Confidence intervals for the overlapping coefficient: The normal equal variance case

The overlapping coefficient, defined as the common area under two probability density curves, is used as a measure of agreement between two distributions. It has recently been proposed as a measure of bioequivalence under the name proportion of similar responses. Confidence intervals for this measure have been considered for the special case of two normal distributions with equal variances. We review and compare two procedures for this confidence interval based on the non-central t-and F-distributions. Our comparison is based on both theoretical considerations and a simulation study. Data on a marker from a study of recurrence of breast cancer are used to illustrate the methodology.