Simultaneous Bootstrap Confidence Intervals for Lorenz Curves Reflecting the Spatial Distribution of Disease Risk

• Activity Number: 344
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Owen J. Devine*+
• Companies: Centers for Disease Control and Prevention
• Keywords: disease rates ; public health surveillance ; spatial analysis ; mapping

Abstract

Lorenz curves are often used to illustrate the distribution of economic measures within a given population. In more recent applications, Lorenz curves have also been used to evaluate spatial heterogeneity in the distribution of disease risk across geographic areas. In this application, an increase in curvature is indicative of an uneven spatial distribution of risk. An observed Lorenz curve, however, is subject to random variability in that, for example, some curvature is expected even if the underlying distribution of the true risk is constant. We propose a parametric bootstrap approach for constructing simultaneous confidence intervals for the coordinates of observed Lorenz curves. In addition, we use Monte Carlo methods to define a null region corresponding to the variability expected in an observed Lorenz curve given spatial homogeneity of true risk. The performance of the approach is evaluated through a simulation study and the method is applied in an examination of the spatial distribution of sexually transmitted disease risk across counties in North Carolina.