Sampling variability of the Kunst-Mackenbach relative index of inequality

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Abstract
Study objective: 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. Results and Conclusion: 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.