Confidence Interval Based on Central Limit Theorem for Correlated Binary Observations

• Activity Number: 175
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Jongphil Kim*+ and Ji-Hyun Lee
• Companies: Moffitt Cancer Center & Research Institute and Moffitt Cancer Center & Research Institute
• Keywords: confidence interval ; Beta-Binomial model ; intraclass correlation coefficient ; sensitivity ; specificity

Abstract

This research proposes the confidence intervals of common success probability when binary observations have the common intraclass correlation. The asymptotic confidence intervals of success probability can be obtained by Central Limit Theorem (CLT), CICLT, based upon Beta-Binomial model. By the duality property between confidence intervals and acceptance intervals, the coverage probabilities of the CICLT and the confidence intervals by Binomial model are evaluated. For the simulation studies, Lunn and Davis (1998) algorithm is employed to generate binary random numbers with common intraclass correlation coefficient and success probability. The proposed method is applied to the data from a study of accuracy in reading screening mammograms in a population of U.S. radiologists (Beam et al., 2003): the confidence intervals for sensitivity and specificity of mammogram are computed.