156.
[20]
Sato S. and Inoue J. (1994). Inverse Gaussian Distribution and Its Application. Electronics and Communications in Japan; 77 (1), 32-42.
[21]
Spiegelhalter DJ, Thomas A, Best NG, et al. (2007). WinBUGS version 1.4 user’s manual. MRC Biostatiscs unit.
[22]
Ntzoufras I. (2011). Bayesian modeling using WinBUGS, volume 698. Wiley.
[23]
Gelman A., Carlin JB., Sternn HS. and Rubin DB. (2004). Bayesian Data Analysis; 2nd edn. Boca Raton: Chapman and Hall.
[24]
Spiegelhalter DJ, Best NG, Carlin BP, et al. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology); 64 (4): 583–639.
[25]
Litière S., Alonso A., and Molenberghs G. (2007). Type i and type ii error under random effects misspecification in generalized linear mixed models. Biometrics, 63 (4), 1038–1044.
[26]
Litière S., Alonso A., and Molenberghs G. (2008). The impact of a misspecified random effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models. Statistics in medicine, 27 (16), 3125–3144.
[27]
McCulloch CE and Neuhaus JM. (2011). Misspecifying the shape of a random effects distribution: why getting it wrong may not matter. Statistical Science; 26 (3), 388–402.
[28]
Gelfand, AE. and Smith, AFM. (1990). Sampling-based approaches to calculating marginal densities. Journal of America Statitistical Association; 85, 398–409.
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