Confidence Regions for Jointly Measuring Benefit and Risk

• Activity Number: 189
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Michele L. Shaffer*+ and Kristi L. Watterberg
• Companies: Pennsylvania State College of Medicine and The University of New Mexico
• Keywords: Benefit-risk ratio ; efficacy ; adverse event ; bootstrap ; nonparametric density estimation

Abstract

The benefit-risk ratio has been proposed to measure the tradeoff between the benefits and risks of two therapies for a single binary measure of efficacy and a single adverse event. The ratio is calculated from the difference in risk and benefit. Confidence intervals based on Fieller's theorem can be constructed, assuming the sample sizes in the therapy groups are large enough that the differences in risk and benefit follow a bivariate normal distribution. Small sample sizes or expected differences in benefit or risk between therapies can lead to no solution or problematic solutions. Bootstrap confidence intervals that do not rely on the bivariate normal assumption can be produced; however, ordering the benefit-risk ratios from the bootstrap samples also is complicated when small differences in benefit or risk are present. Alternatively, confidence regions for the parameter vector composed of the differences in risk and benefit can be constructed either under the bivariate normal assumption or using the bootstrap and nonparametric density estimation. Data from an NICHD trial of hydrocortisone prophylaxis against adrenal insufficiency are used for illustration.