Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, MD, USA.
Clin Trials. 2010 Apr;7(2):109-17; discussion 118-120. doi: 10.1177/1740774510363310. Epub 2010 Mar 25.
Weisberg et al. (Clin Trials 2009, 6: 109-18) illustrate that entry criteria in randomized trials can lead to results that are biased for the target population. Presenting data from a previously published meta-analysis of the effect of antidepressants in children on suicidality, they suggest a relationship between the control event rate and relative risk.
Our purpose is threefold: (1) to show that natural methods of demonstrating a relationship between the control event rate and relative treatment benefit are fraught with danger, (2) to develop better methods, and (3) to assess whether there is evidence of such a relationship in the suicidality meta-analysis.
We propose an improved graphical method and an exact and approximate test of whether the treatment effect increases (or decreases) with the control event rate.
The apparent relationship in the naive plot of relative risk against control rate is actually no stronger than what would be expected by chance. Results of our test do not support the conclusion that the odds ratio for suicidality varies with the control rate (one-sided p = 0.39).
We are not able to apply the exact test to this data set. Simulation results indicate that the relationship would have to be very strong to detect it with these sample sizes and control event rates.
The difficulty in showing that the treatment effect in clinical trials differs by control rate is caused by 3 factors: (1) artificial correlation between a relative risk and control rate, (2) regression dilution bias because the independent variable - the control proportion - is subject to random variability, and (3) low power because we are trying to detect an interaction. Our graph and test are useful tools. Using them, we found no support for a relationship between the control event rate and treatment effect on suicidality.
Weisberg 等人（临床试验 2009 年，6：109-18）表明，随机试验的纳入标准可能导致针对目标人群的结果存在偏差。他们展示了先前发表的抗抑郁药治疗儿童自杀意念的荟萃分析数据，表明对照事件发生率与相对风险之间存在关系。
我们的目的有三个：（1）展示证明对照事件发生率与治疗益处之间关系的自然方法存在危险；（2）开发更好的方法；（3）评估自杀意念荟萃分析中是否存在这种关系的证据。
我们提出了一种改进的图形方法和一种确切且近似的检验方法，用于检验治疗效果是否随对照事件发生率而增加（或减少）。
在相对风险与对照率的直观图中，明显的关系实际上并不比偶然出现的关系更强。我们的检验结果不支持自杀意念的比值比随对照率变化的结论（单侧 p = 0.39）。
我们无法将精确检验应用于这个数据集。模拟结果表明，在这些样本量和对照事件发生率下，必须存在很强的关系才能检测到这种关系。
在临床试验中，治疗效果因对照率而异的证明难度很大，原因有 3 个：（1）相对风险与对照率之间的人为相关性；（2）由于独立变量——对照比例——受到随机变异性的影响，回归稀释偏差；（3）由于我们试图检测相互作用，因此功效较低。我们的图形和检验是有用的工具。使用它们，我们没有发现对照事件发生率与治疗对自杀意念的效果之间存在关系的证据。
