Cautionary note on regional consistency evaluation in multiregional clinical trials with binary outcomes

Multiregional clinical trials (MRCTs) have become increasingly common during the development of new drugs to obtain simultaneous drug approvals worldwide. When planning MRCTs, a major statistical challenge is determination of the regional sample size. In general, the regional sample size must be determined as the sample size such that the regional consistency probability, defined as the probability of meeting the regional consistency criterion, is greater than a prespecified value. The Japanese Ministry of Health, Labour and Welfare proposed two criteria for regional consistency. Moreover, many researchers have proposed corresponding closed-form formulas for calculating regional consistency probabilities when the primary outcome is continuous. Although some researchers have argued that those formulas are also applicable to cases with binary outcomes, it remains questionable whether such an argument can be true. Based on simulation results, we demonstrate that the existing formulas are inappropriate for binary cases, even when the regional sample size is sufficiently large. To address this issue, we develop alternative formulas and use simulation to show that they provide accurate regional consistency probabilities. Furthermore, we present an application of our proposed formulas for an MRCT of advanced or metastatic clear-cell renal cell carcinoma.