Hayes L J, Berry G
Department of Family and Community Nursing, Faculty of Nursing, University of Sydney, New South Wales, Australia.
J Epidemiol Community Health. 2002 Oct;56(10):762-5. doi: 10.1136/jech.56.10.762.
To derive methods of calculating confidence limits for the relative index of inequality, defined by Kunst and Mackenbach as a measure of the influence of socioeconomic status on an adverse health index, such as mortality rate. The methods may be used for a health outcome recorded on a continuous scale, as a Poisson count or as a binomial variable.
The confidence limits depend on the sampling variability of both the mean mortality rate and the slope of the regression line of mortality on the socioeconomic status scale variable. The best method for a continuous health outcome is based on Fieller's theorem but a good approximation is obtained by substituting the confidence limits for the slope of the regression line into the formula for the calculation of the index, or by using the variance of the logarithmic transform of the index. The last method is the most appropriate for the construction of significance tests comparing indices. The mortality rates may show statistically significant departure from linearity, while not suggesting that a linear relation is inappropriate, and the main decision is whether to base the confidence limits on the conventional standard error of the slope derived from the regression analysis or whether to use the standard deviation of the estimates of mortality rates.
推导出计算不平等相对指数置信区间的方法，该指数由昆斯特和麦肯巴赫定义，用于衡量社会经济地位对不良健康指标（如死亡率）的影响。这些方法可用于以连续尺度记录的健康结果、作为泊松计数或作为二项式变量的情况。
置信区间取决于平均死亡率以及死亡率在社会经济地位尺度变量上的回归线斜率的抽样变异性。对于连续健康结果，最佳方法基于菲勒定理，但通过将回归线斜率的置信区间代入指数计算公式，或使用指数对数变换的方差，可得到较好的近似值。最后一种方法最适合用于构建比较指数的显著性检验。死亡率可能在统计上显示出与线性有显著偏差，同时并不表明线性关系不合适，主要决策是基于回归分析得出的斜率的常规标准误差来确定置信区间，还是使用死亡率估计值的标准差。
