Department of Applied Statistics, Yonsei University, Korea.
Stat Med. 2010 Jun 30;29(14):1477-87. doi: 10.1002/sim.3903.
In non-inferiority trials that employ the synthesis method several types of dependencies among test statistics occur due to sharing of the same information from the historical trial. The conditions under which the dependencies appear may be divided into three categories. The first case is when a new drug is approved with single non-inferiority trial. The second case is when a new drug is approved if two independent non-inferiority trials show positive results. The third case is when two new different drugs are approved with the same active control. The problem of the dependencies is that they can make the type I error rate deviate from the nominal level. In order to study such deviations, we introduce the unconditional and conditional across-trial type I error rates when the non-inferiority margin is estimated from the historical trial, and investigate how the dependencies affect the type I error rates. We show that the unconditional across-trial type I error rate increases dramatically as does the correlation between two non-inferiority tests when a new drug is approved based on the positive results of two non-inferiority trials. We conclude that the conditional across-trial type I error rate involves the unknown treatment effect in the historical trial. The formulae of the conditional across-trial type I error rates provide us with a way of investigating the conditional across-trial type I error rates for various assumed values of the treatment effect in the historical trial.
在采用综合方法的非劣效性试验中，由于历史试验中共享相同信息，会出现几种类型的检验统计量之间的依赖性。依赖性出现的条件可以分为三类。第一种情况是当新药物通过单一的非劣效性试验获得批准时。第二种情况是当两个独立的非劣效性试验显示阳性结果时，新药物获得批准。第三种情况是当两种新的不同药物使用相同的活性对照物获得批准时。依赖性的问题在于，它们可能会使 I 型错误率偏离名义水平。为了研究这种偏差，我们引入了非劣效性界值从历史试验中估计时的无条件和条件跨试验 I 型错误率，并研究依赖性如何影响 I 型错误率。我们表明，当根据两个非劣效性试验的阳性结果批准新药时，两个非劣效性试验之间的相关性越强，无条件跨试验 I 型错误率就会急剧增加。我们得出结论，条件跨试验 I 型错误率涉及历史试验中未知的治疗效果。条件跨试验 I 型错误率的公式为我们提供了一种方法，可以针对历史试验中治疗效果的各种假设值来研究条件跨试验 I 型错误率。
