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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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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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.
Disease Mapping, Spatial Analysis, Random Effects, Bayesian Analysis, Markov Chain Monte Carlo, Inverse Gaussian Distribution
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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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