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.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 7, Issue 1) |
| DOI | 10.11648/j.ajtas.20180701.14 |
| Page(s) | 29-34 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Disease Mapping, Spatial Analysis, Random Effects, Bayesian Analysis, Markov Chain Monte Carlo, Inverse Gaussian Distribution
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APA Style
Tonui Benard Cheruiyot, Mwalili Samuel, Wanjoya Anthony. (2018). A More Robust Random Effects Model for Disease Mapping. American Journal of Theoretical and Applied Statistics, 7(1), 29-34. https://doi.org/10.11648/j.ajtas.20180701.14
ACS Style
Tonui Benard Cheruiyot; Mwalili Samuel; Wanjoya Anthony. A More Robust Random Effects Model for Disease Mapping. Am. J. Theor. Appl. Stat. 2018, 7(1), 29-34. doi: 10.11648/j.ajtas.20180701.14
AMA Style
Tonui Benard Cheruiyot, Mwalili Samuel, Wanjoya Anthony. A More Robust Random Effects Model for Disease Mapping. Am J Theor Appl Stat. 2018;7(1):29-34. doi: 10.11648/j.ajtas.20180701.14
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Download@article{10.11648/j.ajtas.20180701.14,
author = {Tonui Benard Cheruiyot and Mwalili Samuel and Wanjoya Anthony},
title = {A More Robust Random Effects Model for Disease Mapping},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {7},
number = {1},
pages = {29-34},
doi = {10.11648/j.ajtas.20180701.14},
url = {https://doi.org/10.11648/j.ajtas.20180701.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180701.14},
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.},
year = {2018}
}
TY - JOUR T1 - A More Robust Random Effects Model for Disease Mapping AU - Tonui Benard Cheruiyot AU - Mwalili Samuel AU - Wanjoya Anthony Y1 - 2018/01/19 PY - 2018 N1 - https://doi.org/10.11648/j.ajtas.20180701.14 DO - 10.11648/j.ajtas.20180701.14 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 29 EP - 34 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20180701.14 AB - 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. VL - 7 IS - 1 ER -
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