The Direct Integral Method for Confidence Intervals for the Ratio of Two Location Parameters

• Activity Number: 29
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Yanqing Wang*+ and Suojin Wang and Raymond J. Carroll
• Companies: Texas A&M and Texas A&M and Texas A&M
• Keywords: Confidence interval ; Direct integral ; Fieller's interval ; Hayya's method ; Ratios of location parameters

Abstract

Motivated by a logistic regression problem involving diet and cancer, we reconsider the problem of forming a confidence interval for the ratio of two location parameters. We develop a new methodology, which we call the Direct Integral Method. In simulations, we compare this method to many others, including Wald's method, Fieller's interval, Hayya's method, the nonparametric bootstrap and the parametric bootstrap. These simulations show that, generally, the Direct Integral Method more closely achieves the nominal confidence level, and in those cases that the other methods achieve the nominal levels, the Direct Integral Method generally has smaller confidence interval lengths. We also show that the Direct Integral Method eliminates the probability of infinite length or enormous length confidence intervals, something that can occur in Fieller's interval. The methodology is applied to a large study of diet and health where the Direct Integral Method is again seen to be a versatile approach, and logistic regression simulations again show that it achieves the nominal confidence level with generally smaller confidence interval lengths.