Use of the Fieller-Hinkley distribution of the ratio of random variables in testing for noninferiority.

We address the noninferiority assessment problem defined in terms of the ratio of population means in a parallel group design analysis of variance setting. The sample ratio as a point estimate of the corresponding population ratio has been considered. It has been shown that the Fieller-Hinkley distribution of the ratio of two correlated normally distributed random variables readily provide a technique for constructing confidence intervals comparable to the bootstrap percentile and Fieller's confidence intervals. A finite parameter space based level alpha test of an inferiority hypothesis formulated in terms of a fixed margin has been derived. We illustrate our approach using the forced vital capacity (FVC) data. We claim that it is easy to construct and straight forward to interpret our bootstrap equivalent confidence intervals that are used to assess noninferiority. We discuss appropriate methods for calculation of sample sizes.