PMC:1247195 / 18364-20544 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1247195","sourcedb":"PMC","sourceid":"1247195","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1247195","text":"In this article we investigate the performance of a related spatial mixture model recently proposed by Green and Richardson (2002) that we refer to as MIX. This model leads to good estimation of the relative risks compared with the BYM model for a variety of cases of discontinuities of the risk surface. The idea underlying the MIX model is to replace a continuous model for θi by a mixture model that uses a variable number of risk classes and a spatially correlated allocation model to distribute each area to a class. By averaging over a large number of possible configurations, the marginal distribution of the relative risk is nevertheless smooth. To be precise, it is assumed that θi = θZi , where Zi, i = 1, 2,…,n are allocation variables taking values in 1, 2,…,k and θj, j = 1,2,…,k are the values of the relative risks that characterize the k different components or risk classes. To have maximum flexibility, the number of components k of the mixture is treated as unknown. Given k, the allocations Zi follow a spatially correlated process, the Potts model, which has been used in image processing and other spatial applications and involves a positive interaction parameter ψ (similar to an autocorrelation parameter) that influences the degree of spatial dependence of the allocations. Specifically, the allocation of an area to a risk component will be favored probabilistically by the number of neighbors currently attributed to that component scaled multiplicatively by ψ. In this way the prior knowledge that areas close by tend to have similar risks can be reflected through the allocation structure. The interaction parameter ψ is treated as unknown and jointly estimated with the number of components and their associated risk. The MIX model can adapt to various patterns of risk and model discontinuities by creating a new risk class if there is sufficient information in the data to warrant this. Further details on the specification of the model are given in Green and Richardson (2002). Thus, in the comparison described later, we have implemented one reference model BYM and two alternative models, the parametric L1-BYM and the semiparametric MIX model.","tracks":[]}