Lorenz Curve

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Wenchung Lee - One of the best experts on this subject based on the ideXlab platform.

  • probabilistic analysis of global performances of diagnostic tests interpreting the Lorenz Curve based summary measures
    Statistics in Medicine, 1999
    Co-Authors: Wenchung Lee
    Abstract:

    Several indices based on the receiver operating characteristic Curve (ROC Curve) have previously been found to possess probabilistic interpretations. However, these interpretations are based on some unrealistic diagnostic scenarios. In this paper, the author presents a new approach using the Lorenz Curve. The author found that the summary indices of the Lorenz Curve, that is, the Pietra index and the Gini index, can be interpreted in several ways ('average change in post-test probability', 'per cent maximum prognostic information', and 'probability of correct diagnosis'). These interpretations have a close tie with real-world medical diagnosis, suggesting that these indices are proper measures of test characteristics.

  • characterizing exposure disease association in human populations using the Lorenz Curve and gini index
    Statistics in Medicine, 1997
    Co-Authors: Wenchung Lee
    Abstract:

    SUMMARY To characterize exposure—disease association in human populations, epidemiologists have long relied upon such indices as ‘relative risk’ and/or ‘attributable risk’. However, the relative risk is not in a common unit which permits comparison across di⁄erent exposures or di⁄erent diseases and the attributable risk may not adequately catch and describe the variation of disease risks in populations. The present paper discusses the possibility of using the summary index of the Lorenz Curve, the Gini index, as an alternative measure of exposure—disease association. It is found that this index can be interpreted in several ways (as the coeƒcient of deviation in disease risk or relative risk, the information content of the exposure, the impact fraction of an exposure-lowering programme, and the averaged impact fraction) and is a promising alternative as a fundamental measure in epidemiology. Further studies are warranted to investigate its statistical properties. ( 1997 by John Wiley & Sons, Ltd.

  • analysis of seasonal data using the Lorenz Curve and the associated gini index
    International Journal of Epidemiology, 1996
    Co-Authors: Wenchung Lee
    Abstract:

    BACKGROUND: Epidemiological inferences about the aetiology of a disease can often be made from its seasonal patterns. However, due to its multifactorial nature, the seasonality component can be obscured by other factors. It is therefore important to develop statistical techniques which are sensitive to minute temporal changes. METHODS: The Lorenz Curve and the associated Gini index are applied for characterizing and testing seasonal variations. Computer simulations were conducted to compare the powers of the Gini test and other seasonality tests. We also show that the Gini index can itself be interpreted as a probability related to temporal clustering. RESULTS: The powers of the proposed tests are shown to be higher than or at least comparable to other tests under various conditions. CONCLUSIONS: Though computer-demanding, the proposed method is well-suited for analysing seasonal data. Language: en

Colin B Begg - One of the best experts on this subject based on the ideXlab platform.

  • using the Lorenz Curve to characterize risk predictiveness and etiologic heterogeneity
    Epidemiology, 2016
    Co-Authors: Audrey Mauguen, Colin B Begg
    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.

  • estimating the empirical Lorenz Curve and gini coefficient in the presence of error with nested data
    Statistics in Medicine, 2008
    Co-Authors: Chaya S Moskowitz, Elyn Riedel, Venkatraman E Seshan, Colin B Begg
    Abstract:

    The Lorenz Curve is a graphical tool that is widely used to characterize the concentration of a measure in a population, such as wealth. It is frequently the case that the measure of interest used to rank experimental units when estimating the empirical Lorenz Curve, and the corresponding Gini coefficient, is subject to random error. This error can result in an incorrect ranking of experimental units which inevitably leads to a Curve that exaggerates the degree of concentration (variation) in the population. We consider a specific data configuration with a hierarchical structure where multiple observations are aggregated within experimental units to form the outcome whose distribution is of interest. Within this context, we explore this bias and discuss several widely available statistical methods that have the potential to reduce or remove the bias in the empirical Lorenz Curve. The properties of these methods are examined and compared in a simulation study. This work is motivated by a health outcomes application that seeks to assess the concentration of black patient visits among primary care physicians. The methods are illustrated on data from this study.

  • estimating the empirical Lorenz Curve and gini coefficient in the presence of error
    2007
    Co-Authors: Chaya S Moskowitz, E S Venkatraman, Elyn Riedel, Colin B Begg
    Abstract:

    The Lorenz Curve is a graphical tool that is widely used to characterize the concentration of a measure in a population, such as wealth. It is frequently the case that the measure of interest used to rank experimental units when estimating the empirical Lorenz Curve, and the corresponding Gini coefficient, is subject to random error. This error can result in an incorrect ranking of experimental units which inevitably leads to a Curve that exaggerates the degree of concentration (variation) in the population. We explore this bias and discuss several widely available statistical methods that have the potential to reduce or remove the bias in the empirical Lorenz Curve. The properties of these methods are examined and compared in a simulation study. This work is motivated by a health outcomes application which seeks to assess the concentration of black patient visits among primary care physicians. The methods are illustrated on data from this study. Estimating the Empirical Lorenz Curve and Gini Coefficient in the

Elvin Geng - One of the best experts on this subject based on the ideXlab platform.

Matti Maltamo - One of the best experts on this subject based on the ideXlab platform.

Sriram Shankar - One of the best experts on this subject based on the ideXlab platform.

  • An alternative single parameter functional form for Lorenz Curve
    Empirical Economics, 2019
    Co-Authors: Satya Paul, Sriram Shankar
    Abstract:

    This paper proposes a single parameter functional form for the Lorenz Curve and compares its performance with the existing single parameter functional forms using Australian income data for 10 years. The proposed parametric functional form performs better than the existing Lorenz functional specifications based on mean-squared error and information accuracy measure. The Gini based on the proposed functional form turns out to be second best closely behind Aggarwal’s Lorenz Curve specification in each year.

  • an alternative single parameter functional form for Lorenz Curve
    Crawford School Research Papers, 2017
    Co-Authors: Satya Paul, Sriram Shankar
    Abstract:

    This paper proposes a single parameter functional form for the Lorenz Curve and compares its performance with the existing single parameter functional forms using Australian income data for 10 years. The proposed parametric functional form performs better than the existing Lorenz functional forms. The Gini based on the proposed functional form is closest to true Gini each year.