A Quasi-three-arm Non-inferiority Design And Sample Size Determination For Regional Evaluation In Simultaneous Global Drug Development

Ethnic sensitivity is one of the critical issues in drug development.Drug metabolic and pharmacodynamic characteristics often have different performance between different races.In view of ethnic difference,if the drug approved in the original region were applied in the New Region,they need to clarify ethnic difference and the impact on drug safety and effectiveness.In order to obtain the most direct pharmacokinetics,pharmacodynamics,efficacy and safety data of the drug for the targeted ethnic?TE?population in the new region,the sponsor is often required to re-conduct the I-IV clinical trial in the new region.However,it will result in resource waste and drug lag.In this regard,ICH E5 suggested that the bridging study could borrow the efficacy information from the MRCT data to the local region if it showed evidence of ethnic similarity across regions.However,due to the lack of clear definition of ethnic "similarity",there are many problems to be solved in practice.Subsequently,the Multi-regional Clinical Trial?MRCT?presented a strategy for multi-regional participation and simultaneous testing in the international context to promote drug within the scope of the simultaneous global drug development.In order to make each region of MRCT meeting the requirements of local drug regulators,the MRCT design and sample size scheme were exceptionally complex.To ensure each local area confirming the efficacy of drugs for the TE population in the region with sufficient power,the sample size of MRCT was often designed to be very large.Therefore,the framework MRCT incorporating an local clinical trial?LCT?in addition to the MRCT became the latest trends in global drug development.Based on the current situation,in this paper,the quasi-three-arm non-inferiority design was proposed by incorporating an MRCT and an LCT within a framework to evaluate the treatment efficacy of targeted region.The specific research contents and results are as follows: ?.Proposing a new framework of bridging studySuppose that the superiority has been confirmed by the placebo-controlled MRCT.Since it is generally inadequate to ensure the treatment effect for the TE population,an additional LCT enrolled only the TE population would be conducted for the local regulatory approval.All the key design features of the LCT,such as inclusion and exclusion criteria,are completely same as the MRCT.However,the following issues are needed to be considered?1?how to determine the sample size of the LCT??2?how to accurately evaluate the treatment effect of LCT??3?how to reasonably interpret results of the LCT based on the information from the MRCT.The quasi-three-arm non-inferiority design is proposed to resolve these problems as depicted in Figure 1.The fundamental assumption in this proposed design is the biological commonality of humankind sharing by kinds of ethnic population.Given that efficacy information of LCT remains unclear in the protocol design,it may be reasonable to tentatively suppose that there are similar placebo effects between the LCT and the MRCT in certain manner.Thus,both placebo groups could be considered as a quasi-placebo arm to verify the effectiveness of treatment groups.Moreover,treatment group of LCT is considered as test arm,and treatment group of MRCT as active reference arm.Here,the quasi-three-arm framework is established.Based on this framework,the treatment effect of LCT is supposed to be non-inferior to that in the MRCT.Defining the mean difference between treatment effect and placebo effect in each trial as effect size and a proportion of the effect size in the MRCT as margin,non-inferiority test can be conducted:?1?to confirm the effective evidence of test arm relative to placebo arm;?2?to retain a certain percentage of the efficacy of active reference arm;and?3?to prove that the efficacy of test arm is not very inferior to that of active reference arm.Therefore,if the non-inferiority hypothesis is true,the treatment effect in the LCT could be confirmed to be not overly inferior to the MRCT.?.Bridging schemes for different endpointGiven the similar placebo effects in the MRCT and the LCT,statistical test and sample size scheme should be considered based on the following two situations.If the placebo effect of LCT is equal to that of MRCT,the test process can refer to the traditional three-arm non-inferiority test.On the other hand,if the placebo effects between the LCT and MRCT are different,the testing problem is still formulated by the ratio of the mean differences between the LCT and the MRCT as hypotheses in the equal placebo situation.The test-statistic is constructed similar to the method of equal situation with an additional parameter.Specific procedure and sample size scheme are elaborated based on the above two situations.i.Continuous endpoint: Assuming the responses of the subjects were normal distribution,statistical methods and sample size consideration were proposed based on the equal and unequal placebo effect situations.The Monte Carlo simulation experiment was carried out.?1?For power of 80% at a level of 0.025,the average conditional power was 0.7993 ± 0.0068,and the average type I error was 0.0250 ± 0.0007 in 109 simulated scenarios.?2?The simulation study of sample size estimation showed that the MRCT sample size N_MRCT,the ratio between the MRCT effect size and the variance ?_M/?,the ratio of the effect sizes between LCT and MRCT ?,and the non-inferiority margin ? were the key factors influencing the sample size of LCT.It showed that increasing ? would contribute to decrease the sample size of LCT.A larger N_MRCT was responsible for a lowerN_LCT.While,raising the non-inferiority margin ? could increase the sample size moderately.And a doubling the mean difference of the MRCT would shrink LCTn to one quarter of its original size.?3?For the targeted power 1-?=0.80 and the significance level of ?=025.0 ?one-sided?,lower powers were observed in this simulation results.The obtained powers were reduced with the average of 69.04%,67.60% and 66.02% for N_MRCT=500 1000 1500.However,type I errors were not inflated significantly with the mean of 0.0250,0.0251 and 0.0249,respectively.ii.Dichotomy endpoint:?1?The trends of the sample size changing with the parameters were similar to that for the continuous endpoint.And there was no significant changing due to the incidence of placebo group in the MRCT.?2?Since the estimation of the variance ?²??? in the T statistic depends on the estimation of ????,researchers suggested that it should use the Restricted maximum likelihood Estimate?RMLE?to estimate the variance ?²???.In this part,simulation study were used to compare the performance of Wald test based on the maximum likelihood estimation?MLE?and the RMLE test.The results showed that,in 156 simulation scenarios,Wald test was not accurate and the variation was bigger compared to the RMLE test.Therefore,we suggested that the RMLE method,which was more precise and robust,should be applied for the dichotomy endpoint in the three-arm non-inferior design.iii.Survival endpoint: Since the log hazard ratio?HR?of the test group and the control group was normal distribution,statistical methods and sample size schemes for the survival endpoint were proposed for the exponential distribution and Weibull distribution.And the logarithmic transformation of HRs was asymptotically normal distribution,therefore we did not detect the performance of the statistics in this section.The main innovations in this research are as follows:?1?Proposing a new bridging strategy.?2?developing statistical methods and the sample size schemes for continuous endpoint,dichotomy endpoint and survival endpoint.?3?Developing the simulation SAS code of the quasi-three-arm non-inferiority design.In summary,the quasi-three-arm non-inferiority design and sample size scheme were put forward in this study.Using the non-inferiority test of the mean differences between the LCT and the MRCT,the treatment effect of LCT could be detected to achieve at least ?×100 percent of the effect of MRCT,each compared to placebo.Moreover,two kinds of test-statistic and sample size estimation were proposed based on the equal and the unequal placebo effect situations.Three episodes in clinical trial scenarios were performed by simulation procedures.As a result,a series of sample size schemes were proposed and both the test methods finely controlled the false positive rate with adequate power at a given level.It is relatively reasonable to consider this design as a novel procedure for a new drug registration in simultaneous global drug development.