Assessing the non-inferiority of a new treatment in a three-arm trial with unknown coefficient of variation

Abstract

We consider a non-inferiority test conducted in the three-arm trials with coefficient of variations (CV) in sample means. A procedure for this non-inferiority test is proposed based on the generalized p-value (GPV) based method under normality assumption and heteroskedasticity. We demonstrated that first, the GPV-based method outperforms the comparable alternative, the Delta method in terms of empirical sizes and powers. Second, under GPV-based method, when the population mean of groups in the trial is estimated by the sample mean with CV, the empirical sizes control the significance level better than when CV is not included, especially when the ratio of the variance of the reference group to that of the experimental group and the ratio of the variance of the placebo group to that of the experimental group are not too small and that the sample size is small. Third, when the CV is included in the sample mean, the empirical powers are always higher, regardless of the sample size and methods. Additionally, when the data violates the normality assumption, it is found that the proposed GPV-based method in conjunction with CV appear to be highly acceptable through simulation results. Finally, the proposed method is illustrated with two data examples.