We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and interim decisions are based on a global summary statistic. An error spending approach to this problem is defined which allows for unpredictable group sizes and nuisance parameters such as the correlation between endpoints. We present and compare three methods for implementation of the testing procedure including numerical integration, the Delta approximation and Monte Carlo simulation. In our evaluation, numerical integration techniques performed best for implementation with error rate calculations accurate to five decimal places. Our proposed testing method is flexible and accommodates summary statistics derived from general, non-linear functions of endpoints informed by the statistical model. Type 1 error rates are controlled, and sample size calculations can easily be performed to satisfy power requirements.

翻译：本文描述了能高效整合多个终点信息的组序贯检验方法，允许在预设的中期分析中提前终止试验。我们构建了一种检验流程，对多个结局指标进行考察，并基于全局汇总统计量做出中期决策。针对该问题定义了一种误差支出方法，可应对不可预知的组规模及终点间相关性等 nuisance 参数。我们提出并比较了三种实施该检验流程的方法：数值积分法、Delta 近似法和蒙特卡洛模拟法。评估表明，数值积分技术在实施中表现最佳，误差率计算精度可达小数点后五位。所提出的检验方法具有灵活性，能适应由统计模型导出的、基于终点的通用非线性函数所生成的汇总统计量。该方法可控制第一类错误率，并能简便地进行样本量计算以满足检验效能要求。