The generalized inference on the ratio of mean differences for fraction retention noninferiority hypothesis

The fraction retention non-inferiority hypothesis is often measured for the ratio of the effects of a new treatment to those of the control in medical research. However, the fraction retention non-inferiority test that the new treatment maintains the efficacy of control can be affected by the nuisance parameters. Herein, a heuristic procedure for testing the fraction retention non-inferiority hypothesis is proposed based on the generalized p-value (GPV) under normality assumption and heteroskedasticity. Through the simulation study, it is demonstrated that, the performance of the GPV-based method not only adequately controls the type I error rate at the nominal level but also is uniformly more powerful than the ratio test, Rothmann’s and Wang’s tests, the comparable extant methods. Finally, we illustrate the proposed method by employing a real example.