Two-group (bio)equivalence tests assess whether two drug formulations provide similar therapeutic effects. These studies are often conducted using two one-sided t-tests, where the test statistics jointly follow a bivariate t-distribution with singular covariance matrix. Unless the two groups of data are assumed to have equal variances, the degrees of freedom for this bivariate t-distribution are noninteger and unknown a priori. This makes it difficult to analytically find sample sizes that yield desired power for the study using an automated process. Popular free software for bioequivalence study design does not accommodate the comparison of two groups with unequal variances, and certain paid software solutions that make this accommodation produce unstable results. We propose a novel simulation-based method that uses Sobol' sequences and root-finding algorithms to quickly and accurately approximate the power curve for two-group bioequivalence tests with unequal variances. We also illustrate that caution should be exercised when assuming automated methods for power estimation are robust to arbitrary bioequivalence designs. Our methods for sample size determination mitigate this lack of robustness and are widely applicable to equivalence and noninferiority tests facilitated via parallel and crossover designs. All methods proposed in this work can be implemented using the dent package in R.

翻译：两组（生物）等效性检验用于评估两种药物制剂是否具有相似的治疗效果。此类研究通常采用双单侧t检验进行，其检验统计量联合服从具有奇异协方差矩阵的二元t分布。除非假设两组数据具有相等方差，否则该二元t分布的自由度为非整数且无法事先确定，这使得通过自动化流程解析计算实现目标检验功效的样本量极为困难。当前流行的生物等效性研究设计免费软件无法处理两组不等方差的情况，而部分可处理此场景的商业软件则会产生不稳定的结果。我们提出了一种基于Sobol'序列和求根算法的新型模拟方法，能够快速准确地逼近不等方差两组生物等效性检验的功率曲线。同时，我们指出应谨慎假设自动化功效估计方法对任意生物等效性设计均具有稳健性。本研究提出的样本量确定方法能够缓解这一稳健性问题，并广泛适用于平行设计和交叉设计下的等效性及非劣效性检验。本文所有方法均可通过R语言的dent包实现。