Confidence Intervals for Relative Risks in Disease Mapping

Several analysis of the geographic variation of mortality rates in space have been proposed in the literature. Poisson models allowing the incorporation of random effects to model extra‐variability are widely used. The typical modelling approach uses normal random effects to accommodate local spatial autocorrelation. When spatial autocorrelation is absent but overdispersion persists, a discrete mixture model is an alternative approach. However, a technique for identifying regions which have significant high or low risk in any given area has not been developed yet when using the discrete mixture model. Taking into account the importance that this information provides to the epidemiologists to formulate hypothesis related to the potential risk factors affecting the population, different procedures for obtaining confidence intervals for relative risks are derived in this paper. These methods are the standard information‐based method and other four, all based on bootstrap techniques, namely the asymptotic‐bootstrap, the percentile‐bootstrap, the BC‐bootstrap and the modified information‐based method. All of them are compared empirically by their application to mortality data due to cardiovascular diseases in women from Navarra, Spain, during the period 1988–1994. In the small area example considered here, we find that the information‐based method is sensible at estimating standard errors of the component means in the discrete mixture model but it is not appropriate for providing standard errors of the estimated relative risks and hence, for constructing confidence intervals for the relative risk associated to each region. Therefore, the bootstrap‐based methods are recommended for this matter. More specifically, the BC method seems to provide better coverage probabilities in the case studied, according to a small scale simulation study that has been carried out using a scenario as encountered in the analysis of the real data.