Although all clinical trials are designed and monitored using more than one endpoint, methods are needed to assure that decision criteria are chosen to reflect the clinically relevant tradeoffs that assure the trial's scientific integrity. This article presents a framework for the design and monitoring clinical trials in a bivariate outcome space. The framework uses a rectangular hyperbola to define a bivariate null curve that divides outcome space into regions of benefit and lack of benefit. The curve is shown to be a flexible mapping of bivariate space that allows a continuous tradeoff between the two endpoints in a manner that captures many previous bivariate designs. The curve is extended to a distance function in bivariate space that allows different decisions in each of the four quadrants that comprise bivariate space. The distance function forms a statistic ( $\delta$); the distribution of its estimate is derived and used as a basis for trial design and group sequential monitoring plans in bivariate space. A recursive form of the bivariate group sequential density is used to evaluate and control operating characteristics for the proposed design. The bivariate designs are shown to meet or exceed the usual standards for size and power. The proposed design is illustrated in the ongoing NHLBI‐sponsored Kids‐DOTT multinational randomized controlled trial comparing shortened versus conventional anticoagulation for the treatment of venous thromboembolism in patients less than 21 years of age. The proposed methods are broadly applicable to a wide range of clinical settings and trial designs.

中文翻译：

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具有双变量终点的临床试验的分组顺序设计

尽管所有临床试验都是通过一个以上的终点进行设计和监测的，但仍需要采取一些方法来确保选择决策标准以反映临床相关的折衷，以确保试验的科学完整性。本文提出了在双变量结果空间中设计和监测临床试验的框架。该框架使用矩形双曲线来定义双变量零曲线，该曲线将结果空间分为受益区域和受益区域。该曲线显示为双变量空间的灵活映射，它允许以捕获许多以前的双变量设计的方式在两个端点之间进行连续权衡。曲线扩展到双变量空间中的距离函数，该函数允许在包含双变量空间的四个象限中的每个象限中做出不同的决策。$\delta$）; 得出其估计值的分布，并将其用作双变量空间中的试验设计和小组顺序监测计划的基础。二元组顺序密度的递归形式用于评估和控制所提出设计的工作特性。显示双变量设计达到或超过尺寸和功率的常规标准。正在进行的NHLBI赞助的Kids-DOTT跨国随机对照试验对拟议的设计进行了说明，该试验比较了短时抗凝与常规抗凝治疗21岁以下患者的静脉血栓栓塞症。所提出的方法广泛适用于广泛的临床环境和试验设计。