Ouyou toukeigaku

Statistical methods to estimate geographical distribution using municipality-specific mortality data were considered. The methods are based on Poisson model with spatial smoothing by a spherical neighborhood system that is prescribed with the population size. The smoothed rates may be corrected by empirical Bayes method with gamma frailty model or crossing-over type likelihood method. The proposed method provides shrinkage estimators, in which the crude SMR is shrunk towards a local neighborhood mean value. We examined the proposed method by analyzing site-specific cancer mortality data in Japan for the period 1993-2002. The results of our study suggested that correction with gamma frailty model has a fairly good performance for grasping a general view of spatial distribution of mortality. However no remarkable improvement was obtained in comparison with the simple smoothing method.

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We consider simultaneous confidence intervals based on rank statistics of Wilcoxon-type in one-way layout. Using exact simultaneous rank tests and using Gauss's notation, we give exact expressions for the procedures of the simultaneous confidence intervals. Furthermore, we give two expressions of the asymptotic simultaneous confidence intervals. Although the distributions for the normal theory pocedures are given by double integrals, the asymptotic distributions for the proposed procedures are expressed as single integrals. Especially, we derive the upper and lower bounds for the asymptotic distribution of Tukey-type statistics. From simulation, we can see that the asymptotic simultaneous confidence intervals are conservative. When sample sizes are large, we recommend the simultaneous confidence intervals based on the Monte Carlo simulation. When the sizes of all samples are large, it is found that the rank procedures are superior to the classical normal theory procedures except the case that an underlying distribution is nearly normal.

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