Bayesian Analysis of Agricultural Field Experiments

Abstract

One of the main aims in epidemiology is the estimation and mapping of spatial variation in disease risk while adjusting for available covariate information. We analyse the spatial distribution of infant mortality cases compared to live-born controls from Porto Alegre, Rio Grande do Sul in a binary spatial regression model. A commonly used approach for such data is a spatial point process. Here the risk measure, which continously varies over the study region is estimated using generalized additive models, as presented by Kelsall and Diggle (1998). In this models, a smoothing parameter has to be chosen, which strongly affects the estimation of the spatial risk surface, and inference for the regression coefficients is conditional on the surface. Instead we discretise space on a square grid and use higher order Gaussian Markov random fields (GMRF). Some of the GMRF models are already described in Besag and Higdon (1999), we expanded their approach up to a GMRF for twelve nearest neighbours. In contrast to the spatial point process approach, the smoothing parameter in this model can be estimated and covariate effects and the spatial surface can be estimated jointly. However the level of discretisation, the choice of the GMRF and the hyper prioris affect the estimated surface, as we show. We follow a Bayesian binary regression approach using a data augmentation technique described by Holmes and Held (2003). Here the resulting conditional likelihood of the regression coefficients and the spatial component is multivariate normal. This allows for efficient simulation using block Gibbs sampler as in Knorr-Held and Rue (2001). The results shows duration of gestation and weight of the new born child as only significant covariates. The spatial analysis shows two regions with significantly higher mortality risk, not explained by the covariates. The results agree well with those presented in Shumakura et.al., who analyse the same data using a spatial point process approach. The Hamburg Leukaemia and Lymphoma study has the aim to investigate the influence of selected environmental emission sources on the incidence of leukaemia, lymphoma and plasmocytoma. As a part of this study the hypothesis of a possible contribution of traffic immissions was analysed. Period of observation was 1988-1999; the case data set (Cases = 10034) was collected by the Hamburg Cancer Registry (additional program for completion). As the control group a 10% sample of Hamburg population was drawn from the residence registry (Controls = 173177). The residential adress was coded to geographic coordinates (precision ± 5 [m]). Indication for exposure to traffic related immission was calculated by (a) a local immission prognosis as the sum of traffic induced hydrocarbons (HC µg/m³, grids 500*500 meter) and (b) by the number of main streets/highways within 250 m distance to the residential adress. Age, sex and exposure stratified calculation as well as unconditional logistic regression methods were applied to analyse the influence structure. For all malignant h...

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