Sample Size Calculation for “Gold-Standard” Noninferiority Trials With Fixed Margins and Negative Binomial Endpoints

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.

针对哮喘、慢性阻塞性肺疾病及复发缓解型多发性硬化症患者的临床试验，监管指南明确非劣效性临床试验为可选设计方案。为确立试验的分析敏感性（assay sensitivity），推荐采用包含试验组、参比治疗组及安慰剂组的三臂非劣效性试验，即所谓的金标准非劣效性临床试验。此外，针对上述三类疾病的临床试验中，单位时间内的事件发生次数常被用作主要终点或关键次要终点。在金标准非劣效性试验的样本量确定环节，需解决两大核心问题：一是用于验证分析敏感性的待检验假设，二是事件计数的过离散（overdispersion）问题。针对上述两大问题，本文提出一种适用于双固定界值且结局服从负二项分布的金标准非劣效性试验的样本量计算方法。通过模拟研究证实，本文提出的假设检验方法可在将一类错误率（Type I error rate）控制在名义检验水准的同时达成预设功效，且所提样本量计算方法具备良好的功效准确性。此外，本文还通过一项轻度哮喘临床试验案例，展示了所提方法的实际应用路径。