Background/aims:

The two-by-two factorial design randomizes participants to receive treatment A alone, treatment B alone, both treatments A and B(AB), or neither treatment (C). When the combined effect of A and B is less than the sum of the A and B effects, called a subadditive interaction, there can be low power to detect the A effect using an overall test, that is, factorial analysis, which compares the A and AB groups to the C and B groups. Such an interaction may have occurred in the Action to Control Cardiovascular Risk in Diabetes blood pressure trial (ACCORD BP) which simultaneously randomized participants to receive intensive or standard blood pressure, control and intensive or standard glycemic control. For the primary outcome of major cardiovascular event, the overall test for efficacy of intensive blood pressure control was nonsignificant. In such an instance, simple effect tests of A versus C and B versus C may be useful since they are not affected by a subadditive interaction, but they can have lower power since they use half the participants of the overall trial. We investigate multiple testing procedures which exploit the overall tests’ sample size advantage and the simple tests’ robustness to a potential interaction.

Methods:

In the time-to-event setting, we use the stratified and ordinary logrank statistics’ asymptotic means to calculate the power of the overall and simple tests under various scenarios. We consider the A and B research questions to be unrelated and allocate 0.05 significance level to each. For each question, we investigate three multiple testing procedures which allocate the type 1 error in different proportions for the overall and simple effects as well as the AB effect. The Equal Allocation 3 procedure allocates equal type 1 error to each of the three effects, the Proportional Allocation 2 procedure allocates 2/3 of the type 1 error to the overall A (respectively, B) effect and the remaining type 1 error to the AB effect, and the Equal Allocation 2 procedure allocates equal amounts to the simple A (respectively, B) and AB effects. These procedures are applied to ACCORD BP.

Results:

Across various scenarios, Equal Allocation 3 had robust power for detecting a true effect. For ACCORD BP, all three procedures would have detected a benefit of intensive glycemia control.

Conclusions:

When there is no interaction, Equal Allocation 3 has less power than a factorial analysis. However, Equal Allocation 3 often has greater power when there is an interaction. The R package factorial2x2 can be used to explore the power gain or loss for different scenarios.

中文翻译：

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二乘二析因试验设计的整体效应和简单效应的联合检验

背景/目标：

二乘二因子设计将参与者随机化为单独接受治疗A、单独接受治疗B、治疗A和 B ( AB ) 或不接受治疗 ( C )。当A和B的组合效应小于A和B效应的总和时（称为次可加交互作用），使用整体检验（即因子分析）检测A效应的功效可能较低，该检验比较A和AB组到C和B组。这种相互作用可能发生在控制糖尿病心血管风险的行动血压试验 (ACCORD BP) 中，该试验同时随机分配参与者接受强化或标准血压、控制和强化或标准血糖控制。对于主要心血管事件的主要结局，强化血压控制有效性的总体测试不显着。在这种情况下，A对C和B对C 的简单效果测试可能有用，因为它们不受子可加性相互作用的影响，但它们的功效可能较低，因为它们使用了整个试验的一半参与者。我们调查了多个测试程序，这些程序利用了整体测试的样本量优势和简单测试对潜在交互的稳健性。

方法：

在 time-to-event 设置中，我们使用分层和普通 logrank 统计的渐近均值来计算各种场景下整体和简单检验的功效。我们认为A和B研究问题是不相关的，并为每个问题分配 0.05 的显着性水平。对于每个问题，我们研究了三个多重测试程序，这些程序将 1 类错误按不同比例分配给整体和简单效应以及AB效应。的均等分配3程序分配等于1型误差的每个的三个效果，该比例分配2程序分配类型1错误的整体的2/3甲分别（，乙) 效应和剩余的 1 类错误分配给AB效应，并且等量分配 2程序将等量分配给简单的A（分别为B）和AB效应。这些程序适用于 ACCORD BP。

结果：

在各种场景中，Equal Allocation 3 具有强大的检测真实效果的能力。对于 ACCORD BP，所有三个程序都会检测到强化血糖控制的好处。

结论：

当没有交互作用时，等量分配 3的功效小于因子分析。但是，当有交互时，Equal Allocation 3通常具有更大的权力。R 包 factorial2x2 可用于探索不同场景的功率增益或损耗。