MRC Clinical Trials Unit, Aviation House, 125 Kingsway, London WC2B 6NH, U.K.
Stat Med. 2013 Nov 20;32(26):4540-9. doi: 10.1002/sim.5869. Epub 2013 Jun 4.
Factorial trials are an efficient method of assessing multiple treatments in a single trial, saving both time and resources. However, they rely on the assumption of no interaction between treatment arms. Ignoring the possibility of an interaction in the analysis can lead to bias and potentially misleading conclusions. Therefore, it is often recommended that the size of the interaction be assessed during analysis. This approach can be formalised as a two-stage analysis; if the interaction test is not significant, a factorial analysis (where all patients receiving treatment A are compared with all not receiving A, and similarly for treatment B) is performed. If the interaction is significant, the analysis reverts to that of a four-arm trial (where each treatment combination is regarded as a separate treatment arm). We show that estimated treatment effects from the two-stage analysis can be biased, even in the absence of a true interaction. This occurs because the interaction estimate is highly correlated with treatment effect estimates from a four-arm analysis. Simulations show that bias can be severe (over 100% in some cases), leading to inflated type I error rates. Therefore, the two-stage analysis should not be used in factorial trials. A preferable approach may be to design multi-arm trials (i.e. four separate treatment groups) instead. This approach leads to straightforward interpretation of results, is unbiased regardless of the presence of an interaction, and allows investigators to ensure adequate power by basing sample size requirements on a four-arm analysis.
析因试验是在单次试验中评估多种治疗方法的有效方法，可以节省时间和资源。然而，它们依赖于各治疗组之间无交互作用的假设。在分析中忽略交互作用的可能性可能会导致偏差和潜在的误导性结论。因此，通常建议在分析过程中评估交互作用的大小。这种方法可以形式化为两阶段分析；如果交互作用检验不显著，则进行析因分析（即比较所有接受治疗 A 的患者与所有未接受 A 的患者，治疗 B 也是如此）。如果交互作用显著，则分析恢复为四臂试验（其中每个治疗组合被视为单独的治疗组）。我们表明，即使没有真正的交互作用，两阶段分析的估计治疗效果也可能存在偏差。这是因为交互作用的估计与四臂分析的治疗效果估计高度相关。模拟表明，偏差可能非常严重（在某些情况下超过 100%），导致 I 型错误率膨胀。因此，两阶段分析不应在析因试验中使用。一种更好的方法可能是设计多臂试验（即四个单独的治疗组）。这种方法可以直接解释结果，无论是否存在交互作用，都不会产生偏差，并且允许研究人员通过基于四臂分析来确保足够的功效来确定样本量要求。
