Devine O J, Louis T A
Radiation Studies Branch, National Center for Environmental Health, Centers for Disease Control and Prevention, Atlanta, GA 30341-3724.
Stat Med. 1994 Jun 15;13(11):1119-33. doi: 10.1002/sim.4780131104.
Maps that show the geographic distribution of incidence rates can be useful tools for analysing spatial variation in mortality and morbidity. To attain the necessary geographic resolution, however, production of such maps often requires estimation of incidence in areas with small populations where the observed rates may be highly unstable. Manton et al. have presented an empirical Bayes stabilization procedure in which the observed rate is combined with an area-specific estimate of the underlying incidence. The approach allows for the mapping of outcomes with varied and possibly unknown etiologies without necessitating covariate dependent modelling of the expected rate. The empirical distribution of a collection of these estimates, however, may not provide an adequate description of the dispersion among the true rates. As a result, decisions based on the histogram of the empirical Bayes estimates may be suspect. We propose a modified version of the approach in which the mean and sample variance of the ensemble of estimates are constrained to equal the appropriate moments of the posterior distribution. The resulting collection of constrained empirical Bayes estimators has nearly the stability of the unconstrained approach and provides an improved estimator of the true rate distribution. We illustrate use of the estimator by producing stabilized county-level maps of U.S. fire- and burn-related mortality rates and validate the analytic results using a simulation analysis.
显示发病率地理分布的地图可成为分析死亡率和发病率空间差异的有用工具。然而，为了获得必要的地理分辨率，制作此类地图通常需要估计人口较少地区的发病率，而这些地区的观测率可能极不稳定。曼顿等人提出了一种经验贝叶斯稳定程序，其中将观测率与潜在发病率的特定区域估计值相结合。该方法允许对病因各异且可能未知的结果进行绘图，而无需对预期率进行依赖协变量的建模。然而，这些估计值集合的经验分布可能无法充分描述真实率之间的离散情况。因此，基于经验贝叶斯估计值直方图做出的决策可能存在疑问。我们提出了该方法的一个修改版本，其中将估计值集合的均值和样本方差约束为等于后验分布的适当矩。由此得到的约束经验贝叶斯估计量集合几乎具有无约束方法的稳定性，并能更好地估计真实率分布。我们通过制作美国火灾和烧伤相关死亡率的稳定县级地图来说明该估计量的使用，并通过模拟分析验证分析结果。
