Strength of evidence of non-inferiority trials-The adjustment of the type I error rate in non-inferiority trials with the synthesis method.

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.