Using the Lorenz Curve to Characterize Risk Predictiveness and Etiologic Heterogeneity

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Abstract

The Lorenz curve is a graphical tool that is used widely in econometrics. It represents the spread of a probability distribution, and its traditional use has been to characterize population distributions of wealth or income, or more specifically, inequalities in wealth or income. However, its utility in public health research has not been broadly established. The purpose of this article is to explain its special usefulness for characterizing the population distribution of disease risks, and in particular for identifying the precise disease burden that can be predicted to occur in segments of the population that are known to have especially high (or low) risks, a feature that is important for evaluating the yield of screening or other disease prevention initiatives. We demonstrate that, although the Lorenz curve represents the distribution of predicted risks in a population at risk for the disease, in fact it can be estimated from a case–control study conducted in the population without the need for information on absolute risks. We explore two different estimation strategies and compare their statistical properties using simulations. The Lorenz curve is a statistical tool that deserves wider use in public health research.

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