For clinical trials in patients with asthma, chronic obstructive pulmonary disease, and relapsing-remitting multiple sclerosis, regulatory guidelines state that a noninferiority clinical trial is an option. Aiming at establishing assay sensitivity, a three-arm noninferiority trial, including an experimental treatment, a reference treatment, and a placebo, the so-called gold-standard noninferiority trial, is recommended. In addition, in the clinical trials for the above diseases, the number of events per unit time is often used as a primary or key secondary endpoint. There are two issues to be addressed in determining the sample size for gold-standard noninferiority trials: the hypotheses to be tested for assay sensitivity, and overdispersion of the number of events. To address these two issues, we propose a sample size calculation method for gold-standard noninferiority trials with two fixed margins and negative binomial endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the target power, while controlling the Type I error rate at a nominal level, and that the sample size calculation method has adequate power accuracy. Moreover, we illustrate an application of our proposed method for a clinical trial of mild asthma.
