The effect of reference treatment over placebo, known as M1, is essential in the development of non-inferiority margin. We proposed a M1 adjustment approach to reduce the selection bias for collected data of historical trials. A quantitative illustration of selection bias of historical data is also defined. Simulation study shows that the proposed approaches would significantly reduce the bias when the proportion of positive studies in historical data is noticeably larger than the power of studies include in historical data. When historical data are constituted by only positive studies, the performance of the proposed method is also appreciable. However, when the proportion of positive studies is close to the power of studies included or the number of studies included is too small, the performance of the proposed approach may not be reliable. A real-data application is also presented. The proposed bias-adjustment approach is a reasonable method to reduce the over-estimate of effect size in the specification of non-inferiority margin. It could also be applied in most non-inferiority margin specification methods or be cooperate used with other bias-adjustment approaches.
Keywords: Effect size; non-inferiority margin; power analysis; selection bias; simulation study.